A methodology for situated and effective design of haptic ...1155519/FULLTEXT01.p… · This haptic...

KTH Industrial Engineering and Management

XUAN SUN

Doctoral Thesis

Department of Machine Design

KTH Royal Institute of Technology

Stockholm, Sweden, 2017

A methodology for situated and effective

design of haptic devices

TRITA – MMK 2017:13 KTH School of Industrial ISSN 1400-1179 Engineering and Management ISRN/KTH/MMK/R-17/13-SE SE-100 44 Stockholm ISBN 978-91-7729-573-0 SWEDEN

Academic thesis, which with the approval of the Royal Institute of Technology, will be presented for public review in fulfilment of the requirements for a Doctorate of Engineering in Machine Design. The public review is held at Kungliga Tekniska Högskolan, Brinellvägen 85, Gladan at 10:00, November 29, 2017.

© Xuan Sun, November 2017

Print: Universitetsservice US AB

Department of Machine Design KTH Royal Institute of Technology SE-100 44 Stockholm SWEDEN

TRITA - MMK 2017:13 ISSN 1400 -1179 ISRN/KTH/MMK/R-17/13-SE ISBN 978-91-7729-573-0 Document type Thesis

Date 2017-11-29

Author Xuan Sun

([email protected])

Supervisor(s) Kjell Andersson, Ulf Sellgren

Sponsor(s)

China Scholarship Council Title A methodology for situated and effective design of haptic devices

Abstract The realism of virtual surgery through a surgical simulator depends largely on the precision and

reliability of the haptic device. The quality of perception depends on the design of the haptic device, which presents a complex design task due to the multi-criteria and conflicting character of the functional and performance requirements. In the model-based evaluation of the performance criteria of a haptic device, the required computational resources increase with the complexity of the device structure as well as with the increased level of detail that is created in the detail design phases. Due to uncertain requirements and a significant knowledge gap, the design task is fuzzy and more complex in the early design phases.

The goal of this thesis is to propose a situated, i.e., flexible, scalable and efficient, methodology for multi-objective and multi-disciplinary design optimization of high-performing 6-DOF haptic devices.

The main contributions of this thesis are:

1. A model-based and simulation-driven engineering design methodology and a flexible pilot framework are proposed for design optimization of high-performing haptic devices. The multi-disciplinary design optimization method was utilized to balance the conflicting criteria/requirements of a multi-domain design case and to solve the design optimization problems concurrently.

2. A multi-tool framework is proposed. The framework integrates metamodel-based design optimization with complementary engineering tools from different software vendors, which was shown to significantly reduce the total computationally effort.

3. The metamodeling methods and sampling sizes for specific performance indices found from case studies were shown to be applicable and usable for several kinds of 6-degrees-of-freedom haptic devices.

4. The multi-tool framework and the assisting methodology were further developed to enable computationally efficient and situated design multi-objective optimization of high-performing haptic devices. The design-of-experiment (DOE) and metamodeling techniques are integrated with the optimization process in the framework as an option to solve the design optimization case with a process that depends on the present system complexity.

Keywords Design optimization, haptic devices, metamodel, multi-criteria, situatedness

Language English

Sammanfattning

För att realisera en simulator för kirurgiska ingrepp i en virtuell värld är den enhet som ger den fysiska återkopplingen till användaren kritisk. Den fysiska återkopplingen sker med hjälp av en haptisk enhet som kan skapa en känsla av kontakt med objekt i den virtuella världen.

Utveckling av en haptisk enhet är en komplex uppgift med många motstridiga krav på funktion och prestanda. En viktig del av utvecklingen av en sådan enhet är att balansera krav och egenskaper för att få en så optimal produkt som möjligt för den tänkta tillämpningen.

En förutsättning för att utveckla en sådan produkt är att använda sig av en modellbaserad ansats för utvärdering av de funktions- och prestandabaserade kriterierna. En sådan ansats medför dock att beräkningsresurserna ökar med komplexiteten hos produkten och även vartefter produkten detaljeras och mer detaljerade beteenden utvärderas. I de tidiga konstruktionsfaserna är komplexiteten större beroende på otydliga krav samt dålig insikt om konceptets egenskaper och beteende.

Syfte med denna avhandling är utveckla en situationsanpassad, d.v.s. flexibel och skalbar metodik för multikriterie- och multidisciplinär optimering av högpresterande haptiska enheter med sex frihetsgrader.

Huvudbidragen i denna avhandling är:

1. En ansats för modellbaserad och simuleringsdriven metodik tillsammans med ett flexibelt ramverk som möjliggör situationsanpassad optimering av högpresterande haptiska enheter. En multidisciplinär optimeringsmetod användes för att balansera de motstridiga kriterierna/kraven i problem som innefattar olika ingenjörsdomäner, och för att lösa de olika optimeringsproblemen samtidigt.

2. En ansats till ett ramverk för integration av olika programvaror. Ramverket baseras på en optimeringsansats där metamodellering används och integrerar programvaror från andra leverantörer, vilket visat sig avsevärt minska beräkningsbehovet och beräkningstiden.

3. De metoder för metamodellering och antalet utfall som de har baserats på för modellering av specifika index testade vid fallstudier har visat sig tillämpliga och användbara för flera typer av haptiska enheter med sex frihetsgrader.

4. Metodiken och ramverket har vidareutvecklats för att möjliggöra beräkningsmässigt effektiv multikriterieoptimering av högpresterande haptiska enheter. Metoden statistisk försöksplanering (DOE) och metoder för metamodellering har integrerats i ramverket.

Nyckelord: Konstruktionsoptimering, haptiska enheter, metamodeller, multi-kriteria, situationsanpassat

i

Acknowledgements

This thesis could not have been possible without the contributions and support by many, to whom I would like to use this opportunity to express my gratitude.

First and foremost, I would like to thank my supervisors Kjell Andersson and Ulf Sellgren for their continuous support, valuable discussions, patience, and guidance throughout my research and the thesis.

My sincere thanks also go to Aftab Ahmad, Mario Sosa, Xinhai Zhang, Lei Feng and Yang Wang for their valuable discussions in different fields of my research.

Thanks to all the lecturers/ professors of the courses I took during the Ph.D. project. And thanks to Anders Söderberg for quality-checking the thesis.

I am grateful to many former and current colleagues at the Department of Machine Design including Patrick Rohlmann, Mattia Alemani, Gabriele Riva, Abbos Ismoilov, Pouya Mahdavipour, Vicki Derbyshire, Peter Carlsson, Martin Törngren, Ellen Bergseth, Katja Gradin, Qian Chen, Kenneth Duvefelt, Jens Wahlström, Ju Shu, Yingying Cha, and Yezhe Lyu for their support, motivation, and providing the enjoyable working environment.

I would like to express my appreciation to Chinese Scholarship Council (CSC) for funding my studies at KTH and my stay in Sweden. I am also thankful to MSC Software Nordics and EnginSoft Nordic for the support they have provided.

I would also like to thank my friends, Manxing Du, Tunhe Zhou, Jiangning Gao, Marie Kindblom, Ludvig Ericson, Michelle Böck and many other friends for sharing many significant moments of my life in Sweden. Special thanks go to Manxing and Tunhe for sharing many tiring nights of working on deadlines together and for their spiritual support remotely. Best of luck to your Ph.D. and postdoctoral projects!

Last but not the least; I am profoundly thankful to my beloved family. Thanks to my husband, Jian Sun, for all his support and company. And thanks to my dear parents for their unconditional love and support.

Xuan Sun

Stockholm, November 2017

iii

List of appended publications

Paper A X. Sun, K. Andersson, U. Sellgren, “Design optimization of haptic device – A systematic literature review”, Submitted for publication.

Sun, Andersson and Sellgren planned the structure and focus of the review. Sun performed the literature study, analyzed the literature and wrote the paper. Andersson and Sellgren provided feedback.

Paper B X. Sun, K. Andersson, U. Sellgren, “Towards a methodology for multidisciplinary design optimization of haptic devices”, Proceedings of ASME 2015 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2015, Boston, Massachusetts, USA, 2015.

Sun, Andersson and Sellgren developed the design optimization methodology and framework. Sun planned and performed the verification case study and wrote the paper. Andersson and Sellgren provided feedback.

Paper C X. Sun, K. Andersson, U. Sellgren, “The search for an efficient design optimization methodology for haptic devices”, Submitted to Engineering with Computers (under review), April 2017.

Sun developed and verified the proposed metamodeling and optimization methodology. Andersson and Sellgren provided feedback.

Paper D X. Sun, U. Sellgren, K. Andersson, “Situated design optimization of haptic devices”, 26th CIRP Design Conference, Stockholm, Sweden, 2016.

Sun developed the situated design optimization framework in collaboration with Sellgren and Andersson. Sun planned and performed the case study and wrote the paper. Sellgren and Andersson provided feedback.

Paper E X. Sun, U. Sellgren, K. Andersson, “Efficient and situated design of haptic devices”, Submitted for publication.

Sun, Sellgren and Andersson jointly elaborated on and defined possible re-design situations. Sun proposed and performed the solutions, and wrote the paper. Sellgren and Andersson provided feedback.

v

Contents

Acknowledgements .......................................................................... i

List of appended publications ........................................................ iii

Contents .......................................................................................... v

1 Introduction .................................................................................. 1

1.1 Haptics background ...................................................................................1

1.2 Challenges for design optimization of high-performing haptic devices .. 4

1.3 Research objective and questions............................................................. 5

1.4 Research approach.................................................................................... 5

1.5 Delimitation .............................................................................................. 7

1.6 Thesis outline ............................................................................................ 7

2 State-of-the-art structures and methodologies .............................. 9

2.1 Haptic devices ......................................................................................... 10

2.2 Multi-objective design optimization ...................................................... 13

2.3 Multidisciplinary design optimization ................................................... 14

2.4 Metamodel-Based design optimization .................................................. 16

2.4.1 Data sampling .................................................................................. 18

2.4.2 Metamodeling methods .................................................................. 19

2.4.3 Metamodel validation and selection ............................................... 20

2.5 Summary ................................................................................................. 21

3 Situated design optimization of haptic devices ............................ 23

3.1 Metamodel-based multidisciplinary design optimization ..................... 27

3.2 Situated design scenarios and re-design process ................................... 32

3.3 Summary ................................................................................................. 36

4 Case study: optimization of the 6-DOF TAU haptic devices .......... 37

4.1 Initial design case ................................................................................... 37

4.1.1 Metamodel-based MDO .................................................................. 39

4.2 Re-design cases and solutions ................................................................ 42

4.2.1 Re-design case 1: change/add the isotropy requirement ............... 43

vi

4.2.2 Re-design case 2: increase the workspace requirement ................. 43

4.2.3 Re-design case 3: Optimize the inertia performance ...................... 44

4.3 Summary ................................................................................................. 48

5 Summary of appended papers .................................................... 49

6 Discussion, conclusion and future work ...................................... 53

6.1 Discussion ............................................................................................... 53

6.2 Conclusions ............................................................................................. 54

6.3 Future work ............................................................................................. 56

References .................................................................................... 59

Appended papers

A. Optimization of high-performing haptic device – A systematic literature review

B. Towards a methodology for multidisciplinary design optimization of haptic devices

C. The search for an efficient design optimization methodology for haptic devices

D. Situated design optimization of haptic devices

E. Efficient and situated design of haptic devices

C H A P T E R 1 . I N T R O D U C T I O N | 1

Chapter 1

Introduction

1.1 Haptics background

Haptics, derived from the Greek haptikos, refers to sense and manipulation through touch. With the development of virtual reality (VR), haptics is gradually applied to VR systems which adds the sense of touch to previously visual-only interfaces. A haptic device (or haptic interface) is an actuated mechanical device that acts as a bridge of communication between the user and the computer (virtual environment, VE). It can track the physical manipulation of the user, and also provide force and torque feedback to the user based on interaction with objects in a VE or a tele-operated system. In order words, the user can manipulate a virtual object on a screen or a headset through the haptic device, and also get a realistic touch sensation coordinated with the on-screen event [1].

This haptic technology is applied in various fields, such as medicine, entertainment, education, industry and graphic arts [1][2]. The requirements for haptic devices vary between different applications. However, they share the common goal that the haptic device and system should provide realistic experience to the user. With the development of VR and higher requirements on the haptic technology, the research on haptics, such as the development of an understanding of human perception, force-reflecting haptic interface hardware as well as haptic rendering software, has continuously developed.

A haptic interaction system consists of the human operator, the haptic device, and the haptic rendering software, as shown in Figure 1.1. As the starting and also terminal point of the loop, the operator manipulates the virtual object in the haptic rendering software through the end-effector of the haptic device. The haptic device tracks the position and/or orientation of the end-effector in the virtual world and also provides the reflection (tactile and force feedback) of contact with a virtual object to the user in real-time. The haptic rendering software (in the computer) visualizes the virtual object and virtual world to the human operator. And it also detects the collision with the virtual object and calculates in real-time the torque commands to the actuators on the haptic device, so that appropriate reaction forces are applied to the user[1].

The haptic technology is used in many applications, such as medical training, rehabilitation, areas requiring handling of dangerous materials, as well as in the entertainment and gaming industries. Current haptic interfaces available on the market can be classified as either ground-based devices (force reflecting joysticks

2 | C H A P T E R 1 . I N T R O D U C T I O N

Figure 1.1 The loop of the haptic interaction system modified after [2]

and linkage-based devices) or exoskeletal force-reflecting haptic devices (gloves, suits, exoskeletal devices) [1]. As part of a research project on a ‘Haptic milling surgery simulator’ for teeth/bone milling operations, the research presented in this thesis is focused on high- performing ground-based haptic devices. In an earlier part of the research project, a master-slave for tele-robotic surgery was developed by Flemmer [3], followed by the development of a 6 degrees of freedom (DOF) haptics-based VR simulator called Ares [4] based on a Stewart-platform by Khan [5] and Eriksson [6]. Ahmad [7] further improved the realism of force/torque feedback of the Ares haptic device and also developed a new 6-DOF haptic simulator based on a TAU configuration.

