This paper presents a Spatiotemporal Tube (STT)-based control framework for differential-drive mobile robots with dynamic uncertainties and external disturbances, guaranteeing the satisfaction of Temporal Reach-Avoid-Stay (T-RAS) specifications. The approach employs circular STT, characterized by smoothly time-varying center and radius, to define dynamic safe corridors that guide the robot from the start region to the goal while avoiding obstacles. In particular, we first develop a sampling-based synthesis algorithm to construct a feasible STT that satisfies the prescribed timing and safety constraints with formal guarantees. To ensure that the robot remains confined within this tube, we then design analytically a closed-form, approximation-free control law. The resulting controller is computationally efficient, robust to disturbances and {model uncertainties}, and requires no model approximations or online optimization. The proposed framework is validated through simulation studies on a differential-drive robot and benchmarked against state-of-the-art methods, demonstrating superior robustness, accuracy, and computational efficiency.

翻译：本文提出了一种基于时空管（Spatiotemporal Tube，STT）的控制框架，用于处理具有动态不确定性和外部扰动的差速驱动移动机器人，确保满足时间可达-避障-驻留（Temporal Reach-Avoid-Stay，T-RAS）规范。该方法采用圆形时空管，其特征为中心和半径随时间平滑变化，以定义动态安全走廊，引导机器人从起始区域到达目标区域，同时避开障碍物。具体而言，我们首先开发了一种基于采样的综合算法，用于构建满足预设时序与安全约束的可行时空管，并提供形式化保证。为确保机器人始终约束在该管内，我们随后通过解析方法设计了一种闭式、无近似的控制律。所得控制器计算高效，对扰动和模型不确定性具有鲁棒性，且无需模型近似或在线优化。通过差速驱动机器人的仿真研究，并与先进方法进行对比验证，所提框架展现了更优的鲁棒性、精度和计算效率。