Kinematic Design of Manipulators with Seven Revolute Joints Optimized for Fault Tolerance

Abstract

A local definition of fault tolerance, based on properties of the manipulator Jacobian, is used to generate the kinematics of seven degree-of-freedom (DOF) revolute joint manipulators. The measure of fault tolerance used is the smallest singular value over all possible Jacobians resulting from single locked joint failures. The canonical form for an optimal fault-tolerant Jacobian that maximizes this measure has been previously identified. It has also been known that it is not possible to generate a seven DOF revolute manipulator that corresponds to this theoretically optimal Jacobian. However, in this paper, it is shown how to generate physically realizable Jacobians that are very close to being optimal. It is further shown that there exist 7! different manipulators, from a single Jacobian, that have the same local fault tolerance properties. To evaluate the global properties of these different manipulators, a technique for computing six-dimensional fault-tolerant workspaces is presented. The size of these workspaces vary significantly among these 7! manipulators.