In this paper, the inverse kinematics (IK) of redundant manipulators is presented and studied, where the performance of end-effector path planning is guaranteed. A new Jacobian pseudoinverse (JP)-based IK method is proposed and studied using a typical numerical difference rule to discretize the existing IK method based on JP. The proposed method is depicted in a discrete-time form and is theoretically proven to exhibit great performance in the IK of redundant manipulators. A discrete-time repetitive path planning (DTRPP) scheme and a discrete-time obstacle avoidance (DTOA) scheme are developed for redundant manipulators using the proposed method. Comparative simulations are conducted on a universal robot manipulator and a PA10 robot manipulator to validate the effectiveness and superior performance of the DTRPP scheme, the DTOA scheme, and the proposed JP-based IK method.
