This paper presents a modular approach to motion planning with provable stability guarantees for robots that move through changing environments via periodic locomotion behaviors. We focus on dynamic walkers as a paradigm for such systems, although the tools developed in this paper can be used to support general compositional approaches to robot motion planning with Dynamic Movement Primitives (DMPs). Our approach ensures a priori that the suggested plan can be stably executed. This is achieved by formulating the planning process as a Switching System with Multiple Equilibria (SSME) and proving that the system's evolution remains within explicitly characterized trapping regions in the state space under suitable constraints on the frequency of switching among the DMPs. These conditions effectively encapsulate the low-level stability limitations in a form that can be easily communicated to the planner to guarantee that the suggested plan is compatible with the robot's dynamics. Furthermore, we show how the available primitives can be safely composed online in a receding horizon manner to enable the robot to react to moving obstacles. The proposed framework is applied on 3D bipedal walking models under common modeling assumptions, and offers a modular approach towards stably integrating readily available low-level locomotion control and high-level planning methods.

翻译：本文提出了一种模块化运动规划方法，为通过周期性运动行为在变化环境中移动的机器人提供可证明的稳定性保障。我们以动态行走器作为这类系统的研究范式，尽管本文开发的方法可支持基于动态运动基元（DMPs）的通用组合式机器人运动规划。该方法确保所建议的运动规划方案能够先验地被稳定执行。通过将规划过程构建为多平衡点切换系统（SSME），并证明在满足DMPs间切换频率的适当约束条件下，系统演化始终保持在状态空间中明确定义的俘获区域内，从而实现上述保障。这些条件将低层稳定性约束转化为易于传递给规划器的形式，确保所提规划方案与机器人动力学兼容。此外，我们展示了如何以滚动时域方式在线安全组合可用基元，使机器人能够对移动障碍物做出实时反应。该框架应用于常见建模假设下的三维双足行走模型，为稳定集成现成低层运动控制与高层规划方法提供了模块化途径。