1 Final Conference, 19th – 23rd January 2015 Geneva, Switzerland RP 15 Force estimation based on...

1Final Conference, 19th – 23rd January 2015Geneva, Switzerland

RP 15

Force estimation based on proprioceptive sensors for teleoperation in radioactive

environments

Project: 6th June 2011-1st June 2014

Enrique del Sol / Oxford Technologies Ltd.Supervisor: Robin Scott


Background Information

• ESR: Enrique del Sol Acero• Supervisor: Robin Scott• Host institution: Oxford Technologies Ltd.

• University: Universidad Politécnica de Madrid• PhD Supervisor: Manuel Ferre


Contents

1. Aim and Overview

2. Force estimation

3. Closed Loop Simulation

4. Conclusion and additional remarks


Industrial Robot. No backdrivable in general.

Haptic master kinematically dissimilar to the slave

Commanding position

Receiving force feedback based on proprioceptive sensors

Radioactive area. No electronics allowed.

No force sensors due radiation and cost.

Teleoperation of an industrial robot

DEXTER 20 © Oxford Technologies Ltd

1. Aim and Overview


kpm

kps

ke

ep

fh

fm

ep Xs

fe

fs

-

+

+

-

-

+

+

-Xm=Xh

Introduction: Position-Position teleoperation


kf

kps

ke

fh

fm Xm=Xh

ep

fe

fs+

-

-

+

+

-

6 dof Force \ Torque sensor

Introduction: Force-Position teleoperation

Robot model

𝒇=𝝋 (𝑰𝒏𝒑𝒖𝒕 ,𝑺𝒕𝒂𝒕𝒆)


PP VS FP teleoperation

Position – Position

1. Requires positional error to produce the force feedback.

2. Drag effect is produced on the master when moves in free space since appears a positional error with respect the slave.

3. It does not require any force sensor

4. It is very stable and it is very well known

5. It cannot work with non-backdrivable slaves.

Force – Position

1. It does not requires positional error. The force feedback is produced by measuring directly the environmental force or estimating this force.

2. No drag effect is produced.

3. It typically requires a force sensor which are very costly devices (

4. Less stable than Position-Position

5. It can work with non-backdrivable slaves


1. Aim and Overview

2. Force estimation




τm=H (q ) ∙ q +C (q , ˙ q ) · ˙ q +τg (q )+τ f ( ˙ q )+τext

• The starting point is the robotics dynamics equation:

: denotes the vector of motor torques exerted in each joint.H: is the robot inertia matrix.C: is the Coriolis forces vector.: is the gravity forces vector.: is the friction torques vector.: is the external torques vector on each joint produced by the external forces on the end-effector.

• The external forces can be estimated by applying the kinematic information contained in the robot Jacobian, obtaining (2):

(1)

Text= JT† · (τm−H (q ) ∙ q −C (q , ˙ q ) · ˙ q −τg (q )− τf ( ˙ q ) ) (2)

: denotes the vector of forces and torques exerted in the robot end-effector and expressed in the base coordinates system.J: is the robot Jacobian, with † denoting the matrix inverse (or pseudo-inverse when corresponds).

Force estimation: Robotics dynamics equation

Force estimation: Robotics dynamics equation II

Motor torque: 𝜏𝑒=𝐾𝑒 𝑅𝑀𝑆 ∙ 𝑖𝑎𝑅𝑀𝑆

Brushless AC motors 𝑖𝑠

(3)

For hydraulic actuators based on servo valves:

(4)

Friction torque: (5)• A joint is moved at a constant speed and the

average torque is measured. For characterization purposes the friction had to be expressed in a more linear way.

H (q ) ∙ q +C (q , ˙ q ) · ˙ q+ τg (q )Dynamic terms:

A great number of manipulators present a closed loop

j1

j33

2

j2

j4

j32

1

34

5

6 7 8j6j5

j3

3b

3c

67 8

2

3

5

4

1

chord

nodes

arcs

• Defining a spanning tree of the main graph

• Any algorithm like Newton-Euler can be applied to the spanning tree.

𝜏 𝑦=𝐺𝑇 ∙𝜏 𝑡𝑟𝑒𝑒


Force estimation: Parameters identification

Preliminary identification experiments are needed.

Robot in motion Only the robot dynamic coefficients

can be identified (not all the links parameters)

In order to use the model, one needs to know the values of the robot dynamic properties such as: link masses, inertias, centre of gravity of each link, etc.

Robot manufacturers provide at most only a few principal dynamic parameters ( e.g., link masses)

Estimates can be found with CAD tools (e.g. assuming uniform density) but they might not provide enough accuracy for some circumstances.

