High-index norm approach: A redundancy resolution scheme for inverse kinematics of redundant serial manipulators

In this paper, high-index norm approach towards inverse kinematic problem of redundant manipulators is investigated. It is well known that the inverse kinematics problem of redundant manipulator has infinite solutions. Out of these infinite solutions, only those solutions are preferred which fulfill some optimization criterion e.g joint toque minimization, obstacle avoidance, singularity avoidance etc. To calculate the joint velocities, the commonly practiced optimization criterion utilize Euclidean or infinity-norm of vectors in the joint space. This paper investigates the use of high-index norm and its comparison with other norm solutions, in formulating the optimization problem towards inverse kinematic solution of redundant manipulators. Several cases studies are reported to demonstrate the effectiveness of this approach to obtain the inverse kinematic solution, while optimizing secondary criteria like avoiding the joint limits, obstacle avoidance etc.