Training of a surgeon is a complex and multi-dimensional task. Instead of practicing on plastic models, laboratory animals, cadavers, and real patients, medical simulators have been increasingly used to train medical professionals. One advantage of the medical simulators is that they can provide realistic repetitive procedures (such as proper hand and instrument usage and placement) with different virtual surgical environments and ability to assess the trainee’s performance. In contrast to classical training techniques, training with medical simulators has been shown to increase patient safety and quality, reduce medical errors, and reduce healthcare cost by allowing medical students to develop their skills more efficiently and effectively on virtual patients [7][8].

Apart from the developed simulators in the research project mentioned above, many products and prototypes of complex and realistic haptic devices used as surgical simulators for soft and hard tissues have been developed commercially and in academia over the past couple of decades. However, the use of haptic devices in the field of orthopedics and dentistry has not been well exploited yet, and very few of the existing devices have offered a convincing solution for hard tissues. One reason is that in order to provide a realistic interaction with hard tissues, such as in a dental training simulator, the haptic device need to have a mechanical high stiffness and a low inertia to control which results in a complex design task and a need for multi-domain considerations to obtain a realistic force/torque feedback from the device [7][8].


The performance requirements define the most elemental electrical and mechanical target attributes of a haptic device. In prior work, researchers have categorized and listed the most relevant performance requirements [9][10][11][12]. In general, there are no typical values for these attributes, i.e., they depend on the specific application. But there is a consensus on what the idealities are [13][14][15][10]. The meaning of the most commonly used performance requirements and their qualitative ideal are presented in Table 1.1.

Table 1.1 The physical performance requirements of high-performing haptic devices [9][10][11][12]

Performance criterion

Qualitative Ideal Meaning

Degrees-of-freedom ↑ The number of orthogonal motions either permitted or

driven by the device

Workspace ↑ The area or volume in real-world space that the end-effector can reach

Isotropy ↑ The uniformity of the end-effector moving in all generalized workspace directions

Dexterity/ Manipulability ↑ Quantification of the device’s ease of arbitrarily changing

position and orientation for a given posture Inertia ↓ The resistance felt by the user while moving the end-effector Friction ↓ Forces of resistance that oppose motion Stiffness ↑ The ability of a device to mimic a solid virtual wall or object Input position resolution ↑ The smallest change of position which can be detected by

sensors Output force resolution ↑ The smallest incremental force that can be generated by the

device Operating bandwidth ↑ The speed of response at a given excitation

Peak force ↑ The maximum force that the actuators of a device can generate over a very small time interval

Continuous force ↑ The force that the end-effector can exert for an extended period

Peak acceleration ↑ The ability of a device to simulate the stiffness of virtual objects

↑: large/high value of the index; ↓: low value of the index

Since a haptic device is not only a manipulator but also a force-feedback device, the degrees-of-freedom (DOF) for a haptic device is given regarding passive and active DOF. The passive DOF shows the freedom of motion of the end-effector driven by the user, and the active DOF is the number of independent force/torque feedback directions that can be displayed by the device. Meanwhile, the workspace is classified as the reachable workspace and the dexterous workspace. The reachable workspace includes the set points that can be reached by the end-effector, and the dexterous workspace consists of the points reached by arbitrary orientations. Mechanical singularities within the workspace are forbidden.

Considering the context of a haptic device for orthopedics and dental surgery, the surgeon needs to perform various tasks like cutting, milling, and drilling. To create a simulator system to train surgeons for these skills, the preliminary user requirements for the haptic devices are given in [16][17], and they are as follows:


• The device should have 6 actuated degrees of freedom;

• The whole device should fit in the space of 250×250×300[mm];

• The minimum translational workspace should be 50×50×50 [mm];

• The rotational workspace should be ±40° in all directions at the center of the translational workspace;

• The force and torque performance on the TCP should be at least 50 N and 1 Nm, respectively;

• The device stiffness should be at least 50 [N/mm];

• The device should be placed on a table in front of the operator and easy to access for the user;

• Good ergonomics and comfort for the user;

• Low cost and power consumption for commercialization.

1.2 Challenges for design optimization of high-performing haptic devices

It is a complex task to develop a high-performing haptic device for medical simulation in orthopedics and dental surgery, mainly due to the multi-criteria and sometimes interacting or conflicting performance requirements, e.g., large stiffness and small inertia, sufficient workspace and low weight, high functional performance and low cost.

In order to efficiently and effectively develop and improve a haptic device that satisfies all performance requirements, a structured optimization process is usually necessary for all design phases. The classical approach to multi-objective optimization (MOO) is to change the multi-objective problem into a single objective problem by constraining “less important” objective functions and optimizing one remained objective function, or by weighting each objective function and summing them as a single objective function. As a result of the optimization problem using this classical approach, only one optimal solution can be found after the entire optimization process has been completed. Such classical approaches have been applied in most optimization examples published in the literature and they have mainly been focusing on well-defined design cases [18][19][20][21].

However, design of haptic devices is fuzzy [22] and complex, especially in the early design phases, mainly due to the uncertain requirements related to touch and “feel”, a large solution space, significant nonlinearities, and the need for real-time estimation and control. This complexity can potentially be reduced by taking advantage of the knowledge that is gained from simulations and/or physical tests. Knowledge gained in that process will, most likely, trigger new revisions of the principal design solution. These revisions may cause a significant amount of repetitive work and hence a much-prolonged lead time. Consequently, in order to increase the efficiency of the design process, a significant challenge is to enable knowledge gained in the process to be adapted and reused as much as possible, i.e., to be “situated” [23]. The notation of “situated” here indicates that the design is adaptable to new and/or changed situations, which includes a new/changed


application, and/or a modified/new set of performance requirements, and a new design situation based on that new knowledge has been acquired.

Traditionally, the complex design task is resolved into several sub-optimization tasks that are addressed by different domain experts, or disciplines, organized as separate design groups which work in parallel. The interaction of different sub-tasks or disciplines is managed by intermediate synchronizations between the groups during the parallel development phases. However, this traditional design process needs to be repeated several times in order to find a feasible solution which is a time and resources consuming process with no guarantee that an optimal system solution can be found.

Furthermore, predicting the design performance of a high-performing haptic device usually involves computationally intensive simulations and analyses with complex and heterogeneous models. Even with the progressively increasing computational power, it is still crucial to find computationally efficient methods and focused models to use in the design optimization process.

Due to significant uncertainties caused by interacting objectives/disciplines and computationally intensive simulations and analyses, a major challenge is to efficiently and effectively optimize high-performing haptic devices.

1.3 Research objective and questions

The main objective of the research presented in this thesis is to propose a situated, i.e., flexible, scalable and efficient methodology for multi-objective and multi-disciplinary design optimization of high-performing 6-DOF haptic devices.

The objective has been further divided into the following research questions:

RQ1: What is the character of the simulations and analysis required in multi-objective and multidisciplinary haptic design optimization, and how can they be performed significantly more efficient?

RQ2: What are the most important discipline-specific models and tools to assist the model-based design of high-performing haptic devices and how to integrate them in the design and optimization process?

RQ3: What re-design scenarios may occur in the development of haptic devices?

RQ4: What knowledge gained in the optimization process of an initial design task can be potentially reused in other development scenarios, and how to efficiently use them in the optimization of trailing re-design scenarios?

1.4 Research approach

The research questions have been addressed using both qualitative and quantitative research methodologies. The qualitative methodologies include a state-of-the-art literature study and optimization case studies. The quantitative methodologies include mathematical validation, simulation, and evaluation through performance measurements.

RQ1 included two questions. For the first “what” question, a preliminary literature study was done on the state-of-the-art of high-performing haptic device


design, and the most important/ commonly used discipline-models and tools were unveiled. The “how” question was answered by a proposed multidisciplinary design and optimization framework. The effectiveness of the framework was validated with a design and optimization case study of a 6-DOF TAU haptic device. The corresponding simulations and analyses defined and managed with engineering tools were integrated into the framework. The optimization tool modeFRONTIER was used for tool integration as well as for performing multi-disciplinary and multi-objective optimization.

Regarding RQ2, literature studies were performed first to find design optimization methodologies which may enhance the efficiency of complex design cases that normally require computationally intensive simulations and analyses. Such methodologies include the metamodel-based design optimization (MBDO) method, the multidisciplinary design optimization (MDO) method, the design-of-experiment (DOE) method and the Pareto-optimal approach for MOO problems. The effectiveness and efficiency of these methods were validated with a TAU haptic device case study. The computational efficiency of the MBDO method was validated with a comparative study of the same design case, with and without applying this method.

RQ3 was addressed and answered with a design optimization case study of the TAU device. An initial design case was first defined and solved, and several re-design scenarios that might occur were identified based on the initial design case and its findings.

RQ4 is a follow-up question to RQ3. The re-design scenarios found in RQ3 were solved using, as much as possible, the knowledge gained from the initial design case. To study and verify the proposed re-usage approach, a case study of a 6-DOF Ares haptic device, i.e., device with architecture other than the TAU, was performed. The proposed re-design scenarios and the proposed methods to efficiently solve them were categorized and merged into a situated and generic process. The schematics of the two used high-performing haptic devices, the 6-DOF TAU and the Ares haptic device, are illustrated in Figure 1.2.

Figure 1.2 Schematic of 6-DOF a) TAU haptic device and b) Ares haptic device


The mechanism of the TAU haptic device, as shown in Figure 1.2a, consists of a fixed I-column along the Y-axis, two symmetric kinematic chains on each side of the column, and a serial chain placed on the top of the I-column. These three chains connect the end-effector (a platform where the tool-center-point located) to the fixed column. Six active revolute joints around Y-axis are fixed to the I-column located on a1, a2 and a3. The rest of the joints are all passive universal joints, except for the joint at b3 which is a passive revolute joint that only allows rotation along the X-axis.

The mechanism of the Ares haptic device, shown in Figure 1.2b, is a modified version of the Stewart Gough mechanism. This mechanism consists of a fixed base, a moving platform, and six identical legs connecting the platform to the base. Each leg consists of an active linear actuator fixed to the base, a constant length prismatic joint driven by the linear actuator and moving along the linear guideway, a spherical joint, a constant length proximal link, and a universal joint. This 6-PSU (active Prismatic, Spherical, and Universal) joint configuration is used to get the 6-DOF motion at tool center point (TCP) of the platform.

1.5 Delimitation

The aim of the research presented in this thesis is to efficiently and effectively design and optimize haptic devices with situated design scenarios. Situated design scenarios refer to the changes made to the design task during the design process. As part of our research project, the research in this thesis is applied on high-performing ground-based haptic devices with force feedback, and focus mostly on the 6-DOF TAU haptic device. The model-based and simulation-driven design approach proposed in this thesis can be applied in any stage of the design phase (conceptual or detailed design phase), but no physical experiments have been treated. In this thesis, we focus on deterministic design optimization, and robust design optimization, such as the approach proposed by Ahmad et al. [18], is not addressed. Many design aspects, such as structure, control, cost, energy consumption, etc., can be considered and optimized in the design phase. However, in our case studies, we focused on optimization of the device structure. Hence, the control system (such as gravity and friction compensation) and the other related aspects are not considered. However, both the kinematic and dynamic performances of the device that are affected by the device structure are also included in the study.

1.6 Thesis outline

The thesis is divided into six chapters:

Chapter 1 provides an introduction to the thesis, research background, and discusses the problems that have been identified. Furthermore, research questions, research approach, and delimitations of the thesis are given. Chapter 2 firstly presents the state-of-the-art in design and optimization of haptic devices. Methodologies and optimization methods which may contribute to the research goal, such as Multi-objective optimization (MOO) method, Multidisciplinary design optimization (MDO) method and Metamodel-based design optimization (MBDO) method, are briefly described. Chapter 3 proposes a model-based and simulation-


driven design approach. Chapter 4 presents a case study of the proposed methodology as verification using both the Ares and TAU 6-DOF haptic devices. Chapter 5 presents a summary of the appended papers. Chapter 6 discusses and concludes the thesis work and outlines future work.

CHAPTER 2. STATE-OF-THE ART | 9

Chapter 2

State-of-the-art structures and methodologies

An engineering design process starts with conceptual design, where various design concepts are searched and evaluated, and the concept(s) that is/are potentially best is/are selected to be further studied and optimized with respect to a set of initially stated requirements. The selected concept(s) that fulfill the requirements is/are further analyzed and refined in the later design phases, e.g., the preliminary and detail design phases. Significant research efforts have been devised in the development of haptic devices, and several studies of design and optimization are presented in the commercial and academic literature.

Most published design and optimization examples are mainly focusing on well-defined design cases. However, the design of haptic devices is fuzzy and complex especially in the early design phase and can definitely not be considered as well-defined. Along with the knowledge gained from simulations and/or physical tests performed in the design and optimization process, the designers have to take new actions or make revisions to proceed with the process. The course of designing determined by the interaction between the designer(s) and the changing situations is defined as “situatedness” [23]. It means that the design task may change based on the knowledge gained by the designers in the process. However, performance evaluation of high-performing haptic devices often involves computationally intensive simulations and analyses with complex and heterogeneous models. This makes the new actions or revisions of the design process demand a significant amount of computational resources and a potentially prolonged lead time, and hence make progress exhaustive and inefficient. Many methodologies, such as the Multi-objective optimization (MOO) method, the Multidisciplinary design optimization (MDO) method, the Metamodel-based design optimization (MBDO) method, have been proposed to increase the efficiency in design and optimization of complex systems

This chapter firstly provides an overview of the current state-of-the-art in development of haptic devices in section 2.1. The review includes an overview of different architectures for haptic devices and related design and optimization approaches. After that, a selection of methodologies and optimization methods which may improve the efficiency of the design and optimization process, such as the MOO method, the MDO method and the MBDO method, are briefly described in section 2.2, section 2.3 and section 2.4, respectively.

