用几何方法优化轮式与水中机器人的步态，实现复杂运动控制。
Geometric Gait Optimization for Kinodynamic Systems Using a Lie Group Integrator
- 基于李群积分器和对称性设计变分步态优化方法
- 在三种系统上实现加速、定速、转向及步态切换等多样动作
- 适用于具有非完整约束的机器人，适合运动规划研究者
本文提出一种针对兼具运动学与动力学特性的移动系统（如带非完整约束的轮式机器人、具各向异性流体附加质量和水动力阻力的游泳机器人）的步态优化与运动规划框架。通过拉格朗日约化与微分几何推导出通用动力学模型，结合李群积分器与群对称性，构建了适用于这类系统的变分步态优化方法。通过整合多个步态及其转换，生成涵盖多种运动模式的完整运动规划。在滚轮赛车、蛇板和游泳器三个典型系统上进行了仿真与硬件实验，验证了该方法能实现加速、稳态维持、步态切换与转向等多样化运动，结果表明其有效性和对其他生物及机器人系统的可扩展潜力。
原文摘要 · Abstract (English)
This paper presents a gait optimization and motion planning framework for a class of locomoting systems with mixed kinematic and dynamic properties. Using Lagrangian reduction and differential geometry, we derive a general dynamic model that incorporates second-order dynamics and nonholonomic constraints, applicable to kinodynamic systems such as wheeled robots with nonholonomic constraints as well as swimming robots with nonisotropic fluid-added inertia and hydrodynamic drag. Building on Lie group integrators and group symmetries, we develop a variational gait optimization method for kinodynamic systems. By integrating multiple gaits and their transitions, we construct comprehensive motion plans that enable a wide range of motions for these systems. We evaluate our framework on three representative examples: roller racer, snakeboard, and swimmer. Simulation and hardware experiments demonstrate diverse motions, including acceleration, steady-state maintenance, gait transitions, and turning. The results highlight the effectiveness of the proposed method and its potential for generalization to other biological and robotic locomoting systems.
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