1. Model Predictive Impedance ControlMPIC

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

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

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

5. Example 1: Rhythmic Movement

6. Rhythmic Movement Errors

7. Model Response for Rhythmic Movement Time (s)

8. External Disturbances Time (s)

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

10. Example 2: Tracking Movement

11. Tracking Movement Errors

12. Tracking Movement

13. Errors of Parameter Mismatch ( Rhythmic Movement ) Parameter(s) 0% 15% 30% 45% 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 Error is root mean square errors (rad).

14. Errors of Parameter Mismatch ( Tracking Movement ) Parameter(s) 0% 15% 30% 45% 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 Error is root mean square errors (rad).

15. Example 3: Gait

17. 1 _____________ (T1S+1)(T2S+1) . X =AX+BU Y =CX+DU Desired Trajectory Control Identification M P C 1 2 Step Function Dynamic Impedance PD Controller) bS + s x0 Pendulum Dynamics Angle of Ankle Joint

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