2. MURI High- Level Control Biomimetic Robots - ONR Site Visit - August 9, 2000 Human Computational Modeling PurposePurpose: to understand arm impedance adaptation and apply it as biomimetic principle. Experiment designedExperiment designed to isolate corrective terms (feedback) from lumped control force (feedforward + feedback)? perturbedModeling of arm impedance based on data from perturbed responses of reaching movements. ParametricParametric modeling of impedance.

3. MURI High- Level Control Biomimetic Robots - ONR Site Visit - August 9, 2000 Control of arm impedance – by modulation of  to the muscles. feedback pathways Three feedback pathways: 1. Near zero-latency mechanical stiffness/viscosity of the muscles. 2. Short latency sensory f/b through spinal structures. Direct Model 3. Long latency sensory f/b through cortex (Direct Model). Biological Controller Structure

4. MURI High- Level Control Biomimetic Robots - ONR Site Visit - August 9, 2000 Assumption 1: Assumption 1: Feed-forward Inverse dynamics model sufficient after learning. Assumption 2: Assumption 2: Feed-forward Inverse dynamics model does not receive state feedback. Assumption 3: Assumption 3: Short-latency sensory feedback plays no role in adaptation. Understanding Biomechanical Controller

5. MURI High- Level Control Biomimetic Robots - ONR Site Visit - August 9, 2000 Direct dynamics modelDirect dynamics model – feedback control, correcting unmodeled disturbances Estimate states by  History of descending motor commands and  Delayed state Hypothesis: Hypothesis: Long-latency feedback system adapts to external force field, possibly through adaptation of the direct dynamics model.

6. MURI High- Level Control Biomimetic Robots - ONR Site Visit - August 9, 2000 KicksKicks: a tool to separate feedback response only. randomUniform experiment accomplished by random kicks. Force fieldForce field: velocity dependent; curled. ExperimentsExperiments: NF vs. FF and/or kicks/no kicks. Experiment Design

7. MURI High- Level Control Biomimetic Robots - ONR Site Visit - August 9, 2000 Null Field; No KicksNull Field; No Kicks: adaptation to robot. Experiment Design: equations Null Field; With KicksNull Field; With Kicks: desired trajectory the same as Force Field; No KicksForce Field; No Kicks: adaptation to robot and environment Kicks – no KicksKicks – no Kicks: Force Field; With KicksForce Field; With Kicks: Kicks – no KicksKicks – no Kicks: Adaptation in FF:Adaptation in FF:

8. MURI High- Level Control Biomimetic Robots - ONR Site Visit - August 9, 2000 We measureWe measure: Feedback responseFeedback response: can NOT be measured. We compute feedback response using:We compute feedback response using: oHuman Arm inertia measurement (fitting to linear model) oPrediction of where human arm would have gone if there were no perturbations (Principal Component Analysis on early data in motion) BothBoth problems have been solved and presented at MURI meeting last year. Experiment – Data Robot jointshandle

9. MURI High- Level Control Biomimetic Robots - ONR Site Visit - August 9, 2000 Raw data: with Kicks and in Null Field. Experimental Data – 1 {Fx, Fy}

10. MURI High- Level Control Biomimetic Robots - ONR Site Visit - August 9, 2000 Experimental data – 2 Assumption Assumption: Inverse Model receives NO state-space feedback; Estimatedtrajectory Estimated trajectory: only due to Inverse Dynamics Model - force along planned and actual trajectory - Control Force along planned traj.

11. MURI High- Level Control Biomimetic Robots - ONR Site Visit - August 9, 2000 Experimental data – 3 Feedback controller force induced by kicks in different dirs. Adaptation in Direct model results in motions towards planned trajectory

12. MURI High- Level Control Biomimetic Robots - ONR Site Visit - August 9, 2000 Raw data w/Kicks: Null Field vs. Force Field. Experimental Data – 4 - after sufficient training in Force Field - compare same statesProblem: how to compare changes in feedback due to adaptation? At same states? Trajectories (NF vs. FF) are associated with state-space dependent forces.

