1. Motor Control Engineering View Motor Control Engineering View

2. Topics: 1- Muscle and Spinal Cord Models 1- Muscle and Spinal Cord Models 2- Classic Control/Control Variables 2- Classic Control/Control Variables 3- Model Based Strategies 3- Model Based Strategies

3. Stark, Lawrence W. 1968. Neurological Control Systems; Studies in Bioengineering. New York: Plenum Press. Classic Control (Modeling Eye Movement)

4. Control Variables 1- Force !? 1- Force !? 2- Position !? 2- Position !? 3- Velocity !? 3- Velocity !? 4- Stiffness !? 4- Stiffness !? 5- Viscosity !? 5- Viscosity !? 6- Impedance !? 6- Impedance !?

5. Stein, R.C. (1982) Behavioral and Brain Sciences What Muscle Variable(s) Does the Nervous System Control in Limb Movements? What Muscle Variable(s) Does the Nervous System Control in Limb Movements?

6. Stiffness Control

7. F = k ( X – X 0 ) :رابطه يك فنر (عضله) Muscle Stiffness

8. K = F/X K = F/X K >> 1 => Force Control K >> 1 => Force Control K Position Control K Position Control Stiffness Control (cont.)

9. 1- Feldman & Bizzi (EPH), 1966,1979,1986 1- Feldman & Bizzi (EPH), 1966,1979,1986 2- Houk (Stiffness and Reflex), 1979 2- Houk (Stiffness and Reflex), 1979 3- Hasan, 1986 3- Hasan, 1986

10. How CNS May Changes Joint Stiffness? 1- Muscle active characteristic 1- Muscle active characteristic 2- Muscle passive characteristic 2- Muscle passive characteristic 3- α-γ co-activation & spinal reflex loop (muscle spindle) 3- α-γ co-activation & spinal reflex loop (muscle spindle) 4- Co-contraction 4- Co-contraction

12. Stiffness Control Diagram

13. βv = Θf - Td/σ Load Effect

14. Stiffness Control Diagram (cont.) Optimizer Program Inverse Dynamic Controller Disturbance G f (s) Delay T d     d G(s)  Delay  v CNS

15. Impedance Definition: Winters et al. (1988): Winters et al. (1988): “the automatic capability of the system to resist an applied load before voluntary intervention takes place” “the automatic capability of the system to resist an applied load before voluntary intervention takes place”

16. Impedance Control 1- Hoffer (1982). Central Control and Reflex Regulation of Mechanical Impedance: The Basis for a Unified Motor-Control Scheme. Behavioral and Brain Sciences 1- Hoffer (1982). Central Control and Reflex Regulation of Mechanical Impedance: The Basis for a Unified Motor-Control Scheme. Behavioral and Brain Sciences

17. Impedance Control (cont.) 2- Stein, R. C., (1982). What Muscle Variable(s) Does the Nervous System Control in Limb Movements? Behavioral and Brain Sciences 2- Stein, R. C., (1982). What Muscle Variable(s) Does the Nervous System Control in Limb Movements? Behavioral and Brain Sciences

18. Impedance Control (cont.) 3-Hogan, N., (1984a). Adaptive Control of Mechanical Impedance by Coactivation of Antagonist Muscles. IEEE Trans. on Automatic Control, 3-Hogan, N., (1984a). Adaptive Control of Mechanical Impedance by Coactivation of Antagonist Muscles. IEEE Trans. on Automatic Control, Hogan, N., (1985a). Impedance Control: An Approach to Manipulation: Part I-Theory. Journal of Dynamic Systems, Measurement, and Control, Hogan, N., (1985a). Impedance Control: An Approach to Manipulation: Part I-Theory. Journal of Dynamic Systems, Measurement, and Control, Hogan, N., (1985c). The Mechanics of Multi- Joint Posture and Movement Control. Biological Cybernetic, 52, 315-331. Hogan, N., (1985c). The Mechanics of Multi- Joint Posture and Movement Control. Biological Cybernetic, 52, 315-331.

19. Muscle 2-D Characteristic Muscle 2-D Characteristic

20. Joint Impedance

21. Is Joint Impedance Short- Term Predictor?

22. Joint Impedance (cont.) Plant PD Control Signal OutputReference

23. Smith, A. M. (1996), Smith, A. M. (1996), Does the Cerebellum Learn Strategies for the Optimal Time-Varing Control of Joint Stiffness? Behavioral and Brain Sciences