用时空管方法实现不确定环境下的安全动态任务规划
Spatiotemporal Tubes for Probabilistic Temporal Reach-Avoid-Stay Task in Uncertain Dynamic Environment
- 构建随时间变化的时空管，基于传感器信息在线更新中心与半径
- 无需模型、近似或优化，实现概率安全与任务完成的严格保证
- 适用于移动机器人、无人机和机械臂，真实场景验证有效
本文将时空管（STT）框架扩展至处理动态环境中存在不确定障碍物的随机时间可达-避障-停留（PrT-RAS）任务。提出一种实时管生成方法，显式考虑时变不确定性障碍物，并提供形式化概率安全保证。时空管在状态空间中表示为随时间变化的球体，其中心与半径根据不确定感知信息在线演化。推导出闭式、无近似的控制律，确保系统轨迹始终位于管内，从而保障概率安全性与任务满足性。所提方法为模型无关、无近似、无优化，支持高效实时执行并保证收敛至目标。通过移动机器人、无人机及7自由度机械臂在杂乱不确定环境中的仿真与硬件实验，验证了该框架的有效性与可扩展性。
原文摘要 · Abstract (English)
In this work, we extend the Spatiotemporal Tube (STT) framework to address Probabilistic Temporal Reach-Avoid-Stay (PrT-RAS) tasks in dynamic environments with uncertain obstacles. We develop a real-time tube synthesis procedure that explicitly accounts for time-varying uncertain obstacles and provides formal probabilistic safety guarantees. The STT is formulated as a time-varying ball in the state space whose center and radius evolve online based on uncertain sensory information. We derive a closed-form, approximation-free control law that confines the system trajectory within the tube, ensuring both probabilistic safety and task satisfaction. Our method offers a formal guarantee for probabilistic avoidance and finite-time task completion. The resulting controller is model-free, approximation-free, and optimization-free, enabling efficient real-time execution while guaranteeing convergence to the target. The effectiveness and scalability of the framework are demonstrated through simulation studies and hardware experiments on mobile robots, a UAV, and a 7-DOF manipulator navigating in cluttered and uncertain environments.
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