Temporal Reach-Avoid-Stay Control for Differential Drive Systems via Spatiotemporal Tubes

TL;DR

This paper introduces a lightweight control framework using spatiotemporal tubes for differential-drive robots, ensuring safety and goal achievement despite uncertainties and disturbances.

Contribution

It develops a novel sampling-based synthesis and a closed-form control method for safe, robust, and efficient robot navigation within dynamic corridors.

Findings

The method guarantees safety and goal reachability with formal assurances.

Simulation shows superior robustness and efficiency compared to existing methods.

The control framework is computationally lightweight and suitable for real-time applications.

Abstract

This paper presents a computationally lightweight and robust 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 spatiotemporal tubes (STTs), 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 analytically design a closed-form control that is computationally efficient and robust to disturbances. 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.