Enhancing Robotic System Robustness via Lyapunov Exponent-Based Optimization

Abstract: We present a novel approach to quantifying and optimizing stability in robotic systems based on the Lyapunov exponents addressing an open challenge in the field of robot analysis, design, and optimization. Our method leverages differentiable simulation over extended time horizons. The proposed metric offers several properties, including a natural extension to limit cycles commonly encountered in robotics tasks and locomotion. We showcase, with an ad-hoc JAX gradient-based optimization framework, remarkable power, and flexi-bility in tackling the robustness challenge. The effectiveness of our approach is tested through diverse scenarios of varying complexity, encompassing high-degree-of-freedom systems and contact-rich environments. The positive outcomes across these cases highlight the potential of our method in enhancing system robustness.