Input relegation control for gross motion of a kinematically redundant manipulator

Abstract

This report proposes a method for resolving the kinematic redundancy of a serial link manipulator moving in a three-dimensional workspace. The underspecified • problem of solving for the joint velocities based on the classical kinematic velocity model is transformed into a well-specified problem. This is accomplished by augmenting the original model with additional equations which relate a new vector variable quantifying the redundant degrees of freedom (DOF) to the joint velocities. The resulting augmented system yields a well specified solution for the joint velocities. Methods for selecting the redundant DOF quantifying variable and the transformation matrix relating it to the joint velocities are presented so as to obtain a minimum Euclidean norm solution for the joint velocities. The approach is also applied to the problem of resolving the kinematic redundancy at the acceleration level. Upon resolving the kinematic redundancy, a rigid body dynamical model governing the gross motion of the manipulator is derived. A control architecture is suggested, which according to the model, decouples the Cartesian space DOF and the redundant DOF.

New insights into input relegation control for inverse kinematics of a redundant manipulator. Part 1, On the orthogonality of matrices B and J and comparison to the extended Jacobian method

“…To review how the kinematic modeling method [l, 21 and the concept of IRC [3 base, open chain, serial link redundant manipulator in [6 , it is convenient to present for kinematically modeling a constrained rigid body mechanical system [l, 2 a theory for controlling such a system termed input relegation control (IRC) pseudovelocities, was introduced and de 2 ned as a linear function of the coupled genContro f laws are designed for each task, and the control inputs to the actuators are A classical example of a control law base d on the principles of IRC was provided DOF can be utilized to explicit 1 y control the pseudove f ocities and the pseudocoordiwere first applied to the kinematic redundancy resolution during motion of a fixe d the classical kinematic velocity model for such a manipu 1 ator: The original application of IRC to kinematic redundancy resolution [6] Here I k x k denotes a (k x k) identity matrix and Okxl a (k x I) matrix of zeros.…”