Model Predictive Impedance Control MPIC

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, …

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

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

Example 1: Rhythmic Movement

Rhythmic Movement Errors

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

External Disturbances External Disturbances Time (s)

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

Example 2: Tracking Movement

Tracking Movement Errors

Tracking Movement

J J B K T g J-B-K J-B-K 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).

J B K T g td J-B-K J-B-K 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).

Example 3: Gait

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

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