Multibody Dynamic Modeling for Optimal
Motions of Robotic and Biological Systems
- Research activities in the
Applied Dynamics and Optimization Lab
at NYU-Poly
Joo H. KIM, Ph.D.
Assistant Professor
Department of Mechanical and Aerospace Engineering
NYU-Poly
Brooklyn, NY
Joo H. Kim
RESEARCH AREAS
 Dynamics, Control, and Motion Generation
 Multibody Dynamic Modeling
 Optimization Theory and Applications
 Biomechanics, Bioengineering, and Biomimetics
Joo H. Kim
Robotic
Dynamics &
Control
Biomechanical
Engineering
Joo H. Kim
Modeling, Design, and Control
Robots,
Construction
machineries,
Mechanism
components,
Etc.
Mechanical Systems
Biological Systems
Humans,
Animals,
Insects,
Etc.
Principles of Motions and Structures
Joo H. Kim
RESEARCH AREAS
 Dynamics, Control, and Motion Generation
 Multibody Dynamic Modeling
 Optimization Theory and Applications
 Biomechanics, Bioengineering, and Biomimetics
Joo H. Kim
RESEARCH AREAS
 Dynamics, Control, and Motion Generation


left foot
- Manipulation and locomotion
- Comprehensive dynamic model
Multibody
Dynamic
- Load-effective
motions forModeling
large payload
- Alternative criteria for design and control
- Efficient formulation of dynamic balance
- Dynamic environments
withand
uncertainties
Optimization
Theory
Applications
ZMP
tipping moments are zero
0.25
Foot support region
0.2
Left foot
 Biomechanics, Bioengineering, and Biomimetics
0.15
right foot
x0 (lateral)
0.1
0.05
t = 0.0
0
Dynamic Balance
-0.05
-0.1
-0.15
Right foot
-0.2
t = 2.0
-0.25
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
z0 (fore-aft)
0.8
ZMP trajectory during pulling
Joo H. Kim
t=0
q3
t = 0.6
t = 2.0 (s)
Pulling Force
1N
t=0
q1
t = 1.4
t = 0.6
t = 1.4
t = 2.0 (s)
q2
10000 N
Pulling Force
Load-effective motions of a manipulator
Initial Posture
Foot Stride
Foot Contact
Execution
Release Point
Follow-through
A Numerical result of motion planning for overarm throw
Humanoid motion planning and control
Input:
Throwing Distance 35 m
Object mass 0.45 kg
Joo H. Kim
RESEARCH AREAS
 Dynamics, Control, and Motion Generation
 Multibody Dynamic Modeling
 Optimization Theory and Applications
 Biomechanics, Bioengineering, and Biomimetics
Joo H. Kim
Tangential
contact force
Normal
contact force
Fj
RESEARCH AREAS
Fj
Mj
F1
 Dynamics, Control, and Motion Generation
-Rs
-M
Welding surface
-Rn
Rt
-Rt
Rn
M
Rs
Prediction of external reactions
 Multibody Dynamic Modeling
- Algorithms for internal reactions
Mj
- Prediction of external reactions
F1
Optimization
and Applications
- Ground reactionTheory
forces
- Human injury prediction and prevention
- Stability analysis
Fictitious Joints
Modeling
of
contact
and
impact
Biomechanics, Bioengineering, and Biomimetics


Left foot contact
1000
SS
900
Normal GRFs (N)
W
N1
N2
Fj
q4 q5
Fj
DS2
q4
Left foot
700
600
F1
q1
q2
Mj
q3
500
400
300
200
R2
Fj
Release
800
R1
Fj
Right foot
100
0
0.07
0.17
0.27
0.37
0.47
Time (s)
0.57
Method of fictitious joints for internal reactions
Ground reaction forces
Joo H. Kim
RESEARCH AREAS
 Dynamics, Control, and Motion Generation
 Multibody Dynamic Modeling
 Optimization Theory and Applications
 Biomechanics, Bioengineering, and Biomimetics
Joo H. Kim
RESEARCH AREAS
 Dynamics, Control,
 Multibody Dynamic Modeling
Optimal lifting motion
 Optimization Theory and Applications

