On The Sudden Change of Joint Velocity During Fault Tolerant Operations for Manipulators with Mul Tiple Degrees of Redundancy

The sudden change of joint velocity during fault tolerant operations for redundant manipulators is defined,and the analytical formulation of joint velocity of the reduced manipulator with minimum sudden change of joint velocity 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 sudden change of joint velocity 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.Final results indicate that utilizing the manipulators with multiple degrees of redundancy can obviously reduce sudden change of joint velocity thereby improving their motion stability in fault tolerant operations.