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.

Derivation of three closed loop kinematic velocity models using normalized quaternion feedback for an autonomous redundant manipulator with application to inverse kinematics

“…(64), the values of {II, E, e} need to be determined. In [34], it is assumed that the designer first selects matrix B such that (jT, BT) T is nonsingular, which immediately leads to the determination of (II, E) by eq. (63).…”

“…(63). Several techniques for selecting B are discussed in [34], one of which is described later in this section. However, eq.…”

“…(64) still cannot be solved for (}since e is an unknown quantity. To solve for {e, _}, an optimization scheme was suggested in [34] to pick e to secure a minimum Euclidean norm solution for the generalized velocities. The solutions for these quantities based on eq.…”

“…To overcome this deficiency, the method described in [34] is extended to resolve the redundancy based on any of the three closed loop kinematic velocity models derived here. The basic approach of input relegation control will be discussed without getting into the details.…”

“…An analytical method was presented in [34] to choose B to maximize the determinant of matrix (jT, BT) T with the restriction that B is orthogonal to the rows of J, i.e., d B T = 06×1, for manipulators with one degree of redundancy. Postmultiplying the matrix identity II d + E B = lz×z by jT immediately leads to a symbolic solution for II:…”