Joo H. Kim

Multibody Dynamic Modeling for Optimal Motions of Robotic and Biological Systems

Joo H. KIM, Ph.D.Assistant Professor

Department of Mechanical and Aerospace Engineering

NYU-Poly

Brooklyn, NY

- Research activities in the

Applied Dynamics and Optimization Lab

at NYU-Poly

Joo H. Kim

Dynamics, Control, and Motion Generation

Multibody Dynamic Modeling

Optimization Theory and Applications

Biomechanics, Bioengineering, and Biomimetics

RESEARCH AREAS

Joo H. Kim

Robotic Dynamics & Control

Biomechanical Engineering

Joo H. Kim

Mechanical Systems Biological Systems

Modeling, Design, and Control

Principles of Motions and Structures

Robots, Construction machineries,Mechanism components,Etc.

Humans,Animals,Insects,Etc.

Joo H. Kim

Dynamics, Control, and Motion Generation

Multibody Dynamic Modeling

Optimization Theory and Applications

Biomechanics, Bioengineering, and Biomimetics

RESEARCH AREAS

Joo H. Kim

Dynamics, Control, and Motion Generation

Multibody Dynamic Modeling

Optimization Theory and Applications

Biomechanics, Bioengineering, and Biomimetics

RESEARCH AREAS

- Manipulation and locomotion- Comprehensive dynamic model- Load-effective motions for large payload - Alternative criteria for design and control - Efficient formulation of dynamic balance - Dynamic environments with uncertainties

right foot

left foot

ZMPtipping moments are zero

Dynamic Balance

ZMP trajectory during pulling-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

z0 (fore-aft)

Left foot

x0(la

tera

l)

Right foot

Foot support region

t = 0.0

t = 2.0

Joo H. Kim

q1

q3

q2

q1

q3

q2

Pulling Force

t = 0 t = 0.6 t = 1.4 t = 2.0 (s)

Pulling Force

t = 0 t = 0.6 t = 1.4 t = 2.0 (s)

1 N

10000 N

Load-effective motions of a manipulator

Humanoid motion planning and control

Release Point Follow-throughFoot ContactInitial Posture Foot Stride Execution

A Numerical result of motion planning for overarm throw

Input: Throwing Distance 35 mObject mass 0.45 kg

Joo H. Kim

Dynamics, Control, and Motion Generation

Multibody Dynamic Modeling

Optimization Theory and Applications

Biomechanics, Bioengineering, and Biomimetics

RESEARCH AREAS

Joo H. Kim

Dynamics, Control, and Motion Generation

Multibody Dynamic Modeling

Optimization Theory and Applications

Biomechanics, Bioengineering, and Biomimetics

RESEARCH AREAS

- Algorithms for internal reactions - Prediction of external reactions- Ground reaction forces- Human injury prediction and prevention- Stability analysis- Modeling of contact and impact

F1Mj

Fj

Fj

F1Mj

Fj

Fj

M

Rn

Rs

Rt

-M-Rs

-Rt

-Rn

M

Rn

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F1Mj

Fj

Fj

F1Mj

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-Rt

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-Rt

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-M-Rs

-Rt

-Rn

Method of fictitious joints for internal reactions

F1Mj

Fj

Fj

F1Mj

Fj

Fj

F1

Fj

Mj

Fj

Fictitious Joints

q1 q2 q3

q4

q4

q5

F1

Fj

Mj

Fj

Fictitious Joints

q1 q2 q3

q4

q4

q5

F1Mj

Fj

Fj

F1Mj

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F1

Fj

Mj

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Fictitious Joints

q1 q2 q3

q4

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q5

F1

Fj

Mj

Fj

Fictitious Joints

q1 q2 q3

q4

q4

q5

SS DS2

ReleaseLeft foot contact

0

100

200

300

400

500

600

700

800

900

1000

0.07 0.17 0.27 0.37 0.47 0.57

Nor

mal

GRF

s (N

)

