1. Model Predictive Impedance Control MPIC

2. Motor Control Features 1.Feedback (closed loop) 2.Feedforward (open loop) 3.Learning 4.Predictive Control 5.Joint (muscle) impedance 6.Interaction with environment 7.Hierarchical 8.EPH, Rhythmic & Tracking movements, …

3. Limbic System Associative Cortex Cerebellum Motor Cortex Basal Ganglia Spinal Cord Musculo-Skeletal System Musculo-Skeletal System Movement Motor Program Need Plan Highest Level Lowest Level Middle Level

4. Feedforward Controller Identifier Brain Model Delay  b . M P C and Algorithm Adaptation  EMG Torque Joint-Load + + + + - - Selector Trajectory +    G1 G2 G3 + System- Disturbance Models Receptors dd. Delay Receptors Td Model Predictive Impedance Control Model Predictive Impedance Control

5. Example 1: Rhythmic Movement

6. Rhythmic Movement Errors

7. Model Response for Rhythmic Movement Model Response for Rhythmic Movement Time (s)

8. External Disturbances External Disturbances Time (s)

9. Model Mismatch Responses for Rhtymic Movement Model Mismatch Responses for Rhtymic Movement Time (s)

10. Example 2: Tracking Movement

11. Tracking Movement Errors

12. Tracking Movement

13. J 1.43 1.61 2.30 3.27 J 1.43 1.61 2.30 3.27 B 1.43 1.94 2.51 3.04 K 1.43 1.48 1.59 1.73 T 1.43 2.32 2.50 2.75 g 1.43 1.61 2.28 3.02 J-B-K 1.43 1.53 3.14 6.59 J-B-K 1.43 1.53 3.14 6.59 Errors of Parameter Mismatch ( Rhythmic Movement ) Errors of Parameter Mismatch ( Rhythmic Movement ) Parameter(s) 0% 15% 30% 45% Parameter(s) 0% 15% 30% 45% Error is root mean square errors (rad).

14. J 0.41 0.42 0.44 0.46 B 0.41 0.43 0.45 0.47 K 0.41 0.43 0.46 0.48 T 0.41 0.42 0.43 0.44 g 0.41 0.40 0.48 0.86 td 0.41 0.45 0.50 0.57 J-B-K 0.41 0.44 0.51 0.70 J-B-K 0.41 0.44 0.51 0.70 Errors of Parameter Mismatch ( Tracking Movement ) Errors of Parameter Mismatch ( Tracking Movement ) Parameter(s) 0% 15% 30% 45% Parameter(s) 0% 15% 30% 45% Error is root mean square errors (rad).

15. Example 3: Gait

17. X =AX+BU Y =CX+DU. bS +  M P C x0x0 12 _____________ (T 1 S+1)(T 2 S+1) 1 Step Function Pendulum Dynamics Dynamic Impedance PD Controller) Angle of Ankle Joint Identification Control Desired Trajectory

18. Time (s) Changes of Impulse Response & Control Signal in Double Pendulum Model Changes of Impulse Response & Control Signal in Double Pendulum Model