10 | CHAPTER 2. STATE-OF-THE ART

2.1 Haptic devices

State-of-the-art of commercially available force feedback devices and their application areas was reviewed by Samur [12]. He summarized and compared the reviewed devices, based on their specifications, such as workspace, continuous force, stiffness, etc. Gogu [10] reviewed the parallel mechanisms used in haptic devices. Furthermore, a comparative study was conducted by Khan [5] on the performance of 6-DOF haptic devices based on their kinematic structure, DOF, workspace, stiffness, maximum force, and cost. Currently, there are haptic devices available in the forms of 2, 3, 4, 5, 6 and 7-DOF units [10][24]. Most common commercial haptic devices with force feedback can be classified into serial, parallel and hybrid kinematic structures [12][24][10], as illustrated in Figure 2.1. There is a new type of haptic devices that use magnetic levitation [25]. This type of device will not be further discussed here.

Figure 2.1. Examples of haptic devices with a) serial, b) parallel, and c) hybrid kinematic

structures [26] [27]

Serial haptic devices have a serial kinematic structure which consists of a single open-loop chain of links and joints that connect the end-effector to a fixed base. The main advantages of a serial device are large workspace and high dexterity. However, the low stiffness and precision, poor force exertion capability, low load-to-weight ratio, and high inertia are some disadvantages of serial devices, which limit their usage in many applications.

Parallel haptic devices have a closed-loop kinematic structure which connects the end-effector on the moving platform to the fixed base with several parallel kinematic chains. Each kinematic chain consists of passive and active parallel kinematic pairs. The parallel devices have some structural advantages compared to the serial ones, such as potentially higher stiffness, precision, and robustness. Furthermore, since their actuators are placed in the fixed base, the mechanism has to carry relatively low masses, and hence they have, in general, lower inertia and higher load capacity than serial devices. Their major disadvantages are a limited workspace and low dexterity due to a high motion coupling and multiplicity of singularities inside their workspace. The 6-DOF Ares haptic device, which is based on the Stewart-platform, represents an example of a parallel kinematic device.

A hybrid kinematic device uses a combination of parallel and serial structures where the parallel structure connects to the fixed-based, and the serial structure connects the end-effector to the parallel structure which generates additional


degrees-of-freedom of the end-effector. They embrace the advantages of both serial and parallel devices, such as high load capacity, manipulability, and stiffness, high precision, robustness and a relatively large workspace. The disadvantages of this mechanism are the more complex structure for analysis and control, and higher inertia comparing to the parallel structure.

According to the descriptions and specifications of currently available commercial haptic interfaces and prototypes in laboratory setups developed for different purposes and requirements ([26]- [28]), the most common listed properties are:

• The structure of the device, • The number of degrees-of-freedom, • Translational and/rotational workspace, • Peak and continuous force and/or torque, • Stiffness, • Position and/or force resolution, • Bandwidth.

Table 2.1 Commercial force-feedback ground-based desktop haptic devices

Company Device Structure DOF I/O

Workspace Translation[mm]/ Rotation[deg]

Peak Force[N]/ Torque [Nmm]

Stiffness [N/mm]

3D SYSTEMS Geomagic®

[26]

Touch Touch X Phantom®: Premium 1.0 Premium 1.5 Premium 3.0

Serial Serial Serial Hybrid Hybrid

6/3 6/6

160x120x70 160x120x120 254x178x127 381x267x191/ 335x260x297 838x584x406/ 335x260x297

3.3/0 7.9/0 8.5/0 8.5/ 170-515 22/ 170-515

1.02~2.31 1.48~2.35 3.5 3.5 1

Force Dimension [27]

omega.3 omega.6 omega.7 delta.3 delta.6 sigma.7

Parallel Hybrid Hybrid Parallel Hybrid Hybrid

3/3 6/3 7/3 3/3 6/6 7**/6

Ø 160x110 Ø160x110/ 240x140x320 Ø 400x260 Ø 400x260/±20 Ø 190x130/ 230x140x200

12/0 12/0 12/0 20/0 20/150 20/400

14.5

Novint [29] Falcon® Parallel 3/3 ~101x101x101 8.9 NA Haption [30]

Virtuose 3D Desktop Virtuose 6D Desktop

Serial Serial

6/3 6/6

200x200x200/ 145x115x148 200x200x200/ 200x90x200

10/0 10/400

2 2

Quanser [31] HD2 Parallel 6/6 800x350x350/ 180x180

13.94-19.71/ 1720

3

MPB Technologies Inc. [32]

Freedom 6S Freedom 7S

Serial Serial

6 7**/6

170x220x330/ 340x170x230

2.5/ 150-370

2

CyberGlove Systems [33]

CyberForce Serial 6/3 ~935x305x305* 8.8/0 NA

(NA) Not available from the source. (**) The 7-DOF includes 3 translational and 3 rotational DOF, and the 7th DOF as grasping/ drilling. ( * ) The data was approximated by the author according to the device specifications.


Table 2.1 and Table 2.2 list currently available commercial desktop haptic devices and prototypes in research labs, respectively. The five most common properties are shown in the tables, including the type of kinematic structure (the mechanism), the input and output (I/O) number of DOF, the dimension of the translational and/or rotational workspace, the peak force and/or torque that can be applied on the device end-effector, and the structure stiffness. Only devices or prototypes stating at least three of these properties were considered here.

Table 2.2 Ground-based research prototypes with force feedback and linkage connection

University/ Institute

Device Structure DOF I/O

Workspace Translation[mm]/ Rotation[deg]

Peak Force[N]/ Torque [Nmm]

Stiffness [N/mm]

University of Tsukuba [34]

Haptic Master

Parallel 6/6 Sphere Ø400 ~20.6/549 ~0.28

CEIT [35] LHIfAM Serial 6/3 Ø1110x1500 42.5-72/0 NA Universidad Miguel Hernandez [36]

Magister-P

Parallel 6/6 NA 99.9/NA NA

Northwestern University [37]

Cobotic Hand Controller

Parallel 6/6 NA/22~25 50/NA 20-400

CEA-LIST [38]

CAD like Desktop

Parallel 6/6 150x150x150/ ±45

20/500 NA

University of Colorado [39]

CU HI Parallel 5/5 Sphere Ø300 8/NA NA

KTH Royal Institute of Technology [16]

Ares Parallel 6/6 75x75x100/ ±45 54/1200 60

KTH Royal Institute of Technology [7]

TAU Parallel 6/6 70x80x100/ ±45 48-62/1200 55-70

Tohoku University [40]

Compact 6-DOF

Hybrid 6/6 Sphere Ø150/±70 10/NA NA

Nagoya Institute of Technology [28]

DELTA-4 Hybrid 6/3 Ø500x120/ ±80 50/0 NA

(NA) Not available from the source.

Browsing the specifications of the listed haptic devices, the manufactures and researchers tend to develop stiff haptic devices with a large number of DOF and workspace, and the ability to exert high-fidelity forces and torques. Most of the force feedback devices come equipped with generic end-effectors such as pens, balls, and tubes. But some devices use modified end-effectors instead, such as scissors (Freedom 6S [32]), gloves (CyberForce [33]) and tools, to extend the usage and degrees-of-freedom of the devices. There are also some examples with combination of two commercial haptic devices to provide extra degrees of force feedback for a particular task, for example, the SimQuest’s burr hole surgical


simulator [41] which is a combination of two Falcon [29] haptic devices, and the Delthaptic [42] which combines two Delta haptic devices through a handle.

2.2 Multi-objective design optimization

For the design of high-performing haptic devices, the multi-criteria system requirements usually lead to a multi-objective or multi-criteria constrained nonlinear and nonconvex optimization problem with no explicit analytical solution. Much research have been performed to find an “optimal” haptic device by minimizing or maximizing one or several performance indices, for example, maximum kinematic dexterity and transmission ability [43], maximum stiffness [44], maximum weight and workspace [45], and maximum isotropy and natural frequency while minimizing inertia and torque requirements on the motor actuator [18].

An optimization problem containing n objective functions is formulated as:

≤=≤ ≤

1 2minimize ( ), ( ),... ( )subject to ( ) 0 ( ) 0

n

lower upper

f x f x f xg x

h xx x x

(2.1)

The goal is to find the values of the design variables x that minimize the n objective functions f which satisfied both the inequality and equality constraints g and h. The design variables can be continuous or discrete which must be kept within the upper and lower limits, called xupper and xlower.

The simplest approach to solve a MOO problem is to convert it into a single objective optimization problem. There are two intuitive ways commonly used to reduce the number of objective functions [46]. One way is to select the most important one as the only objective function and treat all the others as constraints (𝜖𝜖-constraint method [46]). The second approach is to generate a single objective function that replaces all the objectives (the weighted sum approach [46]). The weighting coefficients are used to reflect the relative importance of the original objective functions. The drawback of these two methods is that only one optimum is found. If the designer wants to modify the importance of the objective functions, or to do a trade-off study, the optimization process must be performed over again.

An alternative approach is to find a number of optimal solutions as Pareto-optimal solutions. A solution is Pareto-optimal if there is no other solution that could improve any of the objectives without worsening at least one of the other objectives [47]. Instead of a single optimum, the designer will get a set of Pareto optimal solutions which constitute the so-called Pareto front. The Pareto front represents the entire Pareto optimal set, which consequently is a curve, a surface, or a hypersurface for the cases of two, three or more conflicting objectives, respectively. An illustration of optimization with two objective functions is shown in Figure 2.2. By using this approach, the trade-off between conflicting objective functions can be performed and discussed after the optimization process, which means that the decisions caused by uncertainties early in the process can be postponed, and hence adds flexibility to the process. The drawback of the approach


is that it might consume more computational resources, and bring difficulties for the decision maker(s) to select the most satisfactory one from so many solutions.

f1

f2Feasible solutionsPareto optimalsPareto front

Figure 2.2 Illustration of feasible solutions and Pareto front for a two-objective problem

The evolutional algorithms (EAs) [48] are considered as well-suited for the described multi-objective optimization problem. These algorithms are based on several iterations of a principal evolution cycle, as described by Eiben and Smith [48], which can find multiple optimum points in one single optimization run. In general, evolutionary algorithms are divided into genetic algorithms, evolution strategies, evolutionary programming, and genetic programming. Genetic algorithms [49], as the most widely known type of evolutionary algorithms, are often implemented in commercial software (such as modeFRONTIER®[50] and MATLAB[51]). Among these algorithms, the multi-objective genetic algorithm (MOGA) [52] and non-dominate sorted genetic algorithm (NSGA-II) [53] have been widely used for multi-criteria optimization of robotic structures, parallel kinematic machines, and parallel haptic devices [54][55][56][18][57].

2.3 Multidisciplinary design optimization

A complex product cannot be fully understood by one single engineer but by the collective knowledge of all domain engineers in the design group(s). The product development process usually needs different groups to cooperate and solve problems from different perspectives, i.e., by people with different discipline knowledge, in parallel. Multidisciplinary design optimization (MDO), as defined by Giesing and Barthelemy [58], is “A methodology for the design of complex engineering systems and subsystems that coherently exploits the synergism of mutually interacting phenomena.” The advantage of MDO is that it can not only decompose the complex problem into sub-problems which allow parallel analysis and optimization but also consider the interactions of sub-problems or disciplines during the design process. By solving the MDO problem in the early design phase and taking advantage of advanced computational analysis tools, designers may simultaneously improve the design and potentially reduce the time and cost of the design cycle.


The MDO has primarily used in aerospace development projects [59][60][61], and further extended to other engineering systems, such as bridges [62], buildings [63], rail vehicles [64], turbines [65], automotive vehicles [66], robotics [57], etc. In general, it is difficult to assess global optimality due to the nature of multi-criteria design problems. However, it is not necessary to find the global optimum from an engineering point of view, because optimization in engineering design aims to gain an increased understanding of the system and hence obtain a better, or good enough, design solution.

During the last three decades, different MDO methods, also referred to as MDO architectures [67], have been continuously developed to describe the process or framework for solving optimization problems that involve coordination of two or more disciplines, for example, safety, cost, and dynamics of a product. One discipline analysis may require many different load cases which are discipline specific configurations. Each discipline aspect or load case is evaluated using an analyzer, for example, an analysis or a simulation model. For a vector of design variables, the analyzer can return a number of responses which are used to evaluate the specific objective or constraint functions. Traditionally, MDO is applied in different disciplines of a system. But it can also be used to optimize a design with several load cases within a single discipline. Although the problem is not multidisciplinary anymore, the MDO process still can be used to optimize the complex problem with interactions between sub-problems.

Generally, the MDO methods can be classified into two types, “single-level” and “multi-level” formulations [68]. Single-level formulations, which include the All-at-Once (AAO), Individual Discipline Feasible (IDF) approach and Multidisciplinary Feasible (MDF), have a single optimizer at the supervisor level directly using the nonhierarchical structure. With the multilevel methods, the same problem is partitioned into multiple subproblems and each sub-problem has an optimizer [67][68]. This group of methods is continuously expanded by researchers with new methods, but the most common used multi-level methods are Concurrent Subspace Optimization (CSSO), Collaborative Optimization (CO) and Bi-level Integrated System Synthesis (BLISS) approaches [67]. Figure 2.3 illustrates the main concept of the single- and multi-level methods. Martins et al. [67] introduced the architectures of all available methods in a unified notation, and some of the MDO methods were illustrated as flowcharts by Bäckryd [69].

Optimizer& Analyzer

Optimizer

Subspace Analyzer 1

Subspace Analyzer 2

System Optimizer

Subspace optimizer& Analyzer 1

Subspace optimizer& Analyzer 2

a) b)&

Figure 2.3 Conceptual illustration of a) single- and b) multi-level MDO methods

For single-level optimization methods, all design decisions are made at a central level, which requires all groups to be involved in the setup of the optimization problem and the resulting assessment. The drawback of this method is that each group loses the freedom to optimize their sub-problem and make their own domain-specific design decisions. Yi et al. [68] compared several MDO


methods with mathematical examples. It was shown that individual-discipline-feasible (IDF) and all-at-once (AAO) are the most efficient single-level methods, and that the MDF method is not suitable for strongly coupled problems.

