Designing equally fault-tolerant configurations for kinematically redundant manipulators

In this article, the authors examine the problem of designing nominal manipulator Jacobians that are optimally fault-tolerant to multiple joint failures. In this work, optimality is defined in terms of the worst case relative manipulability index. Building on previous work, it is shown that for a robot manipulator working in three-dimensional workspace to be equally fault-tolerant to any two simultaneous joint failures, the manipulator must have precisely six degrees of freedom. A corresponding family of Jacobians with this property is identified. It is also shown that the two-dimensional workspace problem has no such solution.