Fault tolerance force for redundant manipulators

Fault tolerant manipulators maintain their trajectory even if their joint/s fails. Assuming that the manipulator is fault tolerant on its trajectory, fault tolerant compliance manipulators provide required force at their end-effector even when a joint fails. To achieve this, the contributions of the faulty joints for the force of the end-effector are required to be mapped into the proper compensating joint torques of the healthy joints to maintain the force. This paper addresses the optimal mapping to minimize the force jump due to a fault, which is the maximum effort to maintain the force when a fault occurs. The paper studies the locked joint fault/s of the redundant manipulators and it relates the force jump at the end-effector to the faults within the joints. Adding on a previous study to maintain the trajectory, in here the objective is to providing fault tolerant force at the end-effector of the redundant manipulators. This optimal mapping with minimum force jump is presented using matrix perturbation model. And the force jump is calculated through this model for single and multiple joints fault. The proposed optimal mapping is used in different fault scenarios for a 5-DOF manipulator; also it is deployed to compensate the force at the end-effector for the 5-DOF manipulator through simulation study and the results are presented.