On the joint velocity jump during fault tolerant operations for manipulators with multiple degrees of redundancy

The joint velocity jump during fault tolerant operations for redundant manipulators is defined, and the analytical formulation of joint velocity of the reduced manipulator with minimum joint velocity jump is derived. Based on this, the projection of the least-norm velocity vector for the remaining joints of a manipulator onto the null space of the reduced manipulator is mathematically proved to be a zero vector. This implies that when a manipulator follows the motion law determined by the least-norm joint velocity solution, in order to minimize the joint velocity jump at the moment of locking joint, the optimal joint velocity of the reduced manipulator is its least-norm solution. This conclusion is suitable for any planar and spatial manipulators with multiple degrees of redundancy. Simulation examples are implemented with a planar 4R manipulator and a spatial 5R manipulator, and an experiment study is also preliminarily done. Final results indicate that utilizing the manipulators with multiple degrees of redundancy can obviously reduce the joint velocity jump thereby improving their motion stability in fault tolerant operations.