Minimum effort inverse kinematics for redundant manipulators

Abstract

This paper investigates the use of an infinity norm in formulating the optimization measures for computing the inverse kinematics of redundant arms. The infinity norm of a vector is its maximum absolute value component and hence its minimization implies the determination of a minimum effort solution as opposed to the minimum-energy criterion associated with the Euclidean norm. In applications where individual magnitudes of the vector components are of concern, this norm represents the physical requirements more closely than does the Euclidean norm. We first study the minimization of the infinity-norm of the joint velocity vector itself, and discuss its physical interpretation. Next, a new method of optimizing a subtask criterion, defined using the infinity-norm, to perform additional tasks such as obstacle avoidance or joint limit avoidance is introduced. Simulations illustrating these methods and comparing the results with the Euclidean norm solutions are presented.