THE KINEMATIC CONTROL OF REDUNDANT MANIPULATORS (JACOBIAN, SINGULARITY)
Abstract
The kinematic control of a redundant manipulator involves determining a feasible solution to the non-linear kinematic equation which relates the joint motions of the manipulator to the corresponding end effector motions. The need for redundancy in a manipulator arises from the manipulator's inability to produce arbitrary differential end effector motions given any orientation and position of the end effector. In more advanced feedback control schemes, a manipulator is required to provide arbitrary differential end effector motions at all times. Differential motions in the manipulator joint space are transformed into corresponding differential motions in the end effector space using the Jacobian matrix. The Jacobian matrix equation is the first order approximation to the non-linear kinematic equation. Unfortunately, when the Jacobian matrix does not maintain maximal rank, the inverse mapping from the end effector space to the joint space is no longer "onto" and results in the end effector losing a degree of freedom. Even as the Jacobian matrix approaches a singularity, the required joint rates for the manipulator may become excessive and physically unrealizable. Criteria are developed to avoid the Jacobian matrix singularities of a redundant manipulator and still maintain total freedom of its end effector within the workspace. Integrating the criteria into the kinematic control of the manipulator allows for specifying continuously smooth end effector motions with bounded joint rates. Two approaches are presented for obtaining the inverse kinematic solution to a redundant manipulator which will maintain a well-conditioned Jacobian matrix. The first approach developes an exact solution to the non-linear kinematic equation using an innovative technique. The second approach uses the first order approximation to the non-linear kinematic equation and results in an iterative solution scheme.
Degree
Ph.D.
Subject Area
Electrical engineering
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