Adaptive Manipulator Control: A Case Study

Adaptive Manipulator Control: A Case Study

1. JEAN-JACQUES E. SLOTINE, WEIPING LI

2. Manipulator Model

   • where q is the n x 1 vector of joint displacements
   • T is the n x 1 vector of applied joint torques (or forces)
   • g(q) is the n x 1 vector of gravitational torques.
   • H(q) is the n x n symmetric positive definite manipulator inertia matrix
   • C(q, q)q is the n x 1 vector of centripetal and Coriolis torques

3. Controller Design

   • 1) given the desired joint position qd(t), and with some or all the manipulator parameters unknown
   • 2) derive a control law for the actuator torques, and an estimation law for the unknown parameters
   • 3) the manipulator joint position q(t) precisely tracks qd( t) after an initial adaptation process

4. The structure of the adaptive controller given by (3) and (4)

   • special form of full dynamics compensation, with three terms corresponding to inertial, centripetal and Coriolis, and gravitational torques
     • based on the estimated parameters, attempts to provide the joint dynamic torques necessary to make the desired motions
   • actually contains two terms representing PD feedback

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