Measuring and reducing the Euclidean-space effects of robotic joint failures

Robotic joint failures are directly characterized and measured in joint space. A locking failure, for example, is one for which a joint cannot move, and it gives an error equal to the desired value minus the locked value. This article extends the joint-space characterization to Euclidean space by measuring the failure effect. The approach is based on a rudimentary measure of point error that can be defined to be distance or path length. It is used to form comprehensive measures through weighted integration over Euclidean-space regions. For kinematically redundant manipulators, minimizing the measures using the redundancy is a method to induce failure tolerance. This can be applied both before a failure to reduce the likelihood of collision-induced damage and after a failure to reduce end-effector error. Examples for both cases are given.