Maximal admission of joint range of motion for kinematically redundant manipulators with joint limits

This paper presents a trajectory planning method to avoid joint limits for kinematically redundant manipulators. An inverse kinematic problem for a kinematically redundant manipulator admits an infinite number of solutions. Generally, we can select one of them by introducing a performance criterion. Meanwhile, almost all robotic systems are practically subject to some constraints. In particular, violation of joint limits can deteriorate control performance and, at worst, lead to breakdown of the system. Therefore, in this paper, we propose a trajectory planning method base on a new performance criterion function for avoiding joint limits. The main feature of the function is to admit joint range of motion maximally. The difference between the proposed and conventional functions is also discussed. We adopt the proposed function to the gradient projection method to obtain the redundancy resolution. The validity of the function is demonstrated on some simulations and experiments for a three degrees-of-freedom planar manipulator.