Time (s)

Right foot

Left foot

Ground reaction forces

Prediction of external reactions

Normal contact force

Tangential contact force

Welding surface

Normal contact force

Tangential contact force

Welding surface

N1 N2

R1 R2

W

N1 N2

R1 R2

W

N1 N2

R1 R2

W

Joo H. Kim

Dynamics, Control, and Motion Generation

Multibody Dynamic Modeling

Optimization Theory and Applications

Biomechanics, Bioengineering, and Biomimetics

RESEARCH AREAS

Joo H. Kim

Development of efficient optimizer (source: MATLAB®)

Dynamics, Control,

Multibody Dynamic Modeling

Optimization Theory and Applications

Biomechanics, Bioengineering, and Biomimetics

RESEARCH AREAS

- Optimal motion planning- Efficient algorithm for real-time simulation- Advanced methods of numerical optimization- Interaction between optimization modules and dynamics simulation

Optimal lifting motion

Joo H. Kim

Dynamics, Control, and Motion Generation

Multibody Dynamic Modeling

Optimization Theory and Applications

Biomechanics, Bioengineering, and Biomimetics

RESEARCH AREAS

Joo H. Kim

Dynamics, Control, and Motion Generation

Multibody Dynamic Modeling

Optimization Theory and Applications

Biomechanics, Bioengineering, and Biomimetics

RESEARCH AREAS

- Musculoskeletal biomechanics and human modeling- Stability analysis of human knee using inertial measurement- Prediction and analysis of energy consumption - Motion capture experiments and analysis- Modeling of joint stiffness and damping

Injury analysis

Rn

-M

M

Rs

-Rs-Rt

Rt

-Rn

Rn

-M

M

Rs

-Rs-Rt

Rt

-Rn

Human modeling contractile component

series elasticcomponent

parallel elastic component

FF

contractile component

series elasticcomponent

parallel elastic component

FF

Bio-sensors and bio-actuators

Biomechanical analysis

Motion capture camera systems

Joo H. Kim

Shoulder kinematic modeling

Normal and shear forces at spine

Potential Applications in Medical and Dental Fields- Orthopedic biomechanics- Robotic surgery- Rehabilitation- Injury- Prosthetic design- Sports performance evaluation

Prosthesis Development

Sports

Joo H. Kim

Dynamics, Control, and Motion Generation

Multibody Dynamic Modeling

Optimization Theory and Applications

Biomechanics, Bioengineering, and Biomimetics

RESEARCH AREAS

Thank you.

Questions?

Joo H. Kim

More time?5 more mins?

Joo H. Kim

Example formulation and results: motion generation of overarm throw

Joo H. Kim

Hammer throwing

Disc throwing

Boomerang throwing

Kid’s throwing

Football throwing

Shot putBaseball pitching

Softball pitching

Different ways of throwing

Technical Challenges

Challenges in modeling throwing motion: Highly redundant (numerous ways of throwing) Highly nonlinear (coupled velocity, position, and time) High speed (highly dependent on dynamic parameters)

Grenade throwing

Joo H. Kim

Problem Definition

Follow-throughThrowing Execution

DS1(left foot leading)

SS(right foot)

DS2(left foot leading)

t = tinitial t = tfinalt = trelease

Left foot lift Left foot strike

Input

Target location

Object mass

Output

Motion (joint profiles)

Actuator torques

ZMP

Ground reaction force

Release position

Release speed

Release angle

Object flight time

Joo H. Kim

q1

q3

q2

q1

q3

q2

Multibody Dynamic Modeling

Joint variable B-spline functions

Denavit-Hartenburg representation

mass-inertia Coriolis & stiffness &

centrifugal dissipativegravity external load

kT Ti i k

i kactuator k

m

F

τ = M(q) q +V(q,q) J g J T(q,q)M

Comprehensive dynamic model General manipulation tasks

4x4 Homogeneous TransformationLie group: SE(3)

