A Class of Transpose Jacobian‐based NPID Regulators for Robot Manipulators with an Uncertain Kinematics

Abstract

AbstractTranspose Jacobian‐based controllers present an attractive approach to robot set‐point control in Cartesian space that derive the end‐effector posture to a specified desired position and orientation with neither solving the inverse kinematics nor computing the inverse Jacobian. By a Lyapunov function with virtual artificial potential energy, a class of complete transpose Jacobian‐based Nonlinear proportional‐integral‐derivative regulators is proposed in this paper for robot manipulators with uncertain kinematics on the basis of the set of all continuous differentiable increasing functions. It shows globally asymptotic stability for the result closed‐loop system on the condition of suitable feedback gains and suitable parameter selection for the corresponding function set as well as artificial potential function, and only upper bound on Jacobian matrix error and Cartesian dynamics parameters are needed. The existing linear PID (LPID) regulators are the special cases of it. Nevertheless, in the case of LPID regulators, only locally asymptotic stability is guaranteed if the corresponding conditions are satisfied. Simulations demonstrate the result and robustness of transpose Jacobian‐based NPID regulators. © 2002 Wiley Periodicals, Inc.