标题： 最优步态族的几何特性用于操纵运动学移动系统 显示英文标题

标题： The Geometry of Optimal Gait Families for Steering Kinematic Locomoting Systems

摘要： 运动规划对于运动系统通常需要将高层刚体任务转换为低层关节轨迹——这一过程对于具有固定、无限执行器输入的汽车类机器人来说是直接的，但对于蛇形机器人等系统则更具挑战性，因为映射依赖于当前配置，并受到关节限制的约束。 在本文中，我们专注于生成连续的最优步态族——由步长或转向速率参数化的步态集合——以提高可控性和机动性。 我们揭示了这些最优步态族的底层几何结构，并提出了使用全局和局部搜索策略来构建它们的方法，其中局部方法和全局方法相互补充。 全局搜索方法对非光滑行为具有鲁棒性，尽管会得到降阶解，而局部搜索提供更高的准确性，但在非光滑区域附近可能不稳定。 为了展示我们的框架，我们为粘性流体和理想流体的三链接游泳者生成了最优步态族。 这项工作为在复杂的运动系统中将低层关节控制器与高层运动规划器集成奠定了基础。 显示英文摘要

摘要： Motion planning for locomotion systems typically requires translating high-level rigid-body tasks into low-level joint trajectories-a process that is straightforward for car-like robots with fixed, unbounded actuation inputs but more challenging for systems like snake robots, where the mapping depends on the current configuration and is constrained by joint limits. In this paper, we focus on generating continuous families of optimal gaits-collections of gaits parameterized by step size or steering rate-to enhance controllability and maneuverability. We uncover the underlying geometric structure of these optimal gait families and propose methods for constructing them using both global and local search strategies, where the local method and the global method compensate each other. The global search approach is robust to nonsmooth behavior, albeit yielding reduced-order solutions, while the local search provides higher accuracy but can be unstable near nonsmooth regions. To demonstrate our framework, we generate optimal gait families for viscous and perfect-fluid three-link swimmers. This work lays a foundation for integrating low-level joint controllers with higher-level motion planners in complex locomotion systems.