Inverse-free computation for infinity-norm torque minimization of robot manipulators

The minimum infinity-norm redundancy resolution, also known as the minimum-effort solution, explicitly minimizes the largest component of joint vectors. It is useful in situations where focuses are on low individual magnitude, even distribution of workload, and analysis of motion diversity. The minimum-effort solution is well investigated at the velocity level. However, because of the weaknesses of torque instability and matrix computation of O(n3) operations, the infinity-norm torque minimization of redundant manipulators seemed less favorable. In this paper, an elegant treatment is presented by resolving redundancy at the acceleration level and reformulating the task as the online solution to a quadratic programming problem. The new computation scheme incorporates three levels of joint physical limits, thus naturally remedying the torque-instability problem. In addition, this new scheme does not entail any matrix inversion or matrix–matrix multiplication, which was entailed in others’ researches with expensive O(n3) operations. The validity and advantages of the new computation scheme are substantiated by simulation results performed based on the PUMA560 robot arm.