Model Predictive Impedance Control

MPIC

Motor Control Features

1. Feedback (closed loop)2. Feedforward (open loop)3. Learning4. Predictive Control5. Joint (muscle) impedance6. Interaction with environment7. Hierarchical8. 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

MiddleLevel

Trajectory

Selector

FeedforwardController

SpinalCircuits

andMuscles

Joint-LoadDynamics

Torque

Disturbance

ReceptorsDelay

Brain Model

Joint Movement

Td

d

Stiffness Control SchemeStiffness Control SchemeStiffness Control SchemeStiffness Control Scheme

Trajectory

Selector

FeedforwardController

SpinalCircuits

andMuscles

Joint-LoadDynamics

Torque

Disturbance

ReceptorsDelay

Brain Model

Joint Movement

Td

d

Stiffness Control SchemeStiffness Control SchemeStiffness Control SchemeStiffness Control Scheme

Feedforward Controller

Identifier

Brain Model

Delay

b

.

M P C and

Algorithm Adaptation

EMG

TorqueTorque

Joint-LoadJoint-Load

+ +

+ +--

Selector Trajectory

+

G1

G2

G3

+

System-Disturbance

Models

Receptors

dd dd

..

Delay

Receptors

TTdd

Model Model PredictivePredictiveImpedance Impedance

ControlControl

Model Model PredictivePredictiveImpedance Impedance

ControlControl

Example 1: Rhythmic MovementExample 1: Rhythmic MovementExample 1: Rhythmic MovementExample 1: Rhythmic Movement

Rhythmic Movement ErrorsRhythmic Movement ErrorsRhythmic Movement ErrorsRhythmic Movement Errors

Rad

.

-0.10

0.30

0.70

1.10

0.00 0.60 1.20 1.80 2.40 3.00

Ref. Model

Model Response for Rhythmic Model Response for RhythmicMovementMovement

Model Response for Rhythmic Model Response for Rhythmic MovementMovement

Time (s)Time (s)

-100-50

050

100

0 0.6 1.2 1.8 2.4 3

Nm

Dist. Dist.-p Dist.-n

External DisturbancesExternal Disturbances External DisturbancesExternal Disturbances

Time (s)Time (s)

-0.10

0.30

0.70

1.10

0.00 0.60 1.20 1.80 2.40 3.00

Ra

d.

Output Output1 Output2

Model Mismatch Responses Model Mismatch Responses for Rhtymic Movementfor Rhtymic Movement

Model Mismatch Responses Model Mismatch Responses for Rhtymic Movementfor Rhtymic Movement

Time (s)Time (s)

Example 2: Tracking MovementExample 2: Tracking MovementExample 2: Tracking MovementExample 2: Tracking Movement

Tracking Movement ErrorsTracking Movement ErrorsTracking Movement ErrorsTracking Movement Errors

Tracking MovementTracking MovementTracking MovementTracking Movement

JJ 1.43 1.43 1.61 1.61 2.30 2.30 3.27 3.27BB 1.43 1.43 1.94 1.94 2.51 2.51 3.04 3.04KK 1.43 1.43 1.48 1.48 1.59 1.59 1.73 1.73TT 1.43 1.43 2.32 2.32 2.50 2.50 2.75 2.75gg 1.43 1.43 1.61 1.61 2.28 2.28 3.02 3.02

J-B-KJ-B-K 1.43 1.43 1.53 1.53 3.14 3.14 6.596.59

Errors of Parameter MismatchErrors of Parameter Mismatch( Rhythmic Movement ) ( Rhythmic Movement )

Errors of Parameter MismatchErrors of Parameter Mismatch( Rhythmic Movement ) ( Rhythmic Movement )

Parameter(s) 0% Parameter(s) 0% 15% 15% 30% 30% 45% 45%

Error is root mean square errors (rad).Error is root mean square errors (rad).

JJ 0.41 0.41 0.42 0.42 0.44 0.44 0.46 0.46BB 0.41 0.41 0.43 0.43 0.45 0.45 0.47 0.47KK 0.41 0.41 0.43 0.43 0.46 0.46 0.48 0.48TT 0.41 0.41 0.42 0.42 0.43 0.43 0.44 0.44gg 0.41 0.41 0.40 0.40 0.48 0.48 0.86 0.86tdtd 0.41 0.41 0.45 0.45 0.50 0.50 0.57 0.57

J-B-KJ-B-K 0.41 0.41 0.44 0.44 0.51 0.51 0.70 0.70

Errors of Parameter MismatchErrors of Parameter Mismatch( Tracking Movement ) ( Tracking Movement )

Errors of Parameter MismatchErrors of Parameter Mismatch( Tracking Movement ) ( Tracking Movement )

Parameter(s) 0% Parameter(s) 0% 15% 15% 30% 30% 45% 45%

Error is root mean square errors (rad).Error is root mean square errors (rad).

Example 3: GaitExample 3: GaitExample 3: GaitExample 3: Gait

G3 is determined by linearization of the equations for small angle deviationsG3 is determined by linearization of the equations for small angle deviations

X =AX+BU

Y =CX+DU

.

bS +

M P C

x0

1 2

_____________

(T1S+1)(T2S+1)

1

Step Function

Pendulum Dynamics

Dynamic Impedance PD Controller)

Angle of Ankle Joint

Identification Control

Desired Trajectory

-80

-40

0

40

80

0 0.6 1.2 1.8 2.4 3

Impulse Response Control Signal

Time (s)Time (s)

Changes of Impulse Response & Control Changes of Impulse Response & Control Signal in Double Pendulum ModelSignal in Double Pendulum Model

Changes of Impulse Response & Control Changes of Impulse Response & Control Signal in Double Pendulum ModelSignal in Double Pendulum Model