One of the main motivations for using a multi-level optimization method is to allow different groups to work in parallel with freedom to perform their optimization and make their own decisions. The groups can then work concurrently and more autonomously than using a single-level optimization method. However, the drawback of multi-level optimization methods is that they are often quite complicated to implement. The CSSO method deals with all variables at the system level, which restricts the autonomy of the groups responsible for each subspace. Formulation using the CO method is more straightforward due to the absence of coupling variables, but with the lack of transparency for the individual groups. It was shown by Yi et al. [68] that the BLISS method is more efficient especially for strongly coupled MDO problems mainly due to the less number of function calls to find a good optimum solution.

The BLISS method was further extended by Sobieszczanski-Sobieski et al. [70] as BLISS 2000. In their method, the surrogate models [71] of the subspaces are used as the link between the subspace and the system optimizers. Instead of performing sensitivity analyses as in the original BLISS formulation, this method uses the surrogate model to represent each discipline or load case, which requires less computational resources and enables minimum communication between disciplines and hence leading to a potentially higher efficiency. BLISS-2000 performs best for problems with a small number of shared design variables and a large number of local variables. However, the method may be inefficient for problems with a large number of coupling variables because it might increase the number of variables in the system level and also consume too many computational resources to create the huge number of required metamodels. Furthermore, it is not relevant to use BLISS-2000 for problems with no coupling variables.

2.4 Metamodel-Based design optimization

For a complex system, such as a high-performing haptic device, the analytical models and the simulation models are usually complex and computationally intensive to evaluate. During the optimization process, a large number of model evaluations often need to be performed to find an optimum, and it, hence, requires extensive computational resources and time. One way to increase the efficiency of the optimization process is to use metamodels [71]. The metamodel, which is a surrogate model of the “full” system model, is created by a mathematical description based on a dataset of input and the corresponding output from the system model. By replacing the computationally intensive system (simulation) model with its metamodel, the total evaluation time and computational resources required in the optimization process can be dramatically decreased. To further increase the computation efficiency using metamodels, it can be beneficial to reduce the number of design variables and their ranges.

The metamodel-based design optimization (MBDO) approach has been shown to be able to effectively support engineering design in many fields, such as aerospace systems [72], aerodynamics [73], automotive industry [74][75][76], robots [77], etc. The advantage of this approach is that it can decrease the


computational time for evaluating simulation models, and also enable parallel simulation, which enables a larger amount of evaluations, and thus potentially more high-quality solutions. The main drawback of this approach is that it introduces an additional source of error in optimization. Hence it is important to have an “accurate enough” metamodel of the system model that requires “acceptable” computational effort.

Currently, there is a trend in engineering design to use the MBDO approach together with MDO methods, since the MDO problem often involves a larger number of design variables, computationally intensive function evaluations and coupling between discipline-specific functions. Batill et al. [78] used metamodels in solving the coordination between design subspaces. Wang et al. [79] used metamodeling to guide sampling of design solutions that satisfied the coupling requirements between disciplines. Metamodel-based MDO was applied for automotive structures by Ryberg et al. [80], and Tarkian et al. [77] applied the MBDO approach with MDO on industrial robots

The basic process for Metamodel-based design optimization (MBDO) [81] is illustrated in Figure 2.4. As the first step in MBDO, the optimization problem must be defined mathematically including the objective function(s), design variables and their range, and the constraints. A limited number of design points are generated and evaluated with the full model, to enable the metamodels to be constructed. The accuracy of the metamodels has to be validated before using them in the optimization process. Sometimes it is useful to build more than one metamodel for

Data sampling

Sample experiments execution

Metamodel construction

Ref

inem

ent

Accuracy requirement satisfied?

Optimal solution verification

Termination condition satisfied?

End

Metamodel validation

Start

Ref

inem

ent

YES

NO

NO

YES

Problem definition and optimization setup

Optimization on metamdoels

Figure 2.4 The MBDO process


each response and select the best one. When the metamodels that satisfy the requirements are found, the optimization can be performed. Based on the optimization results, one or more optimal designs can be selected and verified using the full system model. To guarantee the accuracy of the constructed metamodels and the quality of the final solutions, it might be necessary to iteratively refine the design space/model by adding design points (infill points) for which additional evaluations of the high fidelity model/experiment are desired. Infill points can be added in a fully sequential manner (one-at-a-time) [82] or can be added in a batch sequential manner [83].

To get reliable and optimal solutions from MBDO, the metamodel(s) must be accurate in the region for the optimum, which is highly dependent on the region of the sample points, the size of the training data, and the used metamodeling method. To find the appropriate sample point region, the Design of Experiment (DOE) [84] method can be utilized for screening and filtering out the infeasible design regions. Besides from that, the DOE method can be used to study the effect of process factors and their interactions on system performance, hence potentially reduce the complexity of the problem by decreasing the number and/or range of the design variables.

Since the 1920s, when the concept of Design of Experiments (DOE) was developed by Sir Ronald Fisher [85], several approaches, such as screening design, full or fractional factorial design [86], Plackett-Burmann design [86] , the response surface method (RSM) [87], and orthogonal arrays [88], have been developed for different distinct purposes. The most suitable DOE method for a specific design case and purpose can be selected from the sequence derived from [84] and [89] ( illustrated in Figure 2.5).

Process robustness study/improvement

Response prediction

Select design variables

number of design variable k

Simple comparison

2-level Full factorial design

Response Surface Method

Taguchi methodsPlackett-

Burmann designFractional

factorial design

Computational effort

The purpose

k=1

k≥6

Screening Design

2≤k≤5

Large

Screening

Small

Figure 2.5 Selection of DOE methods for different cases

2.4.1 Data sampling

Many data sampling methods have been developed and used for generating training data with the best possible information of the system. Classical methods that originate from the theory of DOE, such as factorial or fractional factorial design [87], central composite design (CCD) [87], and Box-Behnken [87], tend to


spread the sample points around the design space boundaries while leaving a few at the center of the design space. These classical DOE methods are primarily used for screening purposes and focus on reducing the effect of noise in physical experiments. Another class of methods is space filling sampling, with methods such as Latin hypercube design [90][91], uniform design [92], and orthogonal arrays [93]. These methods tend to spread the sample points evenly throughout the design space. They are desired when the form of the metamodel is unknown and when interesting phenomena can be found in different regions of the design space. Most published research recommend using space filling methods for deterministic computer experiments [94].

An adequate sample size depends on the complexity and the size of the actual design problem. In general, a larger number of sample points offer more information of the function but requires a larger computational effort. Equation (2.2) given by Santer et al. [95] can be used as a guideline to select a reasonable value for the initial sample size. The minimal number of training points smin depends on the number of design variables k and the order of the polynomial p which could be 1, 2, 3 or more, but usually starts as a second or third order polynomial.

+=min

( )!! !

k pk p

s (2.2)

2.4.2 Metamodeling methods

Many promising methods are available to approximate a response function, e.g., polynomial response surface (PRS) [96], multivariate adaptive regression splines (MARS) [97], Kriging (KR) [98], radial basis function (RBF) [99], neural networks (NN)[36], etc. Scrutinizing the literature indicates that no single metamodeling method that can effectively address all types of optimization problems. The most suitable metamodeling method depends on the nature of the problem, the data sampling method as well as the available computational resources. Jin and et al. [96] have compared four metamodeling methods (MARS, KR, RBF and PRS) with 14 test problems representing different features of engineering design problems. Simpson et al. [94] evaluated some existing metamodeling techniques (response surface, NN, and KR) and provided some recommendations for metamodeling use in computer-based engineering design. Wang et al. [100] reviewed metamodeling techniques in engineering design optimization. The conclusions from these review and comparative studies are;

• RBF is overall the most accurate and robust method for both large- and small-scale high-order nonlinear problems;

• PRS is the best method for low-order nonlinear problem since it is the easiest method to construct and use compared to the others;

• For deterministic applications, both NN and KR are the best, but NN is more computationally demanding to create, and KR performs better for highly nonlinear problem;


• For physical or noisy computer experiments, PRS is the best method while MARS and RBF perform well too, but KR is not suitable at all;

• PR and MARS have the best transparency, which is important to reduce the scale of a problem by removing insignificant factors.

2.4.3 Metamodel validation and selection

The accuracy of a metamodel directly influences which metamodels to select. Many validation methods are proposed for assessing the accuracy of a metamodel and hence assist metamodel selection. Instead of methods requiring additional data for validation, methods that use existing data are more computationally efficient and hence more suitable for complex engineering applications that require computationally intensive simulations and analysis. In general, the accuracy of a metamodel can be evaluated by its residuals/errors between the actual value and the predicted value from the metamodel. Lower error measures indicate a more accurate metamodel. However, the metamodel might have been over-fitted if the error is too small, i.e., smaller than needed.

Generally, error quantification methods can be classified into global and local error estimation methods [101]. The global error measures, such as cross-validation (CV), split sample, bootstrapping, and Akaike’s information criterion (AIC) method [81], evaluate the performance of the surrogate over the entire design domain. And the local error measures evaluate the accuracy of the metamodel in different locations of the design domain. Most of the common standard statistical analysis, such as the root means square error (RMSE), mean square error (MSE), average absolute error (AAE), are global error measures (see Eq.(2.3) to Eq.(2.5)). And the maximum absolute error (MAE) and relative absolute error (RAE) are local error measures (see Eq.(2.6) and Eq.(2.7)). However, all of these statistical analyses are not suitable for interpolation metamodeling methods, e.g., RBF. But, the CV methods make it possible to compare interpolation metamodels with approximation metamodels, e.g., compare RBF with PRS.

12( )1 n

iRMSE y yiin =

= −∑ (2.3)

2

1( )1

i in

iMSE y y

n == −∑ (2.4)

1

1i i

n

iAAE y yn =

= −∑ (2.5)

max , ,...,ni iMAE y y i i= − = (2.6)

, 1,...,i i

i

y yRAE i n

y−

= = (2.7)

where n is the number of the set of test points, and yi and iy are the actual and predicted values at the ith test point, respectively.


There are also many other measures that can be used for metamodel selection. The prediction error sum of squares (PRESS) [87] is an error measure often used in regression analysis. Some researchers have combined standard statistical analysis with cross-validation methods, e.g., the root mean square error of k-fold cross-validation (RMSECV) [102] and relative absolute error of cross-validation (RAECV) [103], as a criterion in metamodel selection. Mehmani et al. [104] made a comprehensive review of metamodeling validation methods and also proposed a new model-independent approach to quantify surrogate model fidelity using all sample points, called Predictive Estimation of Model Fidelity (PEMF) which is based on the k-fold cross-validation method. They compared their proposed PEMF method with the standard leave-one-out cross-validation, using three popular numerical experiments with metamodels constructed by KR, RBF, and E-RBF. They showed that the PEMF provided better accuracy and superior robustness in measuring and quantifying metamodel errors compared to the leave-one-out cross-validation. The pseudo code for performing the standard k-fold cross-validation method is illustrated in Table 2.3.

Table 2.3 k-fold cross-validation method to estimate metamodel errors [104]

k-fold cross-validation INPUT: A dataset D of s sample points The size of each subset k

The number of subsets, c= ( )sk

OUTPUT: error of the metamodel 1 for j = 1,...,c do 2 for m = 1,...,(s-k) do 3 Estimate actual value on mth training point, ym=system(xm) 4 end for 5 Construct the jth metamodel using (s-k) sample points and their system response 6 for i = 1,...,k do 7 Estimate actual value on ith training point, yi=system(xi) 8 Estimate predicted value on ith training point, 𝑦𝑦�𝑖𝑖=metamodelj(xi)

9 Estimate RAE on ith training point; RAEi=i i

i

y yy−

10 end for 11 Evaluate the mean of all RAE values Ej, ( ), 1,...,j iE mean RAE i k= = 12 end for

13 Evaluate the mean of the errors over all c subsets 11 ck fold jjE Ec

−== ∑

2.5 Summary

This chapter first describes the background for the development of haptic devices including the overview of haptic device design and optimization. In order to increase the efficiency of the optimization process for haptic devices, this chapter also briefly describes two existing methods, MDO and MBDO, which might contribute to making optimization significantly more efficient.


CHAPTER 3. SITUATED DESIGN OPTIMIZATION OF HAPTIC DEVICES | 23

Chapter 3

Situated design optimization of haptic devices

Designing is an active recursive learning process between the designers’ actions and observations of the design results. With increasing design knowledge, designers may decide on new actions and revisions of the principal design solution. This situation aware process may be referred to as a “situated design process”. For a 6-DOF haptic device, the design task is originally fuzzy and complex, i.e., due to the knowledge gap, which may lead to a significant amount of revisions and hence a much-prolonged lead time. To efficiently and effectively find the optimal design in a situated design process, it is a significant challenge to be able to adapt and reuse knowledge gained earlier in the process as much as possible so that the design is adaptable to new and/changed situations and/or knowledge state. This challenge is more critical for design tasks with multi- and highly interacting system/discipline models that require computationally intensive simulations and analyses to reduce the knowledge gap. This chapter gives an overview of a proposed and situated methodology for effective design optimization of high-performing 6-DOF haptic devices. The metamodel-based multidisciplinary design optimization method is a core part of the proposed methodology.

The proposed framework is first illustrated using the notation of IDEF0 (Integration DEFinition language 0) [105] describing the sequential generic design and optimization sub-activities. Since the metamodel-based MDO process and the solutions to different situated design scenarios require a large number of decisions and interactive iterations within the design process, it is difficult to describe them using the IDEF0 diagram. Hence separate process graphs are presented in section 3.1 and section 3.2 to illustrate the corresponding activities and their interactions with other activities.

The proposed IDEF0 diagram has three levels (shown in Figure 3.1) including a top-level A-0 (detailed in Figure 3.2) with activity code A0, a second level diagram (see Figure 3.3) with activities from A1 to A7, and a third level (in Figure 3.4) expanding activity A4 into activities A41 to A44.

