Characterizing optimally fault-tolerant manipulators based on relative manipulability indices

Abstract

Abstract-In this article, the authors examine the problem of designing nominal manipulator Jacobians that are optimally fault tolerant to one or more joint failures. In this work, optimality is defined 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 eight degree-of-freedom Gough-Stewart platforms that are optimally fault tolerant for up to two locked joint failures. Examples of optimally faulttolerant seven and eight degree-of-freedom mechanisms are presented.

Designing optimal fault tolerant Jacobian for robotic manipulators

“…The design or control of fault tolerant manipulators aims to maintain the availability of the robot even under partial faults if they occur within their actuators or sensors [10,21]. Within the design level, different structures such as serial or parallel manipulators have been studied [11][12][13][14],or a manipulator with a specific fault tolerant property has been designed or its optimal configurations have been determined [1][2][3][4][5][6]. Literature within the control level has studied the Fault Detection, Fault Isolation and Identification and Fault Recovery techniques as in [15][16].…”

“…This work is adding up to a series of work from Robert and Maciejewski mainly in their latest work in [1][2][3] all are about the design of optimal fault tolerant manipulators. But the main distinction between this study and the method provided in their work is that we are designing on optimal Jacobian based on desired geometric properties compare to the numerical solution of optimisation of measures [5] or using the properties of desired null space of the Jacobian matrix [1][2][3].…”

“…But the main distinction between this study and the method provided in their work is that we are designing on optimal Jacobian based on desired geometric properties compare to the numerical solution of optimisation of measures [5] or using the properties of desired null space of the Jacobian matrix [1][2][3]. Recently the design of optimal fault tolerant Jacobian is shifted from numerical optimisation methods to construction of optimal Jacobian based on desired null space.…”

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

“…(7) indicates the contribution of the kth joint velocity to the translational and orientational velocity of the EEF. Normally, we have n ≥ m that is for a square or fat matrix and in nonkinematic singular configurations of the manipulators, the rank of the Jacobian matrix is m. The common modeling method for the locked joint failures of the manipulators in the literature 14,36,37 is presented in following. When the manipulator has a fault in its kth joint, then it stops to contribute to the velocity of EFF of the manipulator.…”

Quantifying and Optimizing Failure Tolerance of a Class of Parallel Manipulators

“…Investigating the fault tolerant characteristics of a manipulator Jacobian which will take into account the change with respect to time can be of great practical importance. It has recently been shown (Roberts, Yu & Maciejewski, 2007) 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 fault tolerant to three or more joint failures. Due to these constraints in generalization, it would be useful to formulate manipulator Jacobian matrices that possess equal fault tolerance to specified scenarios involving multiple failures.…”