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