Elongate animals and robots use undulatory body waves to locomote through diverse environments. Geometric mechanics provides a framework to model and optimize such systems in highly damped environments, connecting a prescribed shape change pattern (gait) with locomotion displacement. However, the practical applicability of controlling compliant physical robots remains to be demonstrated. In this work, we develop a framework based on geometric mechanics to predict locomotor performance and search for optimal swimming strategies of compliant swimmers. We introduce a compliant extension of Purcell's three-link swimmer by incorporating series-connected springs at the joints. Body dynamics are derived using resistive force theory. Geometric mechanics is incorporated into movement prediction and into an optimization framework that identifies strategies for controlling compliant swimmers to achieve maximal displacement. We validate our framework on a physical cable-driven three-link limbless robot and demonstrate accurate prediction and optimization of locomotor performance under varied programmed, state-dependent compliance in a granular medium. Our results establish a systematic, physics-based approach for modeling and controlling compliant swimming locomotion, highlighting compliance as a design feature that can be exploited for robust movement in both homogeneous and heterogeneous environments.

翻译：细长型动物与机器人利用体波摆动在不同环境中实现运动。几何力学为在高阻尼环境中建模与优化此类系统提供了理论框架，将预设的形态变化模式（步态）与运动位移相关联。然而，控制柔顺性物理机器人的实际应用仍有待验证。本研究建立了基于几何力学的理论框架，用于预测柔顺游动体的运动性能并搜寻其最优游动策略。我们通过在关节处引入串联弹簧，构建了普塞尔三连杆游动体的柔顺性扩展模型。利用阻力理论推导了身体动力学方程。将几何力学方法融入运动预测及优化框架中，以识别控制柔顺游动体实现最大位移的策略。我们在物理缆绳驱动的三连杆无肢机器人上验证了该框架，并在颗粒介质中通过编程实现不同状态依赖的柔顺性，准确预测并优化了运动性能。研究结果建立了基于物理的系统化方法，用于建模与控制柔顺游动运动，揭示了柔顺性作为设计特征在均质与非均质环境中均可用于实现鲁棒运动。