Distributed Inverse Dynamics Control for Quadruped Robots using Geometric Optimization

TL;DR

This work addresses the challenge of robust quadruped locomotion under unactuated base dynamics and friction constraints by introducing a distributed inverse dynamics controller (DIDC) that uses full rigid-body dynamics with exact friction cone enforcement. A geometric optimization-based solver, Geometric Projected Gradient Descent (GPGD), avoids friction-cone linearization, enabling fast, embedded-friendly computation. DIDC maps unactuated base forces to the actuated joint space while preserving orthogonality between base and joint tracking, yielding improved base orientation tracking and reduced foot slip. Experimental results in simulation and on the Unitree Go2 demonstrate faster convergence, lower slip, and modest power savings compared with QP-based and NSPIDC methods, indicating practical viability for real-time on-board control.

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 requirements of whole-body controllers. Current methods either ignore friction constraints entirely or use linear approximations, leading to potential slip and instability, while comprehensive whole-body controllers demand 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 required generalized forces corresponding to the actuated and unactuated spaces by projecting them onto the actuated space while satisfying the physical constraints and maintaining orthogonality between the base and joint tracking objectives. Experimental validation shows that our approach reduces foot slippage, improves orientation tracking, and converges at least two times faster than existing reactive controllers with generic QP-based implementations. The controller enables stable omnidirectional trotting at various speeds and consumes less power than comparable methods while running efficiently on embedded processors.

Figures (15)

• Figure 1: Projection of the iterative solution on the friction cone.
• Figure 2: Variation of maximum achievable velocity with base height for different values of $\beta$.
• Figure 3: Software architecture.
• Figure 4: Controller architecture.
• Figure 5: Estimated and reference $Y^{\mathcal{G}}$-axis velocity of the FL foot in simulation.