We present a novel differentiable approach to quantifying and optimizing stability in robotic systems addressing an open challenge in the field of robot analysis, control, design, and optimization. Our method leverages differentiable simulation over extended time horizons to estimate a robustness metric based on the Lyapunov exponents. The proposed metric offers several properties, including a natural extension to limit cycles (commonly encountered in robotics tasks and locomotion) and independence from the trajectory path for states converging to the attractor. We showcase, with an ad-hoc JAX gradient-based optimization framework, remarkable flexibility in tackling the robustness challenge. 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 quantifying and possibly enhancing system robustness.

This paper presents a computational framework for the design of high-performance legged robotic systems. The framework relies on the concurrent optimization of hardware parameters and control trajectories to find the best robot design for a given task. In particular, we focus on energy efficiency, presenting novel electro-mechanical models to account for the losses of the actuators due to friction and Joule effects. Thanks to a bi-level optimization scheme, featuring a genetic algorithm in the outer loop, our framework can also optimize for the duration of the motion, the actuators, and the size of the robot. We present a novel approach to scale both the actuators and the robot structure in a way that ensures structural integrity by maintaining constant the normalized deflection of the links. We validated our approach by designing a two-joint monoped robot to execute a jumping task. Our simulation results show that our framework can lead to remarkable energy savings (up to 60%) thanks to the concurrent optimization of robot size, motion duration, and actuators.