The main activity A0 in Figure 3.2 is to implement situated design optimization of high-performing haptic devices, by starting with a project mission statement and ending with an optimal design as output. Feasibility considerations achieve the overall control. People, tools, literature, model libraries and different optimization methods are the resources used in this activity. People include the entire team, design and analysis engineers from different disciplines and fields and optimization engineers. Tools represent modeling and analytical tools and the optimization tool.

24 | CHAPTER 3. SITUATED DESIGN OPTIMIZATION OF HAPTIC DEVICES

A0

A1A2

A3A4

A-0

ActivityA0

A4

A41A42

A43A44

A5A6

Input Ouput

Control

Resources

A7

Figure 3.1 The proposed IDEF0 diagrams with 3 levels

Figure 3.2 Proposed IDEF0 top-level activity diagram

The main activity is expanded into seven sub-activities as shown in the second level diagram in Figure 3.3. Figure 3.4 presents a third level decomposition of activity A4 “create models”. To distinguish between control, resources and inputs/ outputs within the activities in Figure 3.3 and Figure 3.4, they are marked in blue, purple, and italics, respectively.

As starting point for the development of a haptic device, the project mission statement is transferred to system requirements as activity A1 shown in the second level diagram in Figure 3.3. The system requirements can refer to the common preliminary requirements of similar haptic devices from literature and interviews


Figure 3.3 Second level IDEF0 diagram

as listed in Table 1.1, such as the number of required DOF, workspace volume, level of isotropy and transparency, etc. According to the system requirements defined in A1, the team needs to select the device architecture (A2) from the model library which will be used as input to the optimization definition task (A3) and the model creation activity (A4). Assisted by the optimization engineer and available knowledge, the team should define the optimization task including performance criteria, model parameters (fixed parameters), objectives (OBJs), design variables (DVs) and constraints (Cons), but the detailed formulation of the optimization task


will be defined and executed in activity A5. The feasibility, such as available time and required computational power, must be considered during activity A3. While creating models in A4, data and information from previous activities, such as device architecture, model parameters, and design variables, are used by the design and analysis engineers from different fields to build the most appropriate models to assess the performance criteria. The optimization task is then performed by the optimization engineers together with other team members in activity A5. The metamodel-based MDO process is performed in this activity using the defined optimization problem and the created models with the project mission and the feasibility as controlling information (see detail in section 3.1). The result of the activities from A1 to A5 is an optimal solution for the defined preliminary mission and requirements. If the project mission is fully satisfied without additional modification or change, the design optimization process can end at this stage with the found optimal solution and design as output. However, if the design case needs to be changed based on the gained knowledge during this process, the system requirements or the optimization task need to be re-defined and resolved in the downstream activities A6 and A7. Possible re-design scenarios and corresponding solving processes are chosen and performed which is more thoroughly described in detail in section 3.2.

The third level diagram in Figure 3.4 expands the activity A4 for model creation. From published research on optimization of manipulators, robotic arms, and haptic devices [18][19][20][45][21][106][107], the four most commonly used models, kinematic models, geometric models, flexible component models, and dynamic system models, are integrated in this diagram. The performance criteria should be assessed by these models which are optional depending on the actual design case. To take advantage of a geometry-based modeling method, the geometric model is used as the master model and used for creating the dynamic system model and flexible component model. Each model is created by design engineers with expertise in the corresponding field using the analytical or simulation tools, such as equation-based tools, CAD, MBS (Multi-Body Simulation) and Finite Element (FE) tools. All models are created based on the pre-defined device architecture, model parameters, and initial guesses for the design variables. As output of this activity,

MBS tool

FE tool

A41

Create kinematic

model

A42

Create geometric

master model

A43

Create dynamic

system model

A44

Create flexible component

model

Model parameters

Numerical modeling

tool

CAD tool

Structure

Peformance criteria

Corresponding models

DVs

Design variables

Mechanical design & analysis engineers

Deometric model

Figure 3.4 Third level IDEF0 diagram for activity A4


the created models are transferred to the next activity to perform the design optimization process. In order to be accessible by the optimization tool in next activity, all models should be parameterized and able to be modified.

3.1 Metamodel-based multidisciplinary design optimization

For multi-criteria optimization of high-performing haptic devices, with its conflicting and coupling characters, we recommend using the MDO method to solve the multi-objective optimization problem. In the design phase of such a device, the complex structure may lead to computational exhaustive and intensive simulations or analyses. The metamodel-based design optimization (MBDO) method can potentially increase the optimization efficiency. Therefore, to efficiently and effectively solve the optimization problem, we propose a metamodel-based MDO approach as shown in Figure 3.5. The metamodeling process is optional, and it could be selected by the design engineer(s) depending on the character of the actual design case. All information, data, and models generated in the process are saved in the database.

As shown in Figure 3.5, before selecting the suitable MDO method for formulating the optimization problem, the DOE process is recommended as a method to analyze the system and to find ways to potentially decrease the size of the optimization problem. The DOE process is illustrated in Figure 3.6. The DOE method selected for screening relates to the sequence shown in Figure 2.5. The results from the statistical analysis of the data obtained from the DOE study. For example, the correlation matrix [108][109] or the student’s T-test [110][111] gives the correlation and independence between and also within the design variables and the objectives. Furthermore, based on the analyses, the complexity of the optimization problem can be potentially decreased by narrowing the range of the design variables or by decreasing the number of design variables or objectives.

In the second step of the proposed approach, the optimization engineers should select the most suitable MDO method for the actual design case based on the most relevant design objectives, constraints, and design variables, as well as their ranges found from the DOE study. We recommend using the single-level MDO method, such as the MDF method, in this stage because a design optimization problem of a haptic device is usually not highly coupled compared to aerospace design cases, and the fact that single-level MDO methods are easier to use compared to multi-level methods. The optimization problem constructed using the MDF method and the Pareto-front approach is formulated in Eq.(3.1), where the output from one simulation or analysis f1 is the input to the other analysis or simulation f2.

1

2 1

minimize ( )minimize ( , ( ))subject to ( ) 0 lower upper

f xf x f x

g xx x x

≤≤ ≤

(3.1)

Before solving the formulated optimization problem, it is recommended to decide whether to replace any of the created full system models (simulations and analyses) by its metamodel depending on the computational resources the model requires. The metamodeling process (see section 2.4) includes data sampling, metamodel construction, and metamodel validation and selection.


Start

Have computational exhaustive model?

DOE study

Metamodelling

Choose suitable MDO method

Formulate the optimization problem

Solve the optimization problem

DVs & Cons & OBJs

Created models

Metamodels

Select the optimal design

Involve metamodel(s)?

Validate optimal design on full model

Satisfy accuracy requirment?

Final solution

End

Yes

No

Yes

No

YesNo

Updated DVs & Cons & OBJs

All evaluated design solutions

Construct Pareto-front(s)

Metamodels & obtained knowlege

Figure 3.5 The proposed metamodel-based MDO approach

Start

Select factors (design variables)

Define/ Select response (objective)

Determine levels and range of each factor

Select DOE method for screening

Perform the experiment

Statistical analyze of results

Derive conclusion

End

Satisfy with the result?

Yes

No

Figure 3.6 The DOE study process


To assist design of haptic devices with deterministic computer experiments, it is recommended to use the space filling methods, such as the Uniform Latin Hypercube (ULH) sampling method. This method generates randomly and uniformly distributed design points in each dimension for metamodel training, which maps marginal probability distributions better, especially for cases with small sample sizes [112].

Based on reviews and comparisons found in literature, we recommend constructing the metamodels of the system models using the Kriging (KR), the radial basis function (RBF) and neural networks (NN) methods.

For selecting the most suitable metamodel for the system, the Predictive Estimation of Model Fidelity (PEMF) proposed by Mehmani et al. [104] can be used. But, if it is to be used for validation of the metamodel constructed by a single metamodeling method, the k-fold cross validation method can be used.

Since the ordinary PEMF method requires a large amount of iterations, we have modified this method to make it useful for engineering design cases that require many software-based analyses which should be executed manually by the design and analysis engineers. The modified PEMF method for metamodel validation and selection is further on referred to as the PEMF-based cross-validation method (abbreviated as PBCV), and its pseudocode is shown in Table 3.1. If the selected best-fit metamodel cannot fulfill its accuracy requirement, the metamodeling process needs to be revised by adding and evaluating more design points for reconstructing a more accurate metamodel.

Basically, the PBCV method follows most of the steps in the PEMF method. However, in the PEMF method, the error measures with different sample sizes are calculated from the mode of the median error distribution, which requires a huge amount of intermediate metamodels. Hence, the mean of relative absolute error (RAE) is used as error measure for the intermediate metamodel for different sample sizes. Furthermore, since this method is used to find the most suitable metamodeling method for a specific task, the steps for predicting the error of the final metamodel are ignored. Instead, the standard k-fold cross-validation method is used to evaluate the error of the metamodel that is trained with the maximum sample size.

The final main step is to solve the optimization problem (detailed in Figure 3.7). The formulated problem and all created models, simulations, analyses or metamodels, are integrated into this step. The commercial software applications, such as iSIGHT® [113], HEEDS® [114], modeFRONTIER®, etc., can be used for process integration and design optimization. An example of a tool integration and optimization workflow in modeFRONTIER is illustrated in Figure 3.8.

As shown with the example workflow in Figure 3.8, two engineering software, MATLAB® [51] and Adams/View® [115], are used to simulate and analyze the performance criteria. i.e., the objectives. The defined optimization problem has two objectives, three design variables, and one constraint. The initial population node is used to define and generate an initial population. The optimization algorithm and the number of generations are defined in the optimization algorithm node.


Table 3. 1 PEMF-based cross-validation for error estimation and selection of metamodels

PEMF-based cross-validation INPUT: A dataset D with s sample points The number of metamodeling methods m The number of iterations n Maximal size of training data tmax=a+b·n<s; (a and b are a constant)

The number of subsets, 𝑐𝑐 ≤ �𝑠𝑠

𝑡𝑡𝑚𝑚𝑚𝑚𝑚𝑚�; recommend c=10 OUTPUT: The best-fit metamodel 1 Estimate system response of all s sample points; ys=System(xs) 2 Save all xs and ys in the dataset D 3 for b = 1,...,m do 4 for j = 1,...,n do 5 tj = a + b·j 6 for p = 1,...,c do 7 Select a random subset of size tj from D 8 Construct metamodelp of the system 9 Save the rest data as validation dataset of size (s-tj) 10 for r = 1,..., (s-tj) do 11 Estimate predicted value on rth validation point, 𝑦𝑦�r=metamodelp(xr)

12 Estimate RAE value on rth valudation point; RAEr=�𝑦𝑦𝑟𝑟−𝑦𝑦�𝑟𝑟𝑦𝑦𝑟𝑟

� 13 end for 14 Evaluate the mean of all RAE values; Ep = mean(RAE1,...,RAEr) 15 end for 16 Evaluate the median value of E for all c combinations; MEj=mean(E1,...,Ep) 17 end for 18 Evaluate the leave-one-out cross-validation error of the metamodel constructed with all sample data, MEn+1 19 Construct the regression function to represent the variation of error with sample density, Fb(h), h = [t1,t2,...,tn, s]; 𝐹𝐹(ℎ) = 𝑎𝑎0𝑒𝑒−𝑚𝑚1ℎ or 𝐹𝐹�𝑡𝑡𝑗𝑗� = 𝑎𝑎0𝑡𝑡𝑗𝑗−ℎ. 20 end for 21 Compare the regression functions of error variation with sample density Fb(h) and select the metamodeling method with the minimal overall error and variance; b= 1,...,m; h=t1,...,tn, s. 22 Select the metamodel constructed with all sample data using the selected metamodeling method

The results of the optimization process, i.e., all evaluated designs and the found optimal solutions, are saved in the database to make it possible to construct the Pareto-fronts and to make decisions based on the front. If the selected optimal design satisfies the system requirements and project mission, and no re-design or modification is needed, the design optimization process can be terminated at this stage. However, if the design case needs to be changed based on the knowledge gained in this process, the system requirements or the optimization task must be re-defined and resolved in the upcoming activities described in the following section.


Start

Import system models

Formulation of the optimziation problemKinematic model

CAD modelMBS modelFE modelMetamodels

Build optimization workflow

Define optimization algorithm & Number of generation

Generate initial population

Execute optimization workflow

Reach Max. generation?

End

Get all evaluated solutions

Yes

No

Figure 3.7 Process for solving the optimization problem

Figure 3.8 Example of the optimization workflow in modeFRONTIER


3.2 Situated design scenarios and re-design process

In this section, we first list the potential re-design scenarios that might follow an already solved design case, further on referred to as the initial design case. The corresponding processes for the different scenarios and the re-usable knowledge for the different scenarios are also presented here. The presented approach can be used not only after designing and optimizing a device but also in later product development if all necessary information and data from the previous design task have been saved in the database.

Generally, the possible re-design scenarios can be characterized by the change of the system and performance requirements that are required. Three groups of main re-design situations are categorized as:

1. Unchanged criteria: The performance criteria are unchanged, but the system requirement and/or the performance criteria limits are changed, e.g., the range of constraints are changed, or new constraints are added;

2. Add criteria: New performance criteria that are important for the system are added;

3. Remove criteria: Currently obsolete or less important performance criteria are removed.

The possible situated design scenarios of each group described above, and their corresponding solution processes are represented in Figure 3.9 as a generic re-design process graph. In this figure, the names of the three groups are simplified as “unchanged criteria”, “add criteria”, and “remove criteria”. Following the paths for different re-design scenarios, the solution methods are abstracted as three types of methods, i.e.; “direct filter”, “rework”, and “re-optimize using BLISS-2000” (boxes with gray background color in Figure 3.9). The re-usable knowledge for each solution method is marked below each action with numbers (①②③④).