- Optimal motion planning
Development of efficient optimizer (source: MATLAB
- Efficient algorithm for real-time simulation
- Advanced methodsBioengineering,
of numerical optimization
Biomechanics,
and Biomimetics
- Interaction between optimization modules and dynamics simulation
®)
Joo H. Kim
RESEARCH AREAS
 Dynamics, Control, and Motion Generation
 Multibody Dynamic Modeling
 Optimization Theory and Applications
 Biomechanics, Bioengineering, and Biomimetics
Joo H. Kim
RESEARCH AREAS
 Dynamics, Control, and Motion Generation
 Multibody Dynamic Modeling
Human modeling
series elastic
component
contractile
component
F and Applications
F
 Optimization Theory
Injury analysis
parallel elastic component
Bio-sensors and bio-actuators
Motion capture camera systems
 Biomechanics, Bioengineering, and Biomimetics
-
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
Biomechanical analysis
Joo H. Kim
 Potential Applications in Medical and Dental Fields
- Orthopedic biomechanics
- Robotic surgery
- Rehabilitation
- Injury
- Prosthetic design
- Sports performance evaluation
Normal and shear forces at spine
Sports
Prosthesis Development
Shoulder kinematic modeling
Joo H. Kim
RESEARCH AREAS
 Dynamics, Control, and Motion Generation
 Multibody Dynamic Modeling
 Optimization Theory and Applications
 Biomechanics, Bioengineering, and Biomimetics
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
Technical Challenges
Softball pitching
Football throwing
Kid’s throwing
Hammer throwing
Boomerang throwing
Different ways of throwing
Baseball pitching
Grenade throwing
Disc throwing
Shot put
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)
Joo H. Kim
Problem Definition
Input
Target location
Object mass
t = tinitial
t = trelease
Follow-through
Throwing Execution
DS1
(left foot
leading)
Left foot lift
SS
(right foot)
t = tfinal
Output
Motion (joint profiles)
Actuator torques
ZMP
Ground reaction force
Release position
Release speed
Release angle
Object flight time
DS2
(left foot leading)
Left foot strike
Joo H. Kim
Multibody Dynamic Modeling
Denavit-Hartenburg representation
q3
q1
q2
4x4 Homogeneous Transformation
Lie group: SE(3)
Joint variable B-spline functions
nc
q j (u)   Ni ,3 (u) Pi , j
i 1
t
0
 u  t f ; j  1,..., DOF 
Comprehensive dynamic model  General manipulation tasks
 Fk 
τ = M(q) q + V(q,q)   J mi g   J 
 T(q,q)

i
k
actuator
M k  stiffness &
mass-inertia
Coriolis &
T
i
centrifugal
gravity
T
k
external load
dissipative
Joo H. Kim
Dynamic Balance - Legged robotic and human mechanisms
Zero-Moment Point (ZMP)
 balance criterion
 physical consistency under unilateral constraints
left foot
ZMP
tipping moments are zero
right foot
Dynamic Balance
Simulation environment  GRFs not measured
Joo H. Kim
Optimal Motion Planning
• Find joint control points
• To minimize energy consumption
t final
n
E  τ (t )   initial  ( i (t )) 2 dt
2
t
i 1
• Subject to constraints:
– Joint variable limits
– Actuator torque limits
– Task-based constraints
Joo H. Kim
 Control variables
Optimization
 Constraints
• Joint B-spline control points
• Object flight time Tflight
•
•
•
•
•
•
•
•
•
•
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)
MR
FR
Dynamics with GRFs:
Joint actuator torques
FL
DS ZMP
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
MR
ML
FR
SS ZMP
Joo H. Kim
Numerical Results – Overarm Throw
Input: Throwing Distance 35 m
Object mass 0.45 kg
Joo H. Kim
Numerical Results – Overarm Throw
Input: Throwing Distance 35 m
Object mass 0.45 kg
Initial Posture
80
Foot Stride
Foot Contact
Execution
Release Point
Follow-through
Shoulder flexion/extension
Actuator Torques (Nm)
60
40
20
Elbow flexion/extension
Wrist flexion/extension
0
0
0.1
0.2
0.3
0.4
0.5
0.6
-20
-40
Shoulder
abduction/adduction Shoulder axial rotation
0.7
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)
Time (s)
Joo H. Kim
Numerical Results – Overarm Throw
Input: Throwing Distance 35 m
Object mass 0.45 kg
Left foot
Foot support region
0.25
Left foot contact
t = 0.513
1000
0.2
Normal GRFs (N)
x0 (lateral)
0.05
0
Right foot
-0.1
t = 0.42
Left foot
700
600
500
400
300
200
-0.15
Right foot
100
-0.2
-0.25
DS2
800
0.1
-0.05
SS
900
t = 0.607
(Release)
0.15
Release
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
z0 (fore-aft)
ZMP trajectory during throwing
0.07
0.17
0.27
0.37
0.47
0.57
Time (s)
Ground reaction forces
Joo H. Kim
Numerical Results – Overarm Throw
Input: Throwing Distance 25 m (shorter)
Object mass 0.45 kg
vs
Input: Throwing Distance 45 m (longer)
Object mass 0.45 kg
Joo H. Kim
Numerical Results – Overarm Throw
25 m
Initial Posture
Foot Stride
Foot Contact
Initial Posture
Foot Stride
Foot Contact
Execution
Release Point
Follow-through
45 m
Execution
Release Point
Follow-through
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)
Joo H. Kim
RESEARCH AREAS
 Dynamics, Control, and Motion Generation
 Multibody Dynamic Modeling
 Optimization Theory and Applications
 Biomechanics, Bioengineering, and Biomimetics
Thank you.
Questions?
Joo H. Kim