Fundamental Limitations on Designing Optimally Fault-Tolerant Redundant Manipulators

Abstract

Abstract-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.

Optimal mapping of joint faults into healthy joint velocity space for fault-tolerant redundant manipulators

“…In ref. [33], the upper limit of an optimal fault-tolerant configuration for redundant manipulators has been studied and it has indicated that the optimal fault-tolerant configuration is not possible for manipulators with more than 12-DOR. In general, the higher the degree of redundancy, the better fault tolerance of the manipulators.…”

“…For instance, some properties of the Jacobian matrix for fault tolerance have been used in refs. [14,29]. The relationship between the fault tolerance and the null space of Jacobian matrix has been addressed.…”

“…In fact, SLRMs have the capability to be used under multiple constraints. 25,27,28 Keeping in mind that having kinematic redundancy does not guarantee the fault tolerance for the operation of SLRMs, because the redundancy has to be effectively used for fault tolerance 29 of SLRMs. Self-X systems are systems with self-assembly, selforganization, self-reconfiguration, self-repair, selfreplication, or self-reproduction capability.…”

Designing equally fault-tolerant configurations for kinematically redundant manipulators

“…In order to study equally fault-tolerant configurations, we use the following result, which was proved in [20]:…”

“…Unfortunately, the requirement that q is an integer automatically eliminates most spatial manipulator designs since only specific values of r are feasible. Indeed, it was shown in [20] that regardless of a manipulator's geometry or the amount of kinematic redundancy present in a manipulator, no fully spatial manipulator Jacobian can be equally faulttolerant to two joint failures. In this article, we will examine the cases when the workspace has dimension m =2and 3.…”