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，能够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验证的稳定性保障。尽管本文所开发的工具可支持基于动态运动基元（DMP）的通用机器人运动规划组合方法，但我们重点以动态行走器作为此类系统的研究范式。该方法确保预先设计的运动方案能够稳定执行，其实现途径是将规划过程构建为多平衡点切换系统（SSME），并通过证明在满足DMP间切换频率的适当约束条件下，系统状态轨迹始终保持在显式表征的吸引域内。这些约束条件以易于传递至规划器的形式封装了底层稳定性限制，从而保证所提方案与机器人动力学特性兼容。此外，我们展示了如何在滚动时域框架下在线安全组合现有运动基元，使机器人能够对移动障碍物做出反应。该框架在通用建模假设下的三维双足行走模型上进行验证，为稳定集成现成底层运动控制与高层规划方法提供了模块化解决方案。