Euclidean-space measures 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 a failure´s effect there. The approach is based on a primitive 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 can be used to induce failure tolerance by either reducing the likelihood of collision-induced damage before a failure or reducing end-effector error after a failure. Examples for both cases are given.