A p

riori

kn

ow

led

ge

Kinematic and geometric information

Modelling

Trajectory parameterization

Robot excitation

Position differentiation

Parameter identification by LMS

Parameter optimization

Rob

ot

iden

tifi

cati

on

pro

ced

ure

Valid

ati

on

Validate model

Satisfactory model?

Not satisfactory

Model specification


3 Different approaches tested

Force estimation: 3 approaches

Direct evaluation of robotics dynamics equation

τm=H (q ) ∙ q +C (q , ˙ q ) · ˙ q +τg (q )+τ f ( ˙ q )+τext

Conventional State observers

]

Conventional + Sliding observers

]


Force estimation: Experimental setup

PC Running LabView 2011

NI-PXI, running slave control

NI-PXI running master control and force estimation algorithm

Kraft GRIPS Hydraulic manipulator


Force estimation: Direct evaluation of robotics dynamics equation

Issues found:

• Errors due position differentiation to obtain speed and acceleration.

Conventional velocity calculation VS Savitzky-Golay filter order 2 with 10 elements

Conventional velocity calculation VS Savitzky-Golay filter order 2 with 51 elements• Estimation problems due model unnacuracies


Force estimation: Conventional observers

u=H (q ) q +C (q , ˙ q ) ˙ q+τg (q )+τf ( ˙ q )+τextDynamic model of the robot with external forces:

Robot space state equations: = H ]

]Robot space state observer:

Robot observer error:

Differentiating the observer error and grouping terms

∅ 4~��1+∅ 3

~x1+∅ 1

~x1=τext0 0

∅ 1~x1=τext

The external torque turns out being proportional to the positional error.

Error dynamics


0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 104

-20

-10

0

10

20

30

40

50

60Force on X direction

Observed Force X

Measured Force X

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 104

0

50

100

150

200

250

Force on Z direction

Observed Force Z

Measured Force Z

• The force estimation with Luenberger (traditional) observers presents steady state errors due the model errors.

Results with conventional observers


Force estimation: Sliding observers

u=H (q ) q +C (q , ˙ q ) ˙ q+τg (q )+τf ( ˙ q )+τextDynamic model of the robot with external forces:

Robot space state equations: = H ]

]Robot space state sliding observer:

Robot observer error:

Differentiating the observer error and grouping terms

∅ 4~��1+∅ 3

~x1+∅ 2𝑠𝑔𝑛(~x1)+∅ 1

~x1+∅ 0𝑠𝑔𝑛(~x1)=τextτ ext=K2~x1+K4 𝑠𝑔𝑛(~x1)0 0

The external torque turns out being the sum of K2 times the positional error and K4 times the sign of the error

0


Force estimation: Force estimation with sliding observers

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 104

0

50

100

150

200

250


Observed Force Z

Measured Force Z

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 104

0

50

100

150

200

250


Observed Force Z

Measured Force Z

Luenberger + Sliding observer

Luenberger observer

The force estimation adding sliding gains improves greatly, moreover during the steady state where the estimation error is now very small even in presence of modelling errors.

12% error


Video: Force estimation with sliding observers


1. Aim and Overview

2. Force estimation




0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-50

0

50

100

150

200

250

300Torques on joint 2

Reaction Torque in PP

Reaction Torque in FP

Environmental Torque

PP VS model based FP teleoperation

• The performance of the PP algorithm depends on the control.

• The performance of FP depends on the observer gains.

• In steady state zeros error is reached with Sliding observers.


1. Aim and Overview

2. Force estimation




• A new method of robust force estimation based on sliding observers has been developed to be used on teleoperation.

• A dissimilar kinematic problem has been solved in order to teleoperate dissimilar master-slave.

• This method does not require a priori any filtering and thus, it produces zero delay.

• Forces at tip can be estimated with a minimum accuracy of 12%.

• It has been tested under a simulator for comparing control methods developed in Simulink.

• It also has been tested under real circumstances.

• A dynamic model of a parallelogram robot has been created.

• It has been developed a methodology for identifying the parameters of such parallelogram robot.

Conclusions and remarks


Conclusions and remarks

PURESAFE RP interactions:

• Interaction with RP 8 on robot modelling, Interaction with RP 11 on assistive teleoperation with augmented reality

• Interaction with UPM researchers

Goals accomplished?

• Succesful results with oportunities of extending the research in OTL.• Impact: 2 conferences, 1 journal already published, 1 journal expected

Future research lines:

• Applying this method closing the loop on a real scenario


Questions?

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1 Final Conference, 19th – 23rd January 2015 Geneva, Switzerland RP 15 Force estimation based on...

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