As a short description of the generic graph, solutions to possible re-design situations are:

• For group #1 (unchanged criteria):

- If the new design case can be found within the existing optimal solutions, new solutions can be obtained by filtering the existing solution space for the initial design case;

- If no solution for the initial design case can satisfy the new re-design case, the current range of the design variables cannot provide feasible solutions. Hence the ranges of the design variables must be expanded, and the design optimization process has to be repeated. But, the DOE study and the effect table from the initial design case can be used to guide the process to find the new ranges for the design variables.

• For group #2 (add criteria):

- If the design variables are unchanged, the shared design variables are not changed, and only coupling and local variables are added, the BLISS-2000 method (further explained in Figure 3.10) can be used to solve this


II: Add criteria

Add coupling and/ local orvariables

I: Unchanged criteria III: Remove criteria

Change range of design variables

Change range of /add constraints on the criteria

Changed requirement on criteria

Add design variables

Rework②

Re-optimize using BLISS-2000①②③④

In existing solution space?

Correlate to other criteria?

Direct filter①

No change on design variables

Change range of design variables

Utilized existing knowledge:① Pareto-front② DOE results & effect table③ Metamodels of original criteria ④ Range of design variables

YES

NO YES

NO

No change on design variables

Figure 3.9 The proposed generic re-design process graph

new optimization problem. The initial design optimization problem can then be treated as optimization on a subsystem level.

- If a re-design optimization problem requires new (shared) design variables added to both the initial and the new criteria, re-work of the entire design and optimization process (described in section 3.1) is required.

• For group #3 (remove criteria):

- If a removed performance criterion is shown to highly interact with other criteria, the range of the design variables might have to be expanded/changed, and the optimization process should, consequently, be re-executed in order to assure a high performance of the remaining criteria. The results of DOE study from the initial design case can be used.

- If a removed criterion does not correlate with the other remaining criteria, the filtered Pareto-front for the initial optimization case without considering the removed criterion can be used directly as Pareto-optimal solutions.

As shown in Figure 3.10, the BLISS-2000 workflow is based on the re-design scenario that the initial optimization problem is unchanged, and an optimization of the new criterion must be performed with additional local and coupling variables. The symbols used in this section and Figure 3.10 are defined when they first appear, but they are also summarized in Table 3.2.


Subspace 1Data sampling

Subspace 2Data sampling

Subspace Optimizer and

Analyzer 2

Subspace 2 Metamodels

*, , ,sh locX X Y W

^1 1^

*1 1

=metamodel( )=metamodel( )

msh

msh

Y XY X

1,o *1,Y Y∧

2 2 12=metamodel( , )∧ *mshY X Y

11,ishX W

Subspace 1Metamodel validation

Subspace 2Metamodel valiadtion

Satisfy accuracy requirement?

*, j12 22, ,j

shX Y W

j=m?

Subspace 1 Metamodels

j=j+12,2, , oloc o YX ∧

Subspace Optimizer and

Analyzer 1


i=i+1

Mod

el re

finem

ent

Mod

el re

fienm

ent

Construct Pareto Front

Decision making

Verify selected optimal design


End

Des

ign

refin

emen

t

Retrieve the optimal Xloc

Des

ign

refin

emen

t

i=n?

System optimization

Figure 3.10 BLISS-2000 adapted for a situated design case


Table 3.2 List of symbols used in this section

Symbol Meaning Xsh Shared design variables appeared in all subspaces Xloc Local variables appeared in only one subspace Y*1 Coupling variables output from subspace 1 Y12* Coupling variables output from subspace 1 as input to subspace 2 W Weighting coefficients of all outputs n, m The size of sample data for metamodeling in each subspace ()^ Functions or variables output from an analyzer ()o Optimal of functions or variables ()m Metamodels of functions or variables g Constraint functions

In a specific re-design scenario, the initial design case can replace Subspace 1, marked as a gray block, and the metamodels of the outputs from the initial design optimization case (Y1^m and Y*1^m) can be used directly. The range of the shared design variables and coupling variables found from the initial design case can also be used here. An added criterion, i.e., a new objective, is treated as Subspace 2, which follows the regular process in the BLISS-2000 method.

The first step in BLISS-2000 is to initialize the shared design variables (Xsh), the local (Xloc), and coupling (Y*) variables as well as the weighting coefficients (W). Since we need to apply the Pareto front approach to solve the problem, the weighting coefficients of all outputs are set to equal and hence as a constant. The iterative process starts with data sampling for each subspace, which creates a number of different input settings for metamodel construction. The sizes of the sample data (n and m) are different based on the different optimization problem in the subspace. The results from the subspace optimization in the subspace 2 for each point in the sample data ( *, j

2 12 2, ,jshX Y W ) are the optimal output (Y2,0^) and its

corresponding value of local variables Xloc2,o. The next step is to construct the metamodels Y^m to represent approximations of how each element of Y^ depends on Xsh and Y*. And the metamodel Y*1^m is constructed for consistency check at the system level. The accuracy of all metamodels needs to be checked before using. In the next step, the system optimizer finds the values of Xsh and Y* that minimize the global objective functions Y1 and Y2 subject to the consistency constraint Y*1^m= *

12Y . The final optimal design selected from the Pareto front should be verified with the full model. In the end, the local variables are retrieved based on the selected optimal design. The subsystem and system optimization problems are formulated as:

The subsystem level optimization problem:

2*12^

*2 12

** *12 12 12

Given: , ,

Find: X ,

Minimize: ( ,Y )subject to: 0

sh

loc

loc

upperlowerlocloc loc

upperlower

X Y W

Y

Y XgX X X

Y Y Y

≤ ≤

≤

≤ ≤

(3.2)


The system level optimization problem:

− =

≤ ≤

^ ^ ^1 2*1

*12

^1^ *

2 12^ *

12*1

*

Given: , ,

Find: ,

minimize: ( )

( , )

subject to: 0

m m m

shm

shm

shm

upperlowershsh sh

lo

Y Y Y

X Y

Y X

Y X Y

Y Y

X X X

Y=

≤ ≤=1

**

12

upperwer Y YW W

(3.3)

By solving the specific re-design scenario with the BLISS-2000 method, the knowledge (the range of shared design variables and coupling variables) and the existing metamodels can be directly used, which decreases half of the effort comparing to completely re-solving the optimization problem, as described in section 3.1.

3.3 Summary

This chapter presents an overview of the proposed methodology with a situated framework for effective design optimization of high-performing 6-DOF haptic devices. The overall framework was first illustrated using a three-level IDEF0 diagram. The flexible optimization activity that relies on the metamodel-based MDO method was then expanded and illustrated in more detail. If the project mission cannot be fulfilled after this activity, a situated re-design process is activated. Based on the initial design case and the knowledge gained in that process, the possible re-design scenarios and their optimization process were described as a generic re-design process. This process can not only be used right after a device has been designed and optimized, but it can also be used to assist future product development tasks, provided that all necessary information and data from the previous design optimization effort are saved in the optimization database.

CHAPTER 4. CASE STUDY | 37

Chapter 4

Case study: optimization of the 6-DOF TAU haptic devices

In order to illustrate and conceptually verify the proposed methodology and the assisting framework, we have formulated an optimization case study of a 6-DOF haptic device for hard tissue surgical usage. The case study is separated into two parts. Section 4.1 applies the proposed process, as represented by the previously presented IDEF0 diagrams, to optimize a well-defined TAU haptic device as an initial design case. Section 4.1.1 presents how the three possible re-design scenarios are solved based on the initial design case using the situated design framework proposed in section 3.2.

4.1 Initial design case

The activity names in the IDEF0 diagrams are used as subheadings in this section. Based on team discussions, the formulated project mission was to optimize an existing 6-DOF haptic device with the proposed metamodel-based MDO methodology. The system requirements (A1) for the surgical haptic device were specified as follows [17]:

• The device should have six actuated degrees of freedom;

• The whole device should fit within a geometric space of 250×250×300 [mm];

• The minimum translational workspace should be 50×50×50 [mm].

With the mission statement and system requirements as input, the object (A2) used for optimization was the 6-DOF TAU haptic device. The TAU configuration (see Figure 4.1) consists of a fixed I-column, a handle located on the Tool-center-point (TCP) of a moving platform, and three kinematic chains which connect the platform to the fixed I-column. Chains 1 and 2 are symmetrical with a serial plus parallel linkage, and chain 3 is a pure serial linkage. Six motors are mounted on the I-column to enable the 6-DOF motion, and the rest of the joints are all passive.

Based on the system requirements and the chosen device architecture, the optimization task (A3) to find the optimal design solution that satisfies the following performance criteria was defined:

• Sufficient dexterous workspace,

• No singularities within the workspace,

38 | CHAPTER 4. CASE STUDY

Figure 4.1 A 3D-model of the TAU haptic device

• High isotropy and transparency.

With these performance criteria, the optimization task was transformed to specific objectives, design variables, and constraints. Dexterous workspace and isotropy were selected as the two objectives to be optimized with some of the geometric dimensions of the device as design variables. The required translational and rotational workspace, the dexterity, singularity and the capability of the joint angles were defined as constraints that limit the optimization solution space.

The dexterous workspace is determined as the end-effector ability to move under the required orientations within the workspace. The kinematic isotropy indicates how evenly the system moves in all six generalized directions in the dexterous workspace.

Based on the defined optimization task, the necessary models (A4) need to be created with the most appropriate modeling tools, each model targeting a specific objective or constraint. For the defined design case, a kinematic MATLAB model

Figure 4.2 Structural design variables for design of the TAU haptic device


was built. This model included the objectives, the workspace volume index (VI) and global kinematic isotropy index (GII), with constraints on singularity condition (gJ), the size of the found workspace volume (gV), the dexterity condition (gα), and the limitation of each joint angle (gβ). Five continuous design variables (L1, L2, Rp, θp and θ6), representing the geometric structure, were defined, as shown in Figure 4.2. The approaches defined by Ahmad et al. [116] and Gao et al. [117] were used for evaluating the dexterous workspace and the kinematic isotropy, respectively.

The dexterous workspace was searched within a pre-defined cylinder which was constructed by a circle with radius 50mm and [-50, 50] [mm] in the Z-direction, while the required orientations were defined as +-10 degrees in all three directions. The dimension of the maximum rectangular workspace volume (Wx, Wy, Wzmax and Wzmin), as shown in Figure 4.3, was searched within the dexterous workspace which should not be smaller than the minimum translational workspace (gV). Only the grid point with a same value of Wx and Wy was picked for finding the maximum rectangle so that the maximal rectangular workspace is (2·Wy)×(2·Wy)×(│Wzmin│+Wzmax) [mm].

Figure 4.3 The dexterous and effective workspace footprint

4.1.1 Metamodel-based MDO

The next activity, in our process, is to perform the optimization process (A5). Before selecting the MDO method and formulating the optimization problem, the DOE study was performed, with the aim to study the main effects of the design variables and their interactions on the objectives, and potentially find ways to decrease the complexity of the design problem.

Based on the size of the design problem (5 design variables and 2 objectives), a 2-level full factorial design was used to generate the DOE study points. The effect size and significance of each design variable for all response factors (objectives and constraints) from the overall T-test chart are shown in Table 4.1. The effect value shows the strength, between -1 to 1, of the relation between the factor and the response. The significance, which varies from 0 to 0.5, indicates whether the effect


size value is reliable or not. If the effect value is close to unity, and the value of significance is close to 0, the design variable has a true and significant positive/negative effect on the response factor.

Table 4.1 Effect and significance of each factor on the system response

L1 L2 Rp θp θ6 GII -0.609 0.209 0.956 -0.406 -1.000 [significance] [0.048] [0.292] [0.005] [0.138] [0.003] VI 0.843 -0.740 0.101 0.845 1.000 [significance] [0.028] [0.049] [0.151] [0.028] [0.053] Wy -0.091 1.000 -0.136 -0.636 -0.341 [significance] [0.409] [0.006] [0.372] [0.048] [0.206] Wzmax 0.585 -1.000 0.113 1.000 0.623 [significance] [0.097] [0.015] [0.408] [0.015] [0.096] Wzmin 0.000 0.000 0.000 0.000 0.000 [significance] [-] [-] [-] [-] [-]

According to Table 4.1, except for design variable Rp, all design variables have contradictive effects on the two response factors, global isotropy index (GII) and volume index (VI). Since the design variable Rp has a significant positive effect on GII and less effect on VI, Rp was set to constant at its maximal value (60 mm) instead of being defined as a design variable. Furthermore, the design variables have no effect on the constraint Wzmin, which has a constant value of -50. The range of the design variables before and after the DOE study is shown in Table 4.2.

Table 4.2 Design variable ranges before and after DOE study

L1[mm] L2[mm] Rp[mm] θp[°] θ6[°] before Lower 100 100 40 30 15 Upper 200 200 60 60 40 after Lower 135 150 27 28 Upper 145 170 60 30 30

As recommended in the proposed methodology, the MDF MDO method and the Pareto-front approach were used to solve the optimization problem, which is formulated in Eq.(4.1).

1

2

1 2 6

maxmin

maximize ( ) ( ) maximize ( , ) ( , ) [ , , , ]subject to ( ) det( ) 0

( ) ( ), ( ), ( ), ( ) 25

( ) ( )

p

J

V x y

x y

f X VI Xf X J GII X J

over X L Lg X J

g X W X W X Wz X Wz X

W X W X

θ θ

==

=

= >

= ≥

=

, 1,...,4upperlowerii iX X X i≤ ≤ =

(4.1)

where X is a vector of the four design variables, and J is the Jacobian matrix. As constraints, the singularity condition (gJ) should not be equal or less than 0, and the four dimensions of the maximum rectangle (Wx, Wy, Wzmin and Wzmax) in the dexterous workspace should be not less than 25 mm in the TCP local coordinate system.


