Transcript What is a simulation?

Physics-based Simulation in
Sports and Character Animation
Kuangyou Bruce Cheng (鄭匡佑)
Institute of Physical Education, Health, & Leisure Studies
National Cheng Kung University, Tainan, Taiwan
Outline:
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Introduction to simulation
Previous and current research topics
Summary of methods and results
Discussion and Conclusions
Additional topics
What is a simulation?
• Reproduce a real event with a different
(usually simplified) approach
• For example, free-fall bodies; multi-segment
rigid body systems
• Generation of equations of motion (based on
physics laws)
• Numerical solution of ODE/PDE
• Advantages: lower cost, no risks, repeatable
and no human-related error factors
Previous research topics
• Jumping from a compliant surface
(application to springboard diving jumps)
• Standing vertical jump (effect of joint
strengthening and effect of arm motion)
• Standing long jump (effect of different
starting posture and additional weight)
• Optimal flight trajectories of the shot-put
and discus
Current research topics
• Multi-stage simulation and optimization of
jumping (swim start, standing long jump,
ski jump, vaulting)
• Biomechanical analysis of Tai Chi Pushhand
• Muscle/joint onset sequence in fast reaching
movements
• Physics-based movement simulation of
animated characters
Forward and Inverse Dynamics
• F = ma
• From the driving forces/torques, what are
the resulting motions?
• From the observed motions, what are the
driving forces/torques?
Motivations for doing forward simulation
• The best control strategies for many human
movements are not clear
• Real subjects’ performance may be affected
by practice and psychological factors
• Computer simulation with optimization
serves as a promising tool
• Very few studies considered multi-stage
simulation and optimization
Summary of previous researches
Discus Flight
Optimization problem formulation:
Goal: Maximize flight distance by optimizing the
initial release angle and two orientation angles (with
fixed release speed and height).
Objective function: Flight distance can be calculated
by numerically solving ODE’s with known
equations of motion and initial conditions.
Simple model of springboard jumping
md
x2
T
a
Massless leg
(length = 2a)
θ
Straight leg at
θ = 180 deg
a
mb
x1
k
g
• Instantaneous joint torque T(t) depends on
maximum isometric torque Tmax and 3 variables:
Angle dependence
Angular velocity dependence
(according to Hill’s muscle model)
1.5
1
1
f(θ)
θ
Knee torque activation level: A(t)
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Resultant effect of related muscle activation
Inputs to actuate the model
Node points representation
A(t) ranges from -1 (full-effort flexion) to +1
(full-effort extension)
• Time constant approximated from rise and
decay time constants for muscle activation
Multi-segment 2-D models (Equations
of motion derived by Autolev)
Trunk &
head
Arms
Thigh
Shank
Feet
Springboard
Torque generators at ankle, knee, hip, and shoulder (5-segment)
Optimization problem formulation:
Goal: Maximize jump height by optimizing joint
activation nodal values during contact.
Objective function: J = y + v2/2g, where y and v are
COM vertical position and velocity at takeoff.
Optimization Implementation:
• Parameter optimization: node points are to
be optimized (since they represent joint
torque activation level)
• Algorithm: Downhill Simplex method (with
different initial guesses for more reliable
optimal solution)
Results overview:
• General agreement between optimal
simulated and measured motions
• Coordination strategies (joint torque
activation patterns) different from those in
rigid-surface jumping
• Predicted optimal fulcrum setting (board
stiffness) is in agreement with experiment
Results overview (continued):
• Kinematic and coordination characteristics
in jumps maximizing somersault rotations
differ from those in pure jumping
• Arm motion has significant effect on
generating more angular momentum
Results of discus flight:
Right: Optimal initial conditions
Left: Effect of wind
Results from simple model:
Simulated optimal jumps with constraint θ ≥ 90 deg (S90), and measured
jumps; board tip (―) and diver c.m. (x) position vs. time
Optimal simulated springboard jumping
(4-segment model)
Stick figure animation plotted using MATLAB
Comparison of simulated and measured jumps
Simulated joint torque (―) and joint activation level (x).
Joint torque is normalized by dividing its value by
maximum isometric torque.
Jump height vs. fulcrum setting
Jumping for maximizing backward
somersault rotations (4-segment model):
Jumping for maximizing backward
somersault rotations with arm swing:
Combining with the flight phase
Results of multi-stage simulation
and optimization for ski jumping
Summary of some current researches
Modeling and experimental validation of swim diving
Walking Animation with Inverted
Pendulum Model
single support
Mass
Center
of
Mass
(COM)
Massless
pendulum
g
Pivot
g
Inverted Pendulum Model
Mass
Massless
pendulum
g
Pivot
single support
Inverted Pendulum Model
Conservation of Energy

1 2 e
1
Is     d  Ie2
2
2
s
where
    mgr sin 
r
θs
θe
g
θs
θe
g
Inverted Pendulum Model
Velocity changes at the double support phase
single support
double
support
m 2 m 2 m
2
E  V1  V2  V1 sin  
2
2
2
V2
V2  V1 cos 
α
V0V
1
α
g
Discussion:
• Adequacy of studying human movement
from simulation and optimization approach
• Maximal joint torque activations are timed
to occur around maximal board deflection
when the board is best able to resist
• An optimal surface compliance for jumping
exists (not a psychological effect)
Discussion (continued):
• When arm motion is restricted, optimal jumping for
backward somersaults involves partially extended
knee and fully extended hip
• With arm motion, however, the knee is fully
extended to create larger angular momentum at
takeoff
• Multi-stage simulation/optimization is necessary
since movements in the current stage affect those in
the following stage
• Real-time responsive human walking can be
simulated with a simple inverted pendulum model
Conclusions:
• Significance of simulation and optimization
approach for studying human movements
• Joint torque activation strategies are different for
different movements and should be subjectspecific
• Advantages in investigating movement
sensitivities to parameter changes (that cannot be
tested in real subjects)
• Other movement application
Additional topics
Musculoskeletal dynamics
Gluteus maximus
Hamstrings
Gastrocnemius
Rectus femoris
Vastus group
Soleus
Other plantarflexors
Tibialis anterior.
Musculotendon model
Musculotendon activation dynamics
L: musculotendon length
V: musculotendon velocity
a: muscle activation
F: musculotendon force
Neural excitation dynamics
u(t): net neural control signal (0 < u(t) < 1)
rise(22 ms) and fall (200 ms) are the rise and
decay time constants for muscle activation.
Forward simulation with muscles:
• Combine excitation, activation dynamics,
and knowledge of muscle insertion
locations
• Forward simulation with node points of u(t)
(muscle excitation) and final time as inputs
• Find node points that optimize the
performance criterion
Pedaling animation (Neptune and Hull, 1999)
Thank you for your participation
Questions