Minimum infinity-norm inverse kinematic solution for redundant manipulators

Redundant manipulators admit infinite solutions to the inverse kinematic problem for given end-effector parameters. The problem of determining a minimum infinity norm solution to the velocity inverse kinematic problem, i.e., computing a joint velocity vector whose maximum absolute value component is minimum among all joint velocity vectors yielding the desired end-effector velocity, is investigated. The proposed method uses duality results from functional analysis to determine the solution from a solution to the dual problem, i.e., by determining a force vector that maximizes the work done by the given end-effector velocity with bounded joint torques. An algorithm for obtaining the solution is presented. The minimum-infinity norm solution thus obtained is compared with the pseudoinverse solution