On the limitations of designing equally fault-tolerant configurations for kinematically redundant manipulators

A probabilistic approach for measuring the fault tolerance of robotic manipulators

“…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].…”

“…There are different fault tolerance indices that have been used for optimization purposes, such as worst-case relative manipulability [18], [22], [5], worst-case minimum singular value [13], [14], and worst-case condition number [3]. These measures are calculated locally and are useful for tasks that do not require large motions.…”

“…For example, Lewis et at. [13] have used the worst-case minimum singular value for the design of fault tolerant manipulators and have determined the optimal configuration for the manipulator based on this index whereas Roberts et al [l7], [19], [18], [22] have applied theworst-case relative manipulability. Kazerounian et at.…”

Optimal fault-tolerant Jacobian matrix generators for redundant manipulators

“…Our aim is to determine a general form for the Jacobian matrix of optimal fault-tolerant positional manipulators. A similar problem was addressed in [4] using an algebraic formulation, whereas here we focus on a geometric approach. There has been extensive study on the design of these manipulators in [5,6] where the main objective is the determination of optimal fault-tolerant Jacobian matrices.…”

“…There has been extensive study on the design of these manipulators in [5,6] where the main objective is the determination of optimal fault-tolerant Jacobian matrices. For instance, the optimal Jacobian matrices proposed in [4][5][6][7] were obtained from: (a) algebraic or numeric solution of an optimisation problem [7,8] or (b) algebraic or numeric solution of the constraints associated with properties of the desired null space of the Jacobian matrix [4][5][6][7]. It has been shown that there are fundamental limitations to the cases where such properties exist [5].…”