Motion Accuracy and Computational Effort in QP-based Robot Control

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. Typical 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. Numerical experiments with a dynamic simulation of a HRP-4 robot indicate that computational effort can be divided by more than 20 while maintaining the desired motion accuracy.