1. Residual Reduction
Chand T. John

2. Subject-Specific Simulation
Preprocess
Marker Position Data
Force Plate Data
Hospitals
Scale Model to Subject
Simulation
Inverse Kinematics
Analysis

3. NMBL Simulation Problem
qexp(t1), …, qexp(tN)
Fleft(t1), …, Fleft(tN)
Fright(t1), …, Fright(tN)
Tleft(t1), …, Tleft(tN)
Tright(t1), …, Tright(tN)
COPleft(t1), …, COPleft(tN)
COPright(t1), …, COPright(tN)
Pad, filter,
spline-fit IK
qexp(t)
Fleft(t), Tleft(t), COPleft(t)
Fright(t), Tright(t), COPright(t)
“Inverse Dynamics” via
Forward Dynamic Simulation
u(t1’), …, u(tM’)
Forces(t1’), …, Forces(tM’)
Tracking
q(t1’), …, q(tM’)

4. Simulation Challenges
Maintain efficiency without losing accuracy
Dynamic optimization is accurate but slow1,2
Maintain consistency between3:
experimental kinematics (from marker data)
experimental kinetics (from force plate data)
1 F. C. Anderson, M. G. Pandy. Dynamic Optimization of Human Walking. Journal of Biomechanical Engineering 123: , 2001.
2 F. C. Anderson, M. G. Pandy. Static and Dynamic Optimization Solutions for Gait Are Practically Equivalent. Journal of Biomechanics 34: , 2001.
3 D. G. Thelen, F. C. Anderson. Using Computed Muscle Control to Generate Forward Dynamic Simulations of Human Walking from Experimental Data. Journal of Biomechanics, in press.

5. Existing Simulation Algorithms
Dynamic Optimization1
Optimal Tracking2
Computed Muscle Control3
Speed
Slow
(weeks)
(days)
10 minutes
Predict
Novel
Movement
Emergent
Behavior
Tracking
(but not all DOFs)
Performance
Criteria
Any
Global
Static
Only at each time step 
(Exp – Model)2
VarExp
1 F. C. Anderson, M. G. Pandy. Dynamic Optimization of Human Walking. Journal of Biomechanical Engineering 123: , 2001.
2 R. R. Neptune. Optimization Algorithm Performance in Determining Optimal Controls in Human Movement Analyses. Journal of Biomechanical Engineering 121(2): , 1999.
3 D. G. Thelen, F. C. Anderson, S. L. Delp. Generating Dynamic Simulations of Movement using Computed Muscle Control. Journal of Biomechanics 36: , 2003.

6. The Model Generalized Coordinates (DOF) Pelvis z position
Pelvis x position
Pelvis y position
Pelvis tilt angle
Pelvis list angle
Pelvis rotation angle
Right hip flexion angle
Right hip adduction angle
Right hip rotation angle
Right knee flexion angle
Right ankle angle
Right subtalar angle
Left hip flexion angle
Left hip adduction angle
Left hip rotation angle
Left knee flexion angle
Left ankle angle
Left subtalar angle
Lumbar extension angle
Lumbar bending angle
Lumbar rotation angle
We ignore metatarsophalangeal (MTP) angles, so our numbering is a bit different from that in the images above.
1 F. C. Anderson, M. G. Pandy. Dynamic Optimization of Human Walking. Journal of Biomechanical Engineering 123: , 2001.
2 D. G. Thelen, F. C. Anderson. Using Computed Muscle Control to Generate Forward Dynamic Simulations of Human Walking from Experimental Data. Journal of Biomechanics, in press.

7. CMC Simulation Pipeline
Preprocess
Marker Position Data
Force Plate Data
Hospitals
Scale Model to Patient
Simulation
Computed Muscle
Control
Inverse Kinematics
Analysis
1 D. G. Thelen, F. C. Anderson, S. L. Delp. Generating Dynamic Simulations of Movement using Computed Muscle Control. Journal of Biomechanics 36: , 2003.

