A Unified Weighted Least Norm Method for Redundant Manipulator Control

Abstract

A redundant manipulator usually has multiple kinematic solutions at the velocity level and can be used to optimize other criteria. Although the pseudo inverse of the Jacobian matrix generates a solution with the least 2 norm (LN), it does not consider other constraints imposed by the system or the environment. The general weighted least norm (GWLN) method handles these general constraints via the concept of virtual joints, but this is not always feasible when the number of constraints exceeds the degrees of freedom. This paper proposes a unified weighted least norm method (UWLN) to unify the LN and the GWLN methods. The UWLN method merges the constraint tasks into a quadratic criterion that poses no limitations on the number of constraint tasks. It also generates a least 2 norm solution when all constraints are deactivated, thereby unifying the LN and GWLN methods. A comparative simulation on a 7-DoF planar manipulator demonstrates the validity of the algorithm.