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.

翻译：本文提出了一种基于李雅普诺夫指数量化与优化机器人系统稳定性的新方法，解决了机器人分析、设计与优化领域的一个开放性挑战。该方法利用长时间尺度上的可微分仿真技术，所提出的度量指标具有若干重要特性，包括对机器人任务与步态控制中常见极限环的自然扩展。我们通过专门构建的JAX梯度优化框架，展示了该方法在应对鲁棒性挑战方面卓越的性能与灵活性。本方法的有效性通过不同复杂度的多样化场景得到验证，涵盖高自由度系统与密集接触环境。这些案例中的积极成果凸显了本方法在提升系统鲁棒性方面的潜力。