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Spatiotemporal Tubes based Control of Unknown Multi-Agent Systems for Temporal Reach-Avoid-Stay Tasks

Ahan Basu, Ratnangshu Das, Pushpak Jagtap

TL;DR

This work tackles decentralized control of unknown multi-agent systems under temporal reach-avoid-stay constraints with time-varying obstacles and inter-agent collision avoidance. It introduces spatiotemporal tubes (STTs) whose boundaries are computed via a sampling-based scenario optimization (SOP) that approximates a robust optimization problem (ROP), enabling formal guarantees (certified confidence 1) that each agent reaches its target within a prescribed time while staying outside unsafe regions and avoiding other agents. A closed-form, approximation-free, decentralized controller is then designed to constrain each agent's trajectory inside its STT, using a backstepping-like scheme with stage-wise error transforms and gains. The approach is demonstrated on two case studies—omnidirectional robots and Euler-Lagrange drones—showing successful T-RAS and CA satisfaction, with practical computation times and explicit tube parameters, highlighting scalability to high-dimensional uncertain MAS. The work advances safe, scalable coordination under uncertainty with formal guarantees and minimal modeling assumptions, suitable for real-time deployment in safety-critical autonomous systems.

Abstract

The paper focuses on designing a controller for unknown dynamical multi-agent systems to achieve temporal reach-avoid-stay tasks for each agent while preventing inter-agent collisions. The main objective is to generate a spatiotemporal tube (STT) for each agent and thereby devise a closed-form, approximation-free, and decentralized control strategy that ensures the system trajectory reaches the target within a specific time while avoiding time-varying unsafe sets and collisions with other agents. In order to achieve this, the requirements of STTs are formulated as a robust optimization problem (ROP) and solved using a sampling-based scenario optimization problem (SOP) to address the issue of infeasibility caused by the infinite number of constraints in ROP. The STTs are generated by solving the SOP, and the corresponding closed-form control is designed to fulfill the specified task. Finally, the effectiveness of our approach is demonstrated through two case studies, one involving omnidirectional robots and the other involving multiple drones modelled as Euler-Lagrange systems.

Spatiotemporal Tubes based Control of Unknown Multi-Agent Systems for Temporal Reach-Avoid-Stay Tasks

TL;DR

This work tackles decentralized control of unknown multi-agent systems under temporal reach-avoid-stay constraints with time-varying obstacles and inter-agent collision avoidance. It introduces spatiotemporal tubes (STTs) whose boundaries are computed via a sampling-based scenario optimization (SOP) that approximates a robust optimization problem (ROP), enabling formal guarantees (certified confidence 1) that each agent reaches its target within a prescribed time while staying outside unsafe regions and avoiding other agents. A closed-form, approximation-free, decentralized controller is then designed to constrain each agent's trajectory inside its STT, using a backstepping-like scheme with stage-wise error transforms and gains. The approach is demonstrated on two case studies—omnidirectional robots and Euler-Lagrange drones—showing successful T-RAS and CA satisfaction, with practical computation times and explicit tube parameters, highlighting scalability to high-dimensional uncertain MAS. The work advances safe, scalable coordination under uncertainty with formal guarantees and minimal modeling assumptions, suitable for real-time deployment in safety-critical autonomous systems.

Abstract

The paper focuses on designing a controller for unknown dynamical multi-agent systems to achieve temporal reach-avoid-stay tasks for each agent while preventing inter-agent collisions. The main objective is to generate a spatiotemporal tube (STT) for each agent and thereby devise a closed-form, approximation-free, and decentralized control strategy that ensures the system trajectory reaches the target within a specific time while avoiding time-varying unsafe sets and collisions with other agents. In order to achieve this, the requirements of STTs are formulated as a robust optimization problem (ROP) and solved using a sampling-based scenario optimization problem (SOP) to address the issue of infeasibility caused by the infinite number of constraints in ROP. The STTs are generated by solving the SOP, and the corresponding closed-form control is designed to fulfill the specified task. Finally, the effectiveness of our approach is demonstrated through two case studies, one involving omnidirectional robots and the other involving multiple drones modelled as Euler-Lagrange systems.
Paper Structure (10 sections, 5 theorems, 36 equations, 2 figures, 6 tables, 1 algorithm)

This paper contains 10 sections, 5 theorems, 36 equations, 2 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Formulation
  3. System Definition
  4. Problem Formulation
  5. Construction of Spatiotemporal Tubes
  6. Controller Design
  7. Case Study
  8. Omnidirectional Robots
  9. Euler-Lagrange System- Multiple Drones
  10. Conclusion and Future work

Key Result

Lemma 3.1

Equation eq:collision implies that for all $j,k \in [1;M], \space j \neq k$, there exists $i\in[1;n]$, such that:

Figures (2)

  • Figure 1: Spatiotemporal tubes for T-RAS tasks in omnidirectional robots.
  • Figure 2: Spatiotemporal tubes for T-RAS tasks in drones.

Theorems & Definitions (21)

  • Definition 2.1: Temporal reach-avoid-stay (T-RAS) task
  • Remark 2.2
  • Remark 2.3
  • Definition 2.4: Inter-agent Collision Avoidance (CA) task
  • Remark 2.5
  • Definition 2.7: Spatiotemporal tubes (STT) for T-RAS task
  • Remark 2.8
  • Lemma 3.1
  • Proof 3.2
  • Remark 3.3
  • ...and 11 more