A local measure of fault tolerance for kinematically redundant manipulators

When a manipulator suffers a joint failure, its performance can be significantly affected. If the failed joint is locked, the resulting manipulator Jacobian is given by the original Jacobian, except that the column associated with the failed joint is removed. The rank of the resulting Jacobian then determines if the manipulator still has the ability to perform arbitrary end-effector motions. Unfortunately, even at an operating configuration that has a relatively high manipulability index, a joint failure may still result in a singular Jacobian. This work examines the problem of determining the reduced manipulability of a manipulator after one or more joint failures. Configurations that result in a minimal reduction of the manipulability index for any set of joint failures are determined.