A coefficient matrix GPM method to avoid joint limits for fault tolerant redundant manipulators

When joint failure occurs in a redundant manipulator, it is required that the end-effector (EEF) continues the trajectory with a minimum velocity jump. This problem has been studied by the joint velocity redistribution method which means mapping the velocity of the faulty joint into healthy joints'. This method can tolerant joint fault successfully but may make joints out of their regions. Therefore the gradient projection method (GPM) is adopted to avoid the redistributed joint limits in this paper. With regard to the selection of the scalar coefficient of GPM, an improved method called the coefficient matrix is proposed. Not only can this method avoid joint limits successfully but also reduce the unnecessary self-motion and control the self-motion of each joint separately. At last the coefficient matrix method is tested in a seven-degree-of-freedom (7-DOF) manipulator and the simulation results indicate the efficiency of this method.