通过环境约束设计高效机器人运动,让系统自适应地自然前行。
Natural Locomotion: Principle and Method

- 用环境约束构建无外部能量输入的内部振荡器,实现自然运动。
- 零均值推进-振荡器交换功率是自然运动的核心条件,需周期性满足。
- 适用于非完整约束系统,适合机器人学与被动动力学研究者。
当机器人运动机制利用被动动力学、柔顺性和共振而非追踪预定轨迹时,其运动可变得高效。本文将自然运动定义为一种由环境约束或相互作用介导的系统交换原则:当内部振荡器周期性返回、身体姿态漂移,且一个周期内推进-振荡器交换功率(POE功率)的均值为零时,该运动即为自然运动。所选族构成自然运动流形(NLM)。我们发展了连续理想环境约束下的保守实现方法:约束不做外功,总机械能守恒,零均值POE功率是系统与环境介导推进通道之间的内部交换,非外部能量输入。方法为闭合/开放构造:先闭合推进通道以揭示有效内部振荡器,其组织结构在单自由度下为标量作用-角变量,在多自由度下为非线性模态分量;再重新打开通道,重构姿态,接受的周期必须保持内部重复性与零均值POE功率。我们在两个理想非完整无滑系统上验证:一个带摆驱动的Chaplygin雪橇/汽车模型及其三体扩展。在单自由度情况下,POE闭合等价于缺失的内部返回条件,给出基于定理的NLM族计算方法;在多自由度下,POE闭合仍必要,但还需模态一致、内部返回、动力学一致性、相同被动架构及非零位移。自然运动由此转化为设计问题:哪些被动架构支持零个、一个或多个经认证的NLM族?
原文摘要 · Abstract (English)
Robotic locomotion can become efficient when mechanisms exploit passive dynamics, compliance, and resonance rather than track prescribed trajectories. This paper formulates natural locomotion as an exchange principle for systems whose motion is mediated by environmental constraints or interactions. A motion is natural when an internal oscillator returns periodically, the body pose drifts, and the mean Propulsion--Oscillator Exchange power (POE power) vanishes over one cycle. The selected family is a Natural Locomotion Manifold (NLM). We develop the conservative realization of this principle for continuous ideal environmental constraints: the constraints do no external work, total mechanical energy is conserved, and zero mean POE power is an internal exchange with the environment-mediated propulsive channel, not external energy input. The method is a closed/open construction. The propulsive channel is first closed to reveal an effective internal oscillator, organized by scalar action-angle structure in one effective degree of freedom or by nonlinear modal sectors in several degrees of freedom. The channel is then reopened, pose is reconstructed, and accepted cycles must preserve internal recurrence and zero mean POE power. We demonstrate the principle on two ideal nonholonomic no-slip systems: a Chaplygin-sleigh / pendulum-driven car and a three-body extension. In the scalar case, POE closure is equivalent to the missing internal return condition, giving a theorem-backed computation of the NLM family. In the multi-degree case, POE closure remains necessary but must be completed by modal identity, internal return, dynamics consistency, same fixed passive architecture, and nonzero displacement. Natural locomotion becomes a design question: which passive architectures support no, one, or several certified NLM families?
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