In order to increase the efficiency of the process, metamodels of the two objectives were constructed and used to replace the two kinematic system models in the optimization. Based on the study presented in Paper C, 300 sample points generated by the ULH method were used to train the metamodels. Furthermore, the metamodeling methods, radial basis function (RBF) and Kriging (KR), were used to construct the metamodels for VI and GII, respectively. This selection of methods was based on the generic findings for all kinds of 6-DOF haptic devices (TAU and Ares) using the PEMF-based cross-validation method. In this case study, the error of each metamodel, verified using the k-fold cross-validation method, was 2.39% and 1.02% for VI and GII, respectively, which satisfies the accuracy requirement (error less than 5%).

Due to the non-linear behavior of the TAU haptic device and the multi-objective character of the design problem, a general optimization process based on the Non-dominated Sorting Genetic Algorithm (NSGA-II) was used to optimize the design solution. In our study, the software modeFRONTIER was used to integrate different heterogeneous models and also to automatically optimize the defined multi-objective and multi-disciplinary design problem. The optimization scheduler is shown in Table 4.3.

Table 4.3 Parameter values for optimization used in modeFRONTIER

Scheduler NSGA-II Number of generation 100 Crossover probability 0.9 Mutation probability for real-coded vectors 1.0 Distribution index for real-coded crossover 20 Distribution index for real-coded Mutation 20 DOE algorithm ULHS DOE number of designs 100 Total number of iterations 100×100=10000

All solution results, as well as the Pareto-front from the optimization process,

are illustrated in Figure 4.4. At this stage, the team could make the decision and defined the importance of each objective. For example, we thought the isotropy performance was more important than the workspace volume. Hence the optimal design with the maximal GII value was selected as the final solution. The optimal configuration in this design point should be validated with the full model before final usage. The error between the metamodel and the full model was 2.64% for VI and 0.8% for GII which satisfied the accuracy requirement (less than 5 %).

The final optimal solution and the corresponding design configuration are shown in Table 4.4. Based on the comparative study made in Paper C, the proposed metamodel-based MDO methodology and framework can reduce the design and computational effort by more than 27 times compared to the process using a full system model.


Figure 4.4 All solutions and the Pareto-front

Table 4.4 Optimal design configuration with maximal GII value

Design Variables System Response Name Value Name Value L1 136.3405

[mm] GII 5.2103 [-]

L2 153.2027 [mm]

VI 3.9767 [dm3]

Rp 60 [mm] Wx (Wy)

28 [mm]

θp 29.6096 [°] Wzmin -50 [mm] θ6 27,00168 [°] Wzmax 25 [mm]

4.2 Re-design cases and solutions

From the solution of the initial design case, we have a set of optimal designs with global isotropy index (GII) values ranging from 0.4246 to 0.5253, and values of workspace volume index (VI) ranging from 0.9932 to 0.3872 dm3.

However, in the further product development, or in new development, we might want to improve or change the device performance targets based on the gained system knowledge and new or modified system requirements. In this case study, we addressed three new design situations with proposed solution processes using the framework described in section 3.2. By using the initial design case as the base design, the three re-design cases were:

1. The device should have a relatively high isotropy performance.

2. The minimum translational workspace should be 80×80×80 [mm].

3. The device should have low inertia at the end-effector.

Based on the changed system requirements, three re-design scenarios are solved in the following subsections.


4.2.1 Re-design case 1: change/add the isotropy requirement

In this re-design case, we search for a device which satisfies the original requirements but also guarantees a relatively high isotropy performance. Since relatively high isotropy is an ambiguous requirement, we sharpen this requirement by explicitly requiring the isotropy index GII to be larger than 0.5.

To handle this new requirement, the isotropy index was treated both as an objective and a constraint in the optimization process. Since solutions fitting the new requirement can be found in the existing solution space from the initial design case (shown in Figure 4.4), the solutions to this new design case could be directly filtered from the existing Pareto-front as shown in Figure 4.5.

Figure 4.5 Filtered Pareto-front of the new design case

4.2.2 Re-design case 2: increase the workspace requirement

The minimum translational workspace was changed from 50x50x50mm to 80×80×80mm. In order to make this changed requirement feasible, the device size requirement was enlarged to 400×400×550mm. Since the new workspace volume requirement cannot be found in the existing solution space for the initial design, the range of the design variables and the searching range were changed based on the effect analysis of the initial design case shown in Table 4.1. The changed ranges for the design variables are shown in Table 4.5. Furthermore, the searching area for the dexterous workspace was changed to a cylinder with a circle with radius 80 mm and [-60, 60] mm in the Z-direction.

Table 4.5 Updated range of design variables for re-design case 2

L1[mm] L2[mm] Rp[mm] θp[°] θ6[°] Lower 260 260 60 35 25 Upper 300 300 100 45 42


The metamodel-based MDO process was re-run, and the new Pareto-front from this activity is illustrated in Figure 4.6. After validation, the design with the maximal GII value was selected as the final design. The optimal design configuration is presented in Table 4.6. The error between the real and predicted value of GII and VI was 2.88% and 4.61%, respectively, which satisfies the accuracy requirement (should be less than 5%).

Figure 4.6 Pareto-front as solutions to the re-design case 2

Table 4.6 The selected optimal design solution to re-design case 2

Design variables System response Name Value Name Value

L1 260 [mm] GII 0.49 [-] L2 280.84 [mm] VI 2.365 [dm3] Rp 100 [mm] Wy 42 θ6 37 [°] Wzmax 60 θp 37.7 [°] Wzmin -40 Translation

workspace 84×84×100[mm]

Device size 380×300×525 [mm]

4.2.3 Re-design case 3: Optimize the inertia performance

In order to provide a realistic force feedback to the user, it is important to have low inertia at the end-effector, which is the inertia experienced by the user. Hence, besides from the system requirements addressed in the initial design case, the inertia at the TCP was also evaluated and optimized in this re-design case.

The inertia performance was evaluated using the geometry-based model in the Adams software from MSC Software. In the Adams model, the TCP was sequentially moved on the bounding surface of the dexterous workspace found previously (13 points as shown in Figure 4.7). The moment of inertia tensor about X-, Y- and Z-axis in each point, with respect to the global coordinate system, was recorded for further inertia analysis.


Figure 4.7 Thirteen points defined for analyzing the TCP-based moment of inertia

Four kinematic inertia indices were analyzed and optimized including, SI, the sum of the median moment of inertia tensor about the X-, Y- and Z-axis (MIxx, MIyy and MIzz), and the variances of mean of moment of inertia about the X-, Y and Z-axis (VMIxx, VMIyy and VMIzz), respectively. The relations between the variables, objectives and constraints for this new design case are shown in Figure 4.8.

L1

Kinematic model

Dynamic model

GII

VI

SI

Rp

θp

Wy(Wx), Wzmax, Wzmin

Shared design variables

ObjectivesConstraints

Coupling variables

Wx, Wy,Wzmax, Wzmin

L2

θ6

VMIxx,VMIyy,VMIzz Figure 4.8 Relations between variables, objectives, and constraints

The metamodel of each inertia index was constructed using the RBF method. The BLISS-2000 MDO method was used to solve this optimization problem which is formulated as:

The subsystem level optimization problem formulation:

θ θ

==== >= ≥

2

1

max min

1 2 6

maximize ( ) ( ) ( , ) ( , ) [ , , , ]subject to ( ) det( ) 0 ( ) ( ), ( ), ( ) 25

y

p

JV

f X VI Xf X J GII X Jover X L Lg X J

g X W X Wz X Wz XW

≤ ≤ =

=

=^ ^ ^ ^ ^ ^max min

( ) ( )

, 1,...,5

Find , , , ,[ ]o o o o o o

yuplow

ii i

x X W X

X X X i

Y VI GII Wy Wz Wz

(4.2)


The system level optimization problem formulation:

= ===

+ +max

123

Given : , , , , , ,Minimize: ( , *) ( , *) ( , *) ( , *) ( , *) ( , ) ( , *) ( , )

**

,a a a a a a a azzxx yya a a

axx

SIWy Wz MIxx MIyy MIzz VMI VMI VMIF X Y X Y MIxx X Y MIyy X Y MIzz X YF X VMI X YF X

YY

θ θ

===

==

<−max

4

5

6

* *

* ^a

1 2 6

( , *) ( , *) ( , *)Maximize : ( ) ( ) ( ) ( ) [ , , , ] * [ , ]subject to: ( ) 5

ayyazz

aa

y z

p

VMI X YF X Y VMI X YF X GII XF X VI X

over X L LY W WWy Wy X

≤ ≤ =

* ^amax max - (X) <5 , 1,...,5uplow

ii i

Wz WzX X X i

(4.3)

where X = Vector of shared design variables affecting two or more modules, Y= Vector of system response (behavior variables),

( )a = Metamodels of functions or variables, *( ) = Functions or variables input into a criterion from other modules, ^( ) = Functions or variables output from a module, ( )o = Optimal of functions or variables.

Since ( )Wx X and ( )yW X were defined to be equal and the value of Wzmin remained at −50 [mm], Wx and Wzmin were not considered at the system level, and hence the metamodels of Wx and Wzmin were removed from the formulations.

A result of the optimization process was that the median moment of inertia tensor and their variance has a linear positive relation (as shown in Figure 4.9). Hence the SI was used to represent the variance indices (VMI) in the analysis of the Pareto-front, as illustrated in Figure 4.10. Table 4.7 shows the optimal design configuration selected from the Pareto-front.

Table 4.7 The selected optimal configuration

Design variables System response Name Value Name Value L1 135.42 [mm] GII 0.4764 [-] L2 150 [mm] VI 0.4867 [dm3] Rp 60 [mm] Wy 35 [mm] θ6 29.507 [°] Wzmax 30 [mm] θp 28.810 [°] Wzmin -50 [mm] SI 0.2231 [kg·m2] VMIxx 5.5382e-4 [kg2·m4] VMIyy 5.3262e-4 [kg2·m4] VMIzz 5.4708e-6 [kg2·m4]


Figure 4.9 MI vs. VMI around x-, y- and z-axis in the Pareto-front

Figure 4.10 Pareto-front including GII, SI and VI


4.3 Summary

This chapter presents design optimization of the 6-DOF TAU haptic devices using the proposed methodology. First, a preliminary design task with two performance criteria was described and solved. For further improvement of the optimal design in the preliminary design task, three re-design scenarios and their solution processes and results were presented. It can be concluded that the proposed methodology can efficiently and effectively solve several situated design optimization cases for high-performing haptic devices.

CHAPTER 5. SUMMARY OF APPENDED PAPERS | 49

Chapter 5

Summary of appended papers

This chapter gives a summary of the appended papers.

Paper A: Design optimization of haptic devices: A systematic literature review

Performance requirements for high-performing haptic devices are usually multi-criteria. Sometimes the requirements are highly interacting, and several of them are conflicting. Optimization is one of the main approaches to scrutinize the design space and to search for a design that satisfies all requirements. The main purpose of Paper A is first to find the most commonly used performance requirements and designs of haptic devices, and secondly to study what approaches have been used to improve optimization effectiveness and efficiency.

In this paper, firstly, the most commonly used performance requirements and their ideal qualitative values found from literature were presented in a table which includes a large number of DOF; high isotropy, dexterity and stiffness; large workspace volume; low inertia and friction; and high resolution, bandwidth, generated force and peak accelerations. Secondly, the properties of currently available commercial haptic devices and prototypes in research labs are presented. According to the listed specifications, the manufactures and researchers tend to develop and research stiff haptic devices with a large number of DOF and a large workspace, and ability to exert high-fidelity forces and torques. Furthermore, parallel and hybrid kinematic structures are more commonly used than serial structures.

Furthermore, several multi-objective optimization tasks or examples of haptic devices found in the literature were synthesized as part of the review. The most common optimization targets are to maximize workspace, kinematic isotropy, as well as the peak force/torque provided by the device, and to minimize the dynamic inertia. Commonly used indices to constrain the design space are a minimum workspace, avoidance of singularities and motion limits of active and passive joints. The number of design variables varies from 2 to 9, and the most commonly used design variables are a set of mechanical parameters, such as the lengths and diameters of the mechanical components. The two commonly used solution methods to the MOO problems are the weighted-sum approach and the Pareto-front approach. However, to increase the efficiency of complex and multi-criteria optimization tasks, the Pareto-front approach, combined with multidisciplinary design optimization (MDO) and metamodel techniques are recommended.

50 | CHAPTER 5. SUMMARY OF APPENDED PAPERS

Paper B: Towards a methodology for multidisciplinary design optimization of haptic devices

The main objective of the research presented in paper B is to include different disciplines and sub-systems, and also integrate discipline-specific models in a design and optimization framework which enables automation of design activities in the concept and detailed design phase.

A model-based and simulation-driven engineering design methodology and a flexible pilot framework are proposed for design optimization of high-performing haptic devices. The main difference compared to traditional multi-objective optimization is that it utilizes Multidisciplinary Design Optimization (MDO) methods in the design phase to balance the conflicting criteria/requirements of a multi-domain design case and solve the design optimization problems concurrently. The Pareto-front found from the optimization process also enables multi-disciplinary reasoning and trade-off negotiations as a post-optimization stage, i.e., it adds flexibility to the process.

In the proposed pilot framework, the four most commonly used behavior models (kinematic model, geometric master model, flexible component model and dynamic system model) are integrated with a coarse-grain system requirement model in the design process. The main activities of the proposed methodology are represented as a hierarchical three-level model with the notation of IDEF0 (Integration DEFinition language 0).

The proposed methodology was verified with a test case to design a 6-DOF haptic device based on a TAU configuration. The optimization goal of this case was to find the design properties that maximize the kinematic performance indices. Global indices such as workspace volume, kinematic isotropy, and weight, were defined in the design evaluation stage. Two models integrated into the pilot framework, a parametrized geometric model, and a kinematic model, were used following the proposed design process. One of the MDO methods, Multidisciplinary Feasible (MDF), was used to solve the optimization problem. The results indicate that the proposed methodology is flexible and situated and that it can potentially support the conceptual design phase. Furthermore, the framework is scalable in terms of size, the level of detail, and a number of domain-specific models, which implies that it can also support the detail design stage.

