1. Motion Control

2. Motion Control
Determine the time history of the generalized forces to be developed by the joint actuators so as to guarantee execution of the commanded task while satisfying given transient and steady-state requirements

3. The Control Problem The goal: Negative feedback control
reference tracking & disturbance rejection
Negative feedback control
System parameters variations
Nonmeasurable disturbance

4. The Control Problem
Joint space control problem
Open loop

5. Difficult to measure directly
The Control Problem
Operational space control problem
Difficult to measure directly

6. Joint Space Control Your control theory textbook Robot manipulator
Linear time-invariant SISO system
Robot manipulator
MIMO
Nonlinear
Strong coupling

7. Joint Space Control Motion equations of manipulator
Let qm denote the joint actuator displacement
Let tao_m denote the actuator driving torques
where Kr is diagonal
如果a静止而B运动

8. Joint Space Control Linear de-coupled Nonlinear coupled
Diagonal constant matrix
Configuration dependent term
Linear de-coupled
Nonlinear coupled

9. Nonlinear coupled
linear decoupled

10. Joint Space Control Decentralized control Centralized control
treat nonlinear interacting term d as disturbance
high gear reduction ratio and/or
limited performance in terms of velocity and acceleration
Centralized control
compensate for nonlinear coupling terms
direct drive and/or
large operational speeds required

11. Two-Link Planar Robot

12. Independent Joint Control
Regard the manipulator as formed by n independent systems (n joints)
control each joint as a SISO system
treat coupling effects as disturbance

13. Independent Joint Control
Assuming that the actuator is a rotary dc motor

14. Feedback Control

15. Position and Velocity Feedback

16. Position and Velocity Feedback
Choose the zero of the controller to cancel the real pole by setting

17. Position and Velocity Feedback
Root locus
Kp determines the radius, Kv can be chosen to set the location

18. Position and Velocity Feedback
The closed loop transfer function
如果是反对称阵，则只有3个元素是独立变量。

19. Position and Velocity Feedback
The closed loop disturbance transfer function
disturbance rejection factor
output recovery time

20. Two-Link Planar Robot
Determine Kp and Kv and Tv