Motion Accuracy and Computational Effort in QP-based Robot Control

TL;DR

This paper investigates how the accuracy of quadratic program solutions affects robot motion precision and demonstrates that reducing solution accuracy can significantly decrease computational effort without sacrificing motion quality.

Contribution

It is the first study to analyze the impact of QP solution accuracy on robot motion and shows how lowering accuracy requirements can optimize computational resources.

Findings

Reducing QP solution accuracy can decrease computational effort by over 27 times.

Motion accuracy remains unaffected when solution accuracy is lowered to practical levels.

QP solver precision beyond physical and task requirements is unnecessary for humanoid robot control.

Abstract

Quadratic Programs (QPs) have become a mature technology for the control of robots of all kinds, including humanoid robots. One aspect has been largely overlooked, however, which is the accuracy with which these QPs should be solved. QP solvers aim at providing solutions accurate up to floating point precision ($\approx10^{-8}$). Considering physical quantities expressed in SI or similar units (meters, radians, etc.), such precision seems completely unrelated to both task requirements and hardware capacity. Typically, humanoid robots never achieve, nor are capable of achieving sub-millimeter precision in manipulation tasks. With this observation in mind, our objectives in this paper are two-fold: first examine how the QP solution accuracy impacts the resulting robot motion accuracy, then evaluate how a reduced solution accuracy requirement can be leveraged to reduce the corresponding computational effort. Experiments with a dynamic simulation of RHPS-1 humanoid robot indicate that computational effort can be divided by more than 27 while maintaining the desired motion accuracy.