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Motion Control

Motion Control. 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. The Control Problem. The goal:

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Motion Control

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  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: • reference tracking & disturbance rejection • Negative feedback control • System parameters variations • Nonmeasurable disturbance

  4. The Control Problem • Joint space control problem Open loop

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

  6. Joint Space Control • Your control theory textbook • 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

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

  9. Nonlinear coupled linear decoupled

  10. Joint Space Control • Decentralized 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

  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

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