用变分方法模拟蠕动机器人的运动，仅需耗散度量即可精准预测轨迹。
A variational approach to geometric mechanics for undulating robotic locomotion
- 基于几何变分原理构建动力学模型，简化复杂力学关系。
- 仿真与实验平均吻合度高，验证了模型在真实场景中的有效性。
- 适合机器人学、生物运动建模方向的研究者参考。
无肢生物无论大小均通过自变形的波浪模式实现运动。几何力学将形变映射为运动，为研究此类运动模式的理论特性与局限性提供了有力框架。然而，其高度抽象性使得理论或仿真与实验之间存在鸿沟。本文通过比较使用变分积分器进行的实验与仿真，研究了建模蠕动机器人运动轨迹的挑战。尽管模型基于几何变分原理存在广泛简化，仿真结果仍表现出良好的平均一致性。值得注意的是，该方法仅需配置空间上的耗散度量（即黎曼度量），而该度量在实际中可通过类似于阻力力理论的方法近似获得。
原文摘要 · Abstract (English)
Limbless organisms of all sizes use undulating patterns of self-deformation to locomote. Geometric mechanics, which maps deformations to motions, provides a powerful framework to formalize and investigate the theoretical properties and limitations of such modes of locomotion. However, the inherent level of abstraction poses a challenge when bridging the gap between theory or simulations and laboratory experiments. We investigate the challenges of modeling motion trajectories of an undulating robotic locomotor by comparing experiments and simulations performed with a variational integrator. Despite the extensive simplifications that the model based on a geometric variation principle entails, the simulations show good agreement on average. Notably, our approach merely requires the knowledge of the \emph{dissipation metric} -- a Riemannian metric on the configuration space, which can in practice be approximated by means closely resembling \emph{resistive force theory}.
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