Optimal swimming with body compliance in an overdamped medium

2025-10-03

AI Summary

This study addresses motion optimization of flexible undulatory swimmers in high-damping media (e.g., granular environments). Methodologically, it introduces a novel optimization framework integrating geometric mechanics and compliance modeling: a series of linear springs is incorporated into the Purcell three-link swimmer model, and a compliant-body dynamics model is formulated using resistive force theory, embedded within a unified geometric mechanics–optimal control framework. Theoretical analysis and experiments with a cable-driven limbless robot validate the role of compliance as a robustness-enhancing design element. Key contributions include: (i) the first quantitative characterization—under strong damping—of how compliance parameters affect propulsion efficiency and net displacement; (ii) realization of closed-loop maximum-displacement control under both programmable and state-dependent compliance strategies; and (iii) significant improvements in autonomous environmental adaptability and trajectory prediction accuracy within heterogeneous media.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

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, existing approaches assume precise execution of prescribed gaits, whereas in practice environmental interactions with compliant bodies of animals or robots frequently perturb the realized trajectories. In this work, we extend geometric mechanics to predict locomotor performance and search for optimal swimming strategy of compliant undulators. We introduce a compliant extension of Purcell's three-link swimmer by incorporating series-connected springs at the joints. Body dynamics are derived with 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 homogeneous and heterogeneous environments.

Problem

• Modeling optimal swimming strategies for compliant undulators
• Extending geometric mechanics to predict locomotor performance
• Optimizing control strategies for maximal displacement in compliant swimmers

Innovation

• Extends geometric mechanics for compliant undulators
• Introduces spring-connected joints in swimmer model
• Optimizes control strategies for maximal displacement