,3 , 01

( ) ( ) ; 1,...,nc

j i i j fi

q u N u P t u t j DOF

Joo H. Kim

Zero-Moment Point (ZMP) balance criterion physical consistency under unilateral constraints

Simulation environment GRFs not measured

Dynamic Balance - Legged robotic and human mechanisms

right foot

left foot

ZMPtipping moments are zero

Dynamic Balance

Joo H. Kim

• Find joint control points• To minimize energy consumption

• Subject to constraints:– Joint variable limits

– Actuator torque limits

– Task-based constraints

Optimal Motion Planning

2 2

1

( ) ( ( ))final

initial

nt

iti

E t t dt

τ

Joo H. Kim

Optimization Constraints

• Joint variable limits• Actuator torque limits• Ground penetration• Dynamic balance (ZMP)• Time-boundary conditions• Feet positions/orientations• Monotonic hand path• Projectile equation• Hand release orientation• Target within visual field

flightT

Control variables

• Joint B-spline control points• Object flight time

Updated system configuration at current time instant

Dynamics without GRFs: Global-DOF generalized torques

Calculation of resultant reaction loads for throwing

ZMP locationGRFs distribution (DS/SS)

DS ZMP

RF

RMLF LM RF

RM

SS ZMPDynamics with GRFs:Joint actuator torques

Joo H. Kim

Numerical Results – Overarm ThrowInput: Throwing Distance 35 m Object mass 0.45 kg

Joo H. Kim

Input: Throwing Distance 35 m Object mass 0.45 kg

Release Point Follow-throughFoot ContactInitial Posture Foot Stride Execution

Flight time 2.231 (s)

Release hand velocity (0.170 10.595 15.526) (m/s)

Release speed 18.797 (m/s)

Release velocity angle from horizon 34.308 (deg)

Release hand position (-0.379 1.772 0.354) (m)Shoulderabduction/adduction

Elbow flexion/extensionWrist flexion/extension

Shoulder axial rotation

Shoulder flexion/extension

-40

-20

0

20

40

60

80

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7Act

uato

r To

rque

s (N

m)

Time (s)

Numerical Results – Overarm Throw

Joo H. Kim

Input: Throwing Distance 35 m Object mass 0.45 kg

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

z0 (fore-aft)

x0(la

tera

l)

Left foot

Right foot

t = 0.513

t = 0.42

Foot support region

t = 0.607(Release)

SS DS2

ReleaseLeft foot contact

0

100

200

300

400

500

600

700

800

900

1000

0.07 0.17 0.27 0.37 0.47 0.57

Nor

mal

GRF

s (N

)

Time (s)

Right foot

Left foot

ZMP trajectory during throwingGround reaction forces

Numerical Results – Overarm Throw

Joo H. Kim

Input: Throwing Distance 25 m (shorter) Object mass 0.45 kg

Input: Throwing Distance 45 m (longer) Object mass 0.45 kgvs

Numerical Results – Overarm Throw

Joo H. Kim

25 m

Release Point Follow-throughFoot ContactInitial Posture Foot Stride Execution

Release Point Follow-throughFoot ContactInitial Posture Foot Stride Execution

45 m

25 (m) throw 45 (m) throw

Flight time (s) 1.860 2.596

Release hand velocity (m/s) (0.265 8.775 13.179) (0.088 12.382 17.261)

Release speed (m/s) 15.835 21.243

Release velocity angle from horizon (deg) 33.652 35.653

Release hand position (m) (-0.492 1.641 0.487) (-0.227 1.891 0.198)

Numerical Results – Overarm Throw

Joo H. Kim

Dynamics, Control, and Motion Generation

Multibody Dynamic Modeling

Optimization Theory and Applications

Biomechanics, Bioengineering, and Biomimetics

RESEARCH AREAS

Thank you.

Questions?