Legged robots offer several advantages when navigating unstructured environments, but they often fall short of the efficiency achieved by wheeled robots. One promising strategy to improve their energy economy is to leverage their natural (unactuated) dynamics using elastic elements. This work explores that concept by designing energy-optimal control inputs through a unified, multi-stage framework. It starts with a novel energy injection technique to identify passive motion patterns by harnessing the system's natural dynamics. This enables the discovery of passive solutions even in systems with energy dissipation caused by factors such as friction or plastic collisions. Building on these passive solutions, we then employ a continuation approach to derive energy-optimal control inputs for the fully actuated, dissipative robotic system. The method is tested on simulated models to demonstrate its applicability in both single- and multi-legged robotic systems. This analysis provides valuable insights into the design and operation of elastic legged robots, offering pathways to improve their efficiency and adaptability by exploiting the natural system dynamics.

翻译：腿式机器人在非结构化环境中导航具有若干优势，但其效率往往不及轮式机器人。一种有前景的策略是利用弹性元件来发挥其自然（无驱动）动力学特性，以改善其能量经济性。本研究通过设计一个统一的多阶段框架来探索这一概念，以获取能量最优的控制输入。该框架始于一种新颖的能量注入技术，通过利用系统的自然动力学来识别被动运动模式。这使得即使在因摩擦或塑性碰撞等因素导致能量耗散的系统中，也能发现被动解。基于这些被动解，我们随后采用延拓方法，为完全驱动、耗散的机器人系统推导出能量最优的控制输入。该方法在仿真模型上进行了测试，以证明其在单腿和多腿机器人系统中的适用性。该分析为弹性腿式机器人的设计与操作提供了有价值的见解，通过利用系统自然动力学，为提高其效率和适应性提供了途径。