Multibody Dynamic Modeling for Optimal Motions of Robotic and Biological Systems

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14 Νοε 2013 (πριν από 3 χρόνια και 7 μήνες)

209 εμφανίσεις

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

mass-inertia
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?