5 Redundancy Resolution via QP Approach and Unification

A redundant manipulator is defined when more degrees of freedom (DOF) are available than the minimum number of DOF required to execute a given end-effector primary task. Our human arm, elephant trunk, and snake are also such redundant systems. Compared to non-redundant manipulators, the redundant manipulator naturally has wider operational space and extra degrees to meet more functional constraints, such as the online avoidance of joint physical limits and environmental obstacles. One of the most fundamental issues in operating the redundant manipulators is the redundancy-resolution problem. That is, given the Cartesian velocity/acceleration trajectories of the end-effector, we are required to generate the corresponding joint velocity, acceleration, and/or torque trajectories in real time.