Fundamental Limitations on Designing Optimally Fault-Tolerant Redundant Manipulators

In this paper, the authors examine the problem of designing nominal manipulator Jacobians that are optimally fault tolerant to one or more joint failures. Optimality is defined here in terms of the worst-case relative manipulability index. While this approach is applicable to both serial and parallel mechanisms, it is especially applicable to parallel mechanisms with a limited workspace. It is shown that a previously derived inequality for the worst-case relative manipulability index is generally not achieved for fully spatial manipulators and that the concept of optimal fault tolerance to multiple failures is more subtle than previously indicated. Lastly, the authors identify the class of 8-DOF Gough--Stewart platforms that are optimally fault tolerant for up to two joint failures. Examples of optimally fault-tolerant 7- and 8-DOF mechanisms are presented.