8. Unconstrained CMC Simulation
Model: 8 segments, 21 DOF, 92 Hill-type muscle-tendon units
Input: experimental kinematic data, kinetic ground reaction data
Output: muscle excitations, forces, torques; resulting kinematics
1 D. G. Thelen, F. C. Anderson, S. L. Delp. Generating Dynamic Simulations of Movement using Computed Muscle Control. Journal of Biomechanics 36: , 2003.
2 D. G. Thelen, F. C. Anderson. Using Computed Muscle Control to Generate Forward Dynamic Simulations of Human Walking from Experimental Data. Journal of Biomechanics, in press.

9. Unconstrained CMC Problems
Dynamic inconsistency between:
Whole-body motion (kinematics)
Foot-floor interaction (kinetics)
Due to:
Measurement errors
Modeling assumptions
So fictitious “residual” forces are needed to keep model from falling over
1 D. G. Thelen, F. C. Anderson. Using Computed Muscle Control to Generate Forward Dynamic Simulations of Human Walking from Experimental Data. Journal of Biomechanics, in press.
2 M. van de Panne, A. Lamouret. Guided Optimization for Balanced Locomotion. Computer Animation and Simulation ‘95, , Springer-Verlag/Wien

10. REA-CMC Simulation Pipeline
Preprocess
Marker Position Data
Force Plate Data
Hospitals
Scale Model to Patient
REA
CMC
Simulation
Inverse Kinematics
Analysis
1 D. G. Thelen, F. C. Anderson. Using Computed Muscle Control to Generate Forward Dynamic Simulations of Human Walking from Experimental Data. Journal of Biomechanics, in press.

11. REA-CMC Simulation qx(t0) qb(t0) qx’’(ti) qb’’(ti)
Nonlinear optimization
Initial states
Accelerations
qx(t0)
qb(t0)
Solve for accelerations using equations of motion
(i = 0, 1, …, N)
qx’’(ti)
qb’’(ti)
qx(ti + 1), qx’(ti + 1)
qb(ti + 1), qb’(ti + 1)
Integrate forward in time
(i = 0, 1, …, N – 1)
Combine with other
experimental kinematics
(i = 0, 1, …, N)
CMC
qexp(t)
Fit with seventh-order
splines
qexp(ti)
1 D. G. Thelen, F. C. Anderson. Using Computed Muscle Control to Generate Forward Dynamic Simulations of Human Walking from Experimental Data. Journal of Biomechanics, in press.

12. REA-CMC Problems
Same data, different time intervals lead to different solutions
Code chops time interval in half automatically
Back angles changed unrealistically when simulating longer than half-gait cycle
Large changes to lumbar extension for small reductions in error
Exaggerated lumbar rotation (transverse trunk rotation)
Model of head, arms, torso may be too simplistic
Residuals are not mass-normalized
Different walking speeds lead to different results
Speed filtering may be altering accelerations
1 D. G. Thelen, F. C. Anderson. Using Computed Muscle Control to Generate Forward Dynamic Simulations of Human Walking from Experimental Data. Journal of Biomechanics, in press.

13. RRA-CMC Simulation Pipeline
Preprocess
Marker Position Data
Force Plate Data
Hospitals
Scale Model to Subject
Simulation
Inverse Kinematics
Analysis
CMC
RRA

14. REA vs. RRA vs. Unconstrained
Kinematics
Kinetics
Constrained
Constrained
RRA + CMC
REA + CMC
Unconstrained CMC
RRA will aim to keep the error that must be allowed due to
modeling errors (like lack of arm motion) while throwing out
excessive error. We expect zero DC offset for periodic motion.
Unconstrained
Unconstrained
Whole-Body Motion
Residuals

15. RRA-CMC Simulation  CMC CMC
Residual Curves
DC Offsets
CMC
Change in Kinematics
Choose clamping values for each residual curve
Alter torso center of mass and back angles to remove DC offsets 
CMC

