Designing optimal fault tolerant Jacobian for robotic manipulators

Abstract

Fault tolerance of robotic manipulators is determined based on the fault tolerance measures. In this study a Jacobian of a 7DOF optimal fault tolerant manipulator is designed based on optimality of worse case relative manipulability and worse case dexterity from geometric perspective instead of numerical solution of constrained optimisation problem or construction of optimal Jacobian through a desired null space. The proposed Jacobian matrix is optimal and equally fault tolerant for a single joint failure within any joint of the manipulators.

A probabilistic approach for measuring the fault tolerance of robotic manipulators

“…The reduced Jacobian matrix kJ is obtained by removing the k-th column of the original Jacobian matrix J [2], [14].…”

“…Then, the worst-case manipulability as a measure of fault tolerance is given by (2) This manipulability defines the worst case post failure ma nipulability of the locked joint faulty robot. 2-Worst-case relative manipulability: The relative manipulability [18] of a faulty manipulator with the k-th joint locked is det(kJkJT) det(JJT) (3) where det(kJkJT), det(JJT), and P k are the k-th joint locked robot manipulability, original robot manipulability, and the k-th joint locked robot relative manipulability measures, respectively.…”

“…The development of fault tolerant manipulators has been possible through the use of kinematic redundancy [2], [5], [13], [14], [19], [18], [22] along with applying fault-tolerant control strategies [7], [11], [13], [16], [15], [20], [21], [23]. The optimal kinematic structures and fault tolerant controllers for the manipulators are commonly obtained by the optimization of the fault tolerance indices [2], [5], [19], [18], [22].…”

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

“…13,14 The design procedure usually optimizes fault-tolerance measures of the manipulators. 12,14 For instance, relative manipulability 15 or worst-case dexterity 16 are two of measures of fault tolerance of manipulators. Condition number of manipulators can also be used for the fault tolerance, this fact has been observed in our previous work 17 where the condition numbers are used for finding optimal configurations for fault tolerance of the manipulator.…”

“…5,6 Research on fault tolerance of the manipulators is on either the design of the manipulators (design of faulttolerant manipulators or fault-tolerant structures) or the control of the manipulators (fault analysis and fault-tolerant motion planning or control). Within the literature of design of fault-tolerant manipulators, either different structure of serial or parallel manipulators have been studied, [7][8][9][10][11][12] or a manipulator with a specific fault-tolerant property has been designed that includes design of degrees of freedom (DOF), link lengths, and redundancy in actuation. 13,14 The design procedure usually optimizes fault-tolerance measures of the manipulators.…”