Paper C: the search for an efficient design optimization methodology for haptic devices

The main objective of the research presented in paper C is to investigate how the efficiency of the process for design optimization of a 6-DOF TAU haptic device is affected by the metamodel-based design optimization (MBDO) method. Furthermore, a secondary task was to generalize the findings, i.e., to see if the results for the TAU device can potentially be used for all types of 6-DOF haptic devices.

The metamodel validation method, Predictive Estimation of Model Fidelity (PEMF), is integrated with metamodel-based design optimization (MBDO) into a multi-tool framework. To take full advantage of the software tools, complementary

CHAPTER 5. SUMMARY OF APPENDED PAPERS | 51

engineering tools from different software vendors, such as modeFRONTIER® and MATLAB®, are integrated into the framework.

In the proposed methodology, a modified PEMF validation method is used to enable the implementation in the multi-tool framework. The methodology and the framework were verified through an optimization test case with a 6-DOF TAU haptic device. The optimization goal was to maximize the kinematic performance of the device. The kinematic performance was quantified as the dexterous workspace (VI) and the kinematic isotropy (GII). Furthermore, the metamodel fidelity for each objective was compared using three different metamodeling methods, Kriging (KR), radial basis function (RBF), and neural network (NN). For a generalization of the findings from the case study, the results were verified by performing a similar optimization of another 6-DOF haptic device based on a Stewart platform configuration.

An analysis of the test cases with the two haptic devices indicates that the proposed metamodel-based approach can dramatically reduce the total computational effort compared to the traditional method to use the “full” system model. Furthermore, the most accurate metamodeling method, with the metamodel errors and errors in the optimal solutions less than 5%, is shown to be Kriging (KR) for GII, and radial basis function (RBF) for VI. Additionally, for the specific design case described in paper B, 300 sample data generated by the Uniform Latin Hypercube sampling (ULHS) method can be used for training the metamodels for all kinds of 6-DOF haptic devices.

Paper D: situated design optimization of haptic devices

Paper D focused on finding an efficient way to deal with uncertainties or changes of the design task during a design optimization process. In the early phase of designing a complex system, such as a high-performing haptic device, the task is uncertain and many times not well-defined, largely because of a significant knowledge gap. With the increasing knowledge gained in the design and optimization process, the design case will likely change, e.g., the system requirements, and/or the performance criteria will be modified.

In this paper, a situated and computationally efficient design framework is proposed for multi-objective optimization of high-performing haptic devices. The notation of “situated” here indicates that the design process is adaptable to new and/or changed situations. The design-of-experiment (DOE) and metamodeling techniques are integrated with the optimization process in the framework as an option to solve the design case depending on the system complexity. Furthermore, two frequently appeared scenarios with changed design cases (change workspace or change the usage of the device) and 5 extend optimization problems (change on design variables, constraints or objectives) are illustrated in a framework with their corresponding solution sequences. Some situations can be solved using the existing knowledge as a post-processing activity. But some should be revised iteratively hence require interaction with the main optimization process.

The solution to one scenario listed in the proposed framework, i.e., changing the size of workspace, was verified by a simplified design case on a 6-DOF TAU haptic device. The initial design optimization task was to maximize the dexterous workspace and global isotropy index of the TAU haptic device, with singularity and

52 | CHAPTER 5. SUMMARY OF APPENDED PAPERS

required workspace as constraints. The two corresponding changed design optimization cases for the scenario were changing the range of constraint, and expand the range of design variables. The verification study showed that to use DOE as a first step in the design process can reduce the complexity of the design problem, and the proposed framework can handle a situation with changed workspace requirement. Furthermore, it is shown that the Pareto-front from initial design case, the correlation between design variables and response factors, and sample size as well as the most suitable metamodeling methods for metamodel construction can be reused in situated design cases or further development.

Paper E: efficient and situated design of haptic devices

Paper E extended the study presented in paper D with a further investigation of the situated design of high-performing haptic devices. The main focus of this paper was to address potential re-design scenarios that may occur and to efficiently solve these scenarios with maximum re-use of previously gained knowledge. The result from an analysis of the studied re-design cases, a generic process for situated design optimization is proposed.

A case that can be categorized as initial design of a 6-DOF TAU haptic device, planned to be used as a surgery training simulator was first studied as the basis for addressing and solving potential re-design scenarios. The initial design optimization task was to maximize the dexterous workspace and the global isotropy index of the device, with no singularities and the required minimum size of the workspace as constraints. Six possible trailing re-design cases were then identified, described and situatedly elaborated on from an optimization efficiency point of view. Based on these six re-design cases, three groups of optimization cases were identified, i.e., case which required adding criteria, removing criteria, and modifying existing criteria.

An analysis of the studied re-design optimization cases shows that the knowledge and information that enable re-design efficiency and situatedness are the effects of the design variables on the system response (the results from the DOE study), the ranges of the design variables, the Pareto-front, and the chosen metamodeling method. Three methods to solve the re-design scenarios efficiently were merged into the proposed framework. The first method: Re-design cases that can be satisfied using existing solutions from the initial design case, i.e., the new solutions can be directly filtered from the exiting Pareto-front. The second method: Re-design cases that require new criteria to be added, compared to the initial optimization case, with local or coupling variables, e.g., add inertia criteria, one of the MDO methods BLISS-2000 is recommended to solve the optimization case which can decouple the design problem and also allows parallel computation. The third method: Other re-design cases that require expansions of the design variables, a revision of the MBDO process is required based on the results of the initial DOE study.

CHAPTER 6. DISCUSSION, CONCLUSTION AND FUTURE WORK | 53

Chapter 6

Discussion, conclusion and future work

In this chapter, the research work presented in this thesis is first briefly discussed. The conclusions are structured based on the sequence of research questions formulated in chapter 1. An outline of recommended further research directions enabled by this research is listed at the end.

6.1 Discussion

Design of a high-performing haptic device is a multidisciplinary task that is quite complex due to its functional and performance multi-criteria requirements. The complexity becomes more critical due to the fuzziness of the design task caused by the soft requirements related to touch and “feel”, a large solution space, significant nonlinearities, and the need for real-time estimation and control. It would thus be beneficial to a situated design process that enables efficient and effective search for solutions in various design cases could be assisted and potentially also automated by a structured usage of different optimization methodologies and powerful computational techniques and tools.

In this thesis, we propose a methodology for situated and effective design optimization of high-performing haptic devices. A major pilot framework, with a potential to enable automation of design optimization in both the concept and detail design phases, was implemented and used to describe the required activities and information transformations within them in the entire design and optimization process. Three groups of re-design scenarios were identified based on different design situations that might occur after a pre-defined initial design case has been completed. The activities to perform those identified design situations were integrated into a generic re-design process that takes as much advantage as possible of knowledge created in the initial design process.

The proposed methodology integrates several discipline-/domain-specific models in the framework. The models could be selected and used depending on the size and level of detail required by the unique design task. Instead of using the traditional approach to only rely on equation-based models to assess the performance of the evolving system, geometry-centric models, i.e., CAD-based design models and dynamic models, with a realistic look and a more directly observable physical behavior are deemed to be more efficient, and they also facilitate multi-objective and multi-disciplinary communication. We have integrated the kinematic, geometric, flexible component, and dynamic system models in the framework. However, many other types of discipline-specific models,

54 | CHAPTER 6. DISCUSSION, CONCLUSTION AND FUTUREWORK

such as cost, energy consumption, and safety models, etc., could also be integrated into the framework.

A number of trailing re-design cases, i.e., design tasks that might be initiated later in time after an initial design task has been completed, were identified and situatedly elaborated on from an optimization efficiency point of view. In the study of the re-design cases, it was shown that reusing information and results from a previous design project can potentially reduce the lead-time of the new product significantly. The proposed situated framework is used for design cases with multi-objective optimization problems, and we rely on the Pareto-optimal approach and MDO methods to solve the actual optimization problems. In the Pareto optimal approach, in contrast to weighted optimization objectives, the designer and/or the team can perform trade-offs between different objectives after the optimization process, which means that it can postpone the decisions caused by uncertainties early in the process when there is a large knowledge gap, i.e., large uncertainties, and fuzziness. Methods that enable design decisions to be postponed add flexibility to the process. The metamodel of the system model can be optionally generated depending on the available computationally resources. Furthermore, it was shown that for a system with computational intensive analysis or simulations, metamodel usage could dramatically increase the efficiency of the process without sacrificing the accuracy of the solutions. Because a design optimization problem of haptic devices is usually not highly coupled compared the aerospace design cases and that the single-level MDO methods are easier to use compared to multi-level methods, we recommend using the single-level MDO methods, such as the MDF method, to solve a well-defined haptic device design optimization task. However, for the trailing situated design cases as defined here, the multilevel MDO methods, such as the BLISS-2000 method, are recommended to use, in order to make as much use as possible of the existing knowledge from a previously performed design project.

Some of the situated scenarios have not been properly verified yet. Furthermore, more complex re-design cases than the ones studied can, of course, be found, e.g., a combination of the re-design cases that have been identified and elaborated. The solutions to such complex of cases may depend on many other situations, which cannot be solved in a single activity. Hence, further analysis is needed to structure and solve more complex cases than those studied here.

6.2 Conclusions

The presented research is here concluded as answers to the research questions formulated in section 1.3, and future challenges that have been identified.

The main objective is decomposed into four interrelated research questions:

RQ1: How can we efficiently solve and interpret a multi-objective haptics design problem with computationally intensive and exhaustive simulations and analysis?

First of all, instead of a single “optimal” design that can be found with the traditional MOO method, the Pareto-front approach can represent all optimal solutions of all objectives as curves or surfaces, which enables reasoning on trade-offs between conflicting objectives in a following decision phase. This


means that uncertain decisions made early in the design process can be postponed, i.e., it adds flexibility to the design process. (Paper B). Furthermore, for a complex design case, especially for cases with coupling criteria, the multidisciplinary design optimization method can decouple the optimization problem and enable parallel analysis and optimization, and hence potentially increase the overall efficiency (paper B and paper E).

The metamodel-based design optimization (MBDO) method can potentially increase the efficiency and effectiveness of the optimization process. By using this method, there is an inverse relation between computational efficiency and result accuracy. A methodology to implement the MBDO method using the modified PEMF metamodel validation method, applicable for haptic devices, was proposed in Paper C. To take advantage of complementary engineering tools from different software vendors, a multi-tool framework has been used to integrate the proposed methodology and domain-specified tools including data transformation between different tools. (Paper C)

In the original MBDO process, the DOE method is used for generating sample data for metamodel construction. However, here DOE is used to study the effects of process factors and their interactions on system performance, which potentially can reduce the complexity of the problem. By performing a DOE study before the start of the MBDO process, brings more knowledge of the system, enables reduction of the number of design variables and their ranges, and hence improves the optimization efficiency. (Paper D)

A design optimization case with a 6-DOF TAU haptic device was used to compare the efficiency as well accuracy by using the full system model and the metamodels. As results, by using the suitable sample size and method for constructing metamodel of each objective, the total computational time was 27 times less compared to using the full system model, and the accuracy of the final optimal was larger than 95%. This study indicates that the MBDO method can efficiently and effectively be used for multi-objective design optimization of haptic devices. (Paper C)

RQ2: What are the most important discipline-specific models and tools to assist the model-based design of high-performing haptic devices and how to integrate them in the design and optimization process?

From published research on optimization of manipulators, robotic arms, and haptic devices, the four most commonly used models are kinematic models, geometric models, flexible component models, and dynamic system models. A framework has been proposed to integrate these four models into the design and optimization process of haptic devices (Paper B). In the framework, three levels of the Integration DEFinition language (IDEF0) diagrams have been used to describe the activities and information flow in the design and optimization process.

RQ3: What redesign scenarios may occur in re-design or development of haptic devices?

The early design and optimization phase for haptic devices are characterized by conflicting requirements with large uncertainties. With the increasing


knowledge gained in the design process, potential re-design scenarios are first categorized into three optimization specific groups: adding performance criteria, removing criteria, and modifying existing criteria. These groups can be further divided depending on optimization task, e.g., change of the design variables, constraints, and the objectives. (Paper D and Paper E)

RQ4: What knowledge gained in the optimization process of an initial design task can be potentially reused in other development scenarios, and how to efficiently use them in the optimization of the trailing re-design scenarios?

To avoid repletion of work and analyses, the knowledge gained in a performed design process should preferably be used to enable situated and efficient redesign. From studies made with situated design optimization cases on a 6-DOF haptic device (Paper D and Paper E), directly reusable knowledge and information are:

• the results from the DOE study, that is, the effects of design variables on system response,

• the ranges of the design variables,

• the Pareto-fronts,

• the created metamodels for the existing criteria.

Furthermore, the corresponding solving methods for the three groups of re-design scenarios were modeled and represented as a situated and generic process graph, including three distinct optimization groups, where each group of problems can be processed with one of the three identifies processes (in Paper E). The graph can be simplified into three methods:

• If the Pareto-optimal solutions for the initial design case satisfy a new re-design case, the new solutions can be directly filtered from the existing Pareto-front.

• If new criteria have to be added to the initial design optimization case and no changes of the shared design variables are made, the initial design optimization problem can be used as a subsystem level problem, and the entire problem can be solved with the BLISS-2000 method.

• For other cases, that require the design variable ranges to be expanded compared to the initial design case, the MBDO process must be re-executed. The new design variable ranges can be changed based on the results of the initial DOE study.

6.3 Future work

The work in this thesis can be extended in several ways as;

• Verify all re-design scenarios shown in the proposed generic re-design process graph shown in Figure 3.9.

• Identify and analyze how to efficiently address other potential re-design scenarios, which represent new, modified or aggregated situations.


• Consider and integrate more discipline-specific models into the proposed framework, such as control system model, cost model, safety model, power consumption model, etc.

• Study the design space and model refinement sub-process in the overall MBDO process, and search for a suitable implementation method for assisting efficient and effective design optimization of haptic devices.

• Generalize the findings to a wider range of devices and applications.


REFERENCES | 59

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