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

The Control Problem Joint space control problem Open loop

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

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

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

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

Nonlinear coupled linear decoupled

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

Two-Link Planar Robot

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

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

Feedback Control

Position and Velocity Feedback

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

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

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。

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

Two-Link Planar Robot Determine Kp and Kv and Tv