Self-reconfiguration of robotic manipulators under joint failure can be achieved via fault-tolerance strategies. Fault-tolerant manipulators are required to continue their end-effector motion with a minimum velocity jump, when failures occur to their joints. Optimal fault tolerance of the manipulators requires a framework that can map the velocity jump of the end-effector to the compensating joint velocity commands. The main objective of the present paper is to propose a general framework for the fault tolerance of the manipulators, which can minimize the end-effector velocity jump. In the present paper, locked joint failures of the manipulators are modeled using matrix perturbation methodology. Then, the optimal mapping for the faults with a minimum end-effector velocity jump is presented. On the basis of this mapping, the minimum end-effector velocity jump is calculated. A generalized framework is derived from the extension of optimal mapping toward multiple locked joint failures. Two novel expressions are derived representing the generalized optimal mapping framework and the generalized minimum velocity jump. These expressions are suitable for the optimal fault tolerance of the serial link redundant manipulators. The required conditions for a zero end-effector velocity jump of the manipulators are analyzed. The generalized framework in this paper is then evaluated for different failure scenarios for a 5-DOF planar manipulator and a 5-DOF spatial manipulator. The validation includes three case studies. While the first two are instantaneous studies, the third one is for the whole trajectory of the manipulators. From the results of these case studies, it is shown that, when locked joint faults occur, the faulty manipulator is able to optimally maintain its velocity with a zero end-effector velocity jump if the conditions of a zero velocity jump are hold.
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