A weighted least-norm solution based scheme for avoiding joint limits for redundant joint manipulators

It is proposed to use weighted least-norm solution to avoid joint limits for redundant joint manipulators. A comparison is made with the gradient projection method for avoiding joint limits. While the gradient projection method provides the optimal direction for the joint velocity vector within the null space, its magnitude is not unique and is adjusted by a scalar coefficient chosen by trial and error. It is shown in this paper that one fixed value of the scalar coefficient is not suitable even in a small workspace. The proposed manipulation scheme automatically chooses an appropriate magnitude of the self-motion throughout the workspace. This scheme, unlike the gradient projection method, guarantees joint limit avoidance, and also minimizes unnecessary self-motion. It was implemented and tested for real-time control of a seven-degree-of-freedom (7-DOF) Robotics Research Corporation (RRC) manipulator