Redundancy resolution of manipulators through torque optimization

TLDR

The study examines methods for resolving kinematic redundancies in manipulators by optimizing joint torque. The authors formulate the generalized inverse using accelerations and dynamics, then select the joint acceleration null‑space vector to minimize joint torque in a weighted least‑squares sense, comparing this with pseudoinverse methods with and without inertia weighting. The experiments reveal that null‑space and inertia‑weighted pseudoinverse methods suffer from stability issues on long trajectories, causing whiplash effects and excessive torques, whereas the unweighted pseudoinverse performs more reliably.

Abstract

Methods for resolving kinematic redundancies of manipulators by the effect on joint torque are examined. When the generalized inverse is formulated in terms of accelerations and incorporated into the dynamics, the effect of redundancy resolution on joint torque can be directly reflected. One method chooses the joint acceleration null-space vector to minimize joint torque in a least squares sense; when the least squares is weighted by allowable torque range, the joint torques tend to be kept within their limits. Contrasting methods employing only the pseudoinverse with and without weighting by the inertia matrix are presented. The results show an unexpected stability problem during long trajectories for the null-space methods and for the inertia-weighted pseudoinverse method, but more seldom for the unweighted pseudoinverse method. Evidently, a whiplash action develops over time that thrusts the endpoint off the intended path, and extremely high torques are required to overcome these natural movement dynamics.