MINIMUM EFFORT INVERSE KINEMATICS FOR REDUNDANT MANIPULATORS

Kinematically redundant manipulators admit an infinite choice of inver se kinematic solutions and hence lend themselves to the optimization o f different performance measures corresponding to various task require ments. Joint velocities for these mechanisms are most often computed b y optimizing various criteria defined using the Euclidean norm of vect ors in the joint space. This paper investigates the use of an alternat e norm, viz. the infinity norm, in formulating the optimization measur es for computing the inverse kinematics of redundant arms. The infinit y norm of a vector is its maximum absolute value component and hence i ts minimization implies the determination of a minimum-effort solution as opposed to the minimum-energy criterion associated with the Euclid ean norm. In applications where individual magnitudes of the vector co mponents are of concern, this norm represents the physical requirement s more closely than does the Euclidean norm. We first study the minimi zation of the infinity-norm of the joint velocity vector itself, and d iscuss its physical interpretation. Next, a new method of optimizing a subtask criterion, defined using the infinity-norm, to perform additi onal tasks such as obstacle avoidance or joint limit avoidance is intr oduced. Simulations illustrating these methods and comparing the resul ts with the Euclidean norm solutions are presented.