Distributed Inverse Dynamics Control for Quadruped Robots using Geometric Optimization

Abstract This paper presents a distributed inverse dynamics controller (DIDC) for quadruped robots that addresses the limitations of existing reactive controllers: simplified dynamical models, the inability to handle exact friction cone constraints, and the high computational and energy requirements of whole-body controllers. Current methods either ignore friction constraints entirely or use linear approximations, which can lead to potential slip and instability, while comprehensive whole-body controllers require significant computational resources. Our approach uses full rigid-body dynamics and enforces exact friction cone constraints through a novel geometric optimization-based solver. DIDC combines the generalized forces required for the actuated and unactuated spaces by projecting them onto the actuated space, while satisfying physical constraints and maintaining orthogonality between the base and joint tracking objectives. Experimental validation shows that our approach reduces the required energy (and the cost-of-transport) and improves orientation tracking. The geometric solver is benchmarked against existing off-the-shelf QP solvers for the quadruped control optimization task. The controller enables stable omnidirectional trotting at various speeds and consumes less power than comparable methods, while running efficiently on embedded processors.