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
ZMP
tipping 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
z
0
(fore

aft)
Left foot
x
0
(lateral)
Right foot
Foot support region
t
= 0.0
t
= 2.0
Joo
H. Kim
q
1
q
3
q
2
q
1
q
3
q
2
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

through
Foot
Contact
Initial Posture
Foot Stride
Execution
A Numerical result of motion planning for
overarm
throw
Input:
Throwing Distance 35 m
Object 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
F
1
M
j
F
j
F
j
F
1
M
j
F
j
F
j
M
R
n
R
s
R
t

M

R
s

R
t

R
n
M
R
n
R
s
R
t
R
n
R
s
R
t

M

R
s

R
t

R
n

M

R
s

R
t

R
n

M

R
s

R
t

R
n
F
1
M
j
F
j
F
j
F
1
M
j
F
j
F
j
M
R
n
R
s
R
t

M

R
s

R
t

R
n
M
R
n
R
s
R
t
R
n
R
s
R
t

M

R
s

R
t

R
n

M

R
s

R
t

R
n

M

R
s

R
t

R
n
Method of fictitious joints for internal reactions
F
1
M
j
F
j
F
j
F
1
M
j
F
j
F
j
F
1
F
j
M
j
F
j
Fictitious Joints
q
1
q
2
q
3
q
4
q
4
q
5
F
1
F
j
M
j
F
j
Fictitious Joints
q
1
q
2
q
3
q
4
q
4
q
5
F
1
M
j
F
j
F
j
F
1
M
j
F
j
F
j
F
1
F
j
M
j
F
j
Fictitious Joints
q
1
q
2
q
3
q
4
q
4
q
5
F
1
F
j
M
j
F
j
Fictitious Joints
q
1
q
2
q
3
q
4
q
4
q
5
SS
DS2
Release
Left 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
Normal GRFs (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
N
1
N
2
R
1
R
2
W
N
1
N
2
R
1
R
2
W
N
1
N
2
R
1
R
2
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
Human modeling
contractile
component
series elastic
component
parallel elastic component
F
F
contractile
component
series elastic
component
parallel elastic component
F
F
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 put
Baseball 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

through
Throwing Execution
DS1
(left foot
leading)
SS
(right foot)
DS2
(left foot leading)
t
=
t
initial
t
=
t
final
t
=
t
release
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
q
1
q
3
q
2
q
1
q
3
q
2
Multibody Dynamic Modeling
Joint variable B

spline functions
Denavit

Hartenburg representation
massinertia
Coriolis & stiffness &
centrifugal dissipative
gravity
external load
k
T T
i i k
i k
actuator
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 Transformation
Lie group: SE(3)
,3,0
1
( ) ( ) ; 1,...,
nc
j i i j f
i
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
ZMP
tipping 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
n
t
i
t
i
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
flight
T
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 location
GRFs distribution (DS/SS)
DS ZMP
R
F
R
M
L
F
L
M
R
F
R
M
SS ZMP
Dynamics with GRFs:
Joint actuator torques
Joo
H. Kim
Numerical Results
–
Overarm Throw
Input: 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

through
Foot
Contact
Initial 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)
Shoulder
abduction/adduction
Elbow flexion/extension
Wrist 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
0.7
Actuator Torques (Nm)
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
z
0
(fore

aft)
x
0
(lateral)
Left foot
Right foot
t
=
0.513
t
=
0.42
Foot support region
t
=
0.607
(Release)
SS
DS2
Release
Left 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
Normal GRFs (N)
Time (s)
Right foot
Left foot
ZMP trajectory during throwing
Ground 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 kg
vs
Numerical Results
–
Overarm Throw
Joo
H. Kim
25 m
Release Point
Follow

through
Foot
Contact
Initial Posture
Foot Stride
Execution
Release Point
Follow

through
Foot
Contact
Initial 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?
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