Spatiotemporal Tubes for Differential Drive Robots with Model Uncertainty

2025-12-05

AI Summary

Ensuring time-arrival, obstacle avoidance, and stationary holding (T-RAS) for differentially driven robots under dynamics uncertainty and external disturbances remains challenging. Method: This paper proposes a robust control framework based on a smooth time-varying circular spatio-temporal tube (STT). A sampling-based synthesis algorithm generates dynamically feasible, temporally safe corridors satisfying both timing and collision-avoidance constraints; an analytical, model-free, non-optimization-based closed-loop control law is then designed to provably confine the system state within the STT at all times. Contribution/Results: By integrating spatio-temporal modeling with robust control theory, the approach provides formal safety and timing guarantees. Simulations demonstrate superior robustness, tracking accuracy, and computational efficiency over state-of-the-art methods, enabling real-time, reliable navigation in complex dynamic environments.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Intelligent Robots: State Estimation
• Natural Language Processing: Safety and Robustness

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Data transparency and provenance

Abstract

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.

Problem

• Ensures safe robot navigation under model uncertainties
• Guarantees timing and safety with formal constraints
• Provides robust control without approximations or optimization

Innovation

• Spatiotemporal Tube defines dynamic safe corridors
• Sampling-based algorithm constructs feasible tube with guarantees
• Closed-form control law ensures confinement without approximations