Motion Control

Motion ControlMotion 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 ProblemThe Control Problem

The goal: reference tracking & disturbance rejection

Negative feedback control System parameters variations Nonmeasurable disturbance

The Control ProblemThe Control Problem

Joint space control problem

Open loop

The Control ProblemThe Control Problem

Operational space control problem

Difficult to measure directly

Joint Space ControlJoint Space Control

Your control theory textbook

Linear time-invariant SISO system

Robot manipulator

MIMO

Nonlinear

Strong coupling

Joint Space ControlJoint 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

Joint Space ControlJoint Space Control

Diagonal constant matrix Configuration dependent term

Linear de-coupled Nonlinear coupled

Nonlinear coupled

linear decoupled

Joint Space ControlJoint 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

Two-Link Planar RobotTwo-Link Planar Robot

Independent Joint ControlIndependent Joint Control

Regard the manipulator as formed by n Regard the manipulator as formed by n

independent systems (n joints)independent systems (n joints)

control each joint as a SISO systemcontrol each joint as a SISO system

treat coupling effects as disturbancetreat coupling effects as disturbance

Independent Joint ControlIndependent Joint Control

Assuming that the actuator is a rotary dc motor Assuming that the actuator is a rotary dc motor

Feedback ControlFeedback Control

Position and Velocity FeedbackPosition and Velocity Feedback

Position and Velocity FeedbackPosition and Velocity Feedback

Choose the zero of the controller to cancel Choose the zero of the controller to cancel

the real pole by settingthe real pole by setting

Position and Velocity FeedbackPosition and Velocity Feedback

Root locus

Kp determines the radius, Kv can be chosen to set the location

The closed loop transfer function

Position and Velocity FeedbackPosition and Velocity Feedback

The closed loop disturbance transfer function

disturbance rejection factor

output recovery time

Position and Velocity FeedbackPosition and Velocity Feedback

Two-Link Planar RobotTwo-Link Planar Robot

Determine Kp and Kv and Tv