13. MURI High- Level Control Biomimetic Robots - ONR Site Visit - August 9, 2000 Task description What makes trajectories different? –Kicks ParametersSo, kicks as Parameters Direction Magnitude –Kick Direction and Magnitude will define shape of path –Time –Time defines sequence of states Set of parameters for Trajectories, Velocities, and Forces Solution Solution: 1.make parametric NF Models of 2.Validate Models 3.Find and validate Matching procedure 4.Match state spaces

14. MURI High- Level Control Biomimetic Robots - ONR Site Visit - August 9, 2000 Modeling tool - properties Parametric approximation? Successive ApproximationsTool: Successive Approximations (Dordevic et al., 1998) Used in –Model-Based Robot Control –Human data modeling –Parametric –Interpolates and extrapolates –Direct and Inverse modeling –Iterative Refinement –Random addressing –Supports superposition of models

15. MURI High- Level Control Biomimetic Robots - ONR Site Visit - August 9, 2000 In First Step: Each trajectory is approximated with polynomial Varying kd and km, coeffs  i vary too. Now, all coefficients  i In Second step: coefficient-wise approximation of  i w/r kick-dir Step-wise procedure

16. MURI High- Level Control Biomimetic Robots - ONR Site Visit - August 9, 2000 Third step: approximate  i, varied w/r kick- magn. with polynomial Animate procedure: Going backwards: we assign third parameter to the Model, then second, and finally, time instant.

17. MURI High- Level Control Biomimetic Robots - ONR Site Visit - August 9, 2000 Model validation confidence intervalkeeping confidence interval within limits, but avoid over fitting bootstrapingbootstraping Modeling is finished and we gained: –Generalization of examples –Analytical model –Inverse and direct modeling –Iterative refinement –Random addressing –Model superposition Typical trajectory in X s-s:

18. MURI High- Level Control Biomimetic Robots - ONR Site Visit - August 9, 2000 Matching GoalGoal: compare long-latency feedback responses of NF vs. FF trajectories. Step 1Step 1: Take state-spaces of trajectory in FF, and compare them with state-spaces from the NF.  {t i, k-dir, k-magn} Step 2Step 2: Take {t i, k-dir, k-magn} and address Null Field Models of Force

19. MURI High- Level Control Biomimetic Robots - ONR Site Visit - August 9, 2000 Matching - example, kick-direction is variableKick-magnitude is constant, kick-direction is variable. Time-respectiveTime-respective matching.

20. MURI High- Level Control Biomimetic Robots - ONR Site Visit - August 9, 2000 Final results Subtract long-latency feedback forces from NF (model) from the feedback forces computed after learning Force Field. Matched Force-field Adaptation in feedback response

21. MURI High- Level Control Biomimetic Robots - ONR Site Visit - August 9, 2000 stiffed arm Control Experiment – stiffed arm –In Force Field –Stronger Kicks –Same Time window Feedback force of desired trajectory subtracted from the force along actual one. Force field Feedback change Stiffed arm overcomes adaptation due to force field.

22. MURI High- Level Control Biomimetic Robots - ONR Site Visit - August 9, 2000 Summary adaptsLong-latency feedback system adapts to external force field, changing Direct Dynamics model. parametric approximatorThe tool –parametric approximator, can be used in biomimetic control of walking robots. randomly addressedFunctional task description on the set of parameters easy modeling of primitive motions (that can be randomly addressed). Overlaidprimitive motionsOverlaid primitive motions result in complex behavior. We need a robot with intrinsic position sensors to test our ideas.

23. MURI High- Level Control Biomimetic Robots - ONR Site Visit - August 9, 2000 Hexapod Model-based control - problems and solutions - Findings from these research – directly applied to design of biomimetic controller Motion primitives – transform state-spaces to command signals Also, more complex primitives to build a model of a primitive action (stence, giat). Higher level control task- oriented primitives responsible for –Load –Ground properties –Obstacle size and position Or, overlaying of simple primitives? Each primitive requires sensor.

24. MURI High- Level Control Biomimetic Robots - ONR Site Visit - August 9, 2000 Task parameterization parameters = sensors Parametric task description: –Robot-oriented –Task-oriented Complex behavior of: –Posture –Walking Parameters in Posture: (tild, bend, swing) Parameters in Walking: speed, path direction, curvature of path… tilt bend rotate