Robotic system performance enhancement through redundant design

A redundant manipulator possesses an infinite number of solutions to the inverse kinematics. The difference between any two solutions is always mapped by the Jacobian matrix to the zero vector of Cartesian space. With a rank solution being defined to represent the execution of the highest priority (main) task, the null solutions can be utilized to represent the execution of lower priority tasks for performance enhancement purposes. This paper presents a 9-joint manipulator design and the utilization of three null space vectors to simultaneously perform three subtasks while a main task of trajectory-tracking is executed. A unified weighting procedure is developed to incorporate three subtasks for their optimization. Through the input-output exact-linearization procedure, a closed-loop state-feedback kinematic control model is proposed