16. Sensitivity Analysis CMC Alterations One subject Torso center of mass
x-coordinate ±0.01, ±0.03, ±0.05, ±0.095
y-coordinate ±0.01, ±0.03, ±0.05, ±0.1
z-coordinate ±0.01, ±0.03, ±0.05, ±0.1
Back angles
Lumbar extension ±0.3, ±1.0, ±3.0, ±5.0, ±7.0, ±10.0
Lumbar bending ±0.3, ±1.0, ±3.0, ±5.0, ±7.0, ±10.0
Lumbar rotation ±0.3, ±1.0, ±2.0, ±5.0, ±7.0, ±10.0
One subject
S26, child with CP
Residual Curves
DC Offsets
CMC

17. Torso COM Sensitivity tx – 0.095 -4.47796 tx – 0.05 -3.93798 tx – 0.03
tx – 0.01
Default tx tx tx tx

18. Lumbar Rotation Insensitivity
lr – 10.0
lr – 7.0
lr – 5.0
lr – 2.0
lr – 1.0
lr – 0.3
Default
lr + 0.3
lr + 1.0
lr + 2.0
lr + 5.0
lr + 7.0 lr

19. Sensitivity Analysis
Changing the lumbar rotation angle does not seem to affect the residual forces or moments significantly
The families of residual curves appear to be smooth functions of the perturbation amount applied to the torso center of mass or back angles
Only small perturbations are needed to make the DC offsets in RRA reasonably small
RRA-CMC running time:
17 hours
60 simulations
60 minutes
1 hour ×
= 17 minutes/simulation

20. Original Residual Curve LimitsFX FY FZ MX MY MZ
Max
Min

21. RRA’s Improvements over REA
Should run for longer time intervals with high accuracy
RRA can run on any model
Residuals applied anywhere on model
Can distribute corrections across parameters using clamping, instead of restricting to back angles and pelvis position

22. REA vs RRA vs BSP Estimation
REA-CMC1
RRA-CMC
BSP
Estimation2
Alterable
Parameters
Initial back, pelvis
All input parameters
Inertial parameters
“Required” Data
Full model kinematics
All tracked kinematics
Arm and leg kinematics
Error Minimized
Back, pelvis kinematics
Overall kinematics
GRFs and torques
1 D. G. Thelen, F. C. Anderson. Using Computed Muscle Control to Generate Forward Dynamic Simulations of Human Walking from Experimental Data. Journal of Biomechanics, in press.
2 B. J. Fregly, J. A. Reinbolt. Estimation of Body Segment Parameters from Three-Dimensional Gait Data Using Optimization. International Symposium on 3D Analysis of Human Movement, 13-16, 2004.

23. Effects of Arm Motion
Arm motion and vertical free moments balance trunk torques caused by lower extremity
Arm motion less important at slower walking speeds
Arm fixation alters vertical free moments and transverse forces more in males than in females
1 Y. Li, W. Wang, R. H. Crompton, M. M. Gunther. Free Vertical Moments and Transverse Forces in Human Walking and Their Role in Relation to Arm-Swing. J Exp Bio 204: 47-58, 2001.

24. Resolving Redundancy

25. Resolving Redundancy
Danger of optimization: falling into local minima that are not global minima; more local minima for longer time intervals cause problem for REA
Monte Carlo simulation
Simulated annealing1,2 better but slower
Surgery for surgery
1 R. R. Neptune. Optimization Algorithm Performance in Determining Optimal Controls in Human Movement Analyses. Journal of Biomechanical Engineering 121(2): , 1999.
2 J. S. Higginson, R. R. Neptune, F. C. Anderson. Simulated Parallel Annealing within a Neighborhood for Optimization of Biomechanical Systems. Journal of Biomechanics 38: , 2005.

26. Next Steps Optimization weights on 100-10-1 scale
Automatic correction suggestions
Command-line repeatable RRA-CMC
Automatic generation of result reports
Software dissemination (February)
Clamping sensitivity analysis
Automatic clamping, suggestions, 