An Algorithm to Design Redundant Manipulators of Optimally Fault-Tolerant Kinematic Structure

One measure of the global fault tolerance of a redundant robot is the size of its self-motion manifold. If this size is defined as the range of its joint angles, then the optimal self-motion manifold size for an n-degree-of-freedom (DoF) robot is n × 2π, which is not typical for existing robot designs. This letter presents a novel two-step algorithm to optimize the kinematic structure of a redundant manipulator to have an optimal self-motion manifold size. The algorithm exploits the fact that singularities occur on large self-motion manifolds by optimizing the robots kinematic parameters around a singularity. Because a gradient for the self-motion manifold size does not exist, the kinematic parameter optimization uses a coordinate descent procedure. The algorithm was used to design 4-DoF, 7-DoF, and 8-DoF manipulators to illustrate its efficacy at generating optimally fault-tolerant robots of any kinematic structure.