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Reach-Avoid-Stay-Collision-Avoidance Negotiation Framework for Multi-Agent Systems via Spatiotemporal Tubes

Mohd. Faizuddin Faruqui, Ratnangshu Das, Ravi Kumar L, Pushpak Jagtap

TL;DR

This work tackles safe, time-constrained navigation for multiple agents with unknown dynamics by formulating a prescribed-time Reach-Avoid-Stay with Collision Avoidance ($RASCA$) problem. It introduces a distributed, abstraction-free method built on Spatiotemporal Tubes (STTs) and a negotiation mechanism that assigns parameterized tubes to agents, ensuring collision-free corridors and adherence to prescribed times $t_p^{(i)}$ for all $i$. A three-segment, negotiation-enhanced tube framework paired with a dynamics-agnostic controller provides robustness to disturbances and unknown dynamics, with theoretical guarantees of collision avoidance via the NEGOTIATECOLLISION algorithm and practical validation in robot and drone simulations. The approach demonstrates scalable, distributed coordination in dense environments and points to future work on game-theoretic prioritization to further mitigate potential negotiation deadlocks.

Abstract

This study presents a multi-agent negotiation-based framework to obtain collision-free paths while performing prescribed-time reach-avoid-stay (RAS) tasks for agents with unknown dynamics and bounded disturbance. By employing spatiotemporal tubes to generate time-varying state constraints, we ensure that all agents adhere to RAS specifications using synthesized controllers. To prevent inter-agent collisions, a negotiation mechanism is proposed where successful negotiations result in spatiotemporal tubes for each agent fulfilling desired tasks. This approach results in a completely distributed, approximation-free control law for each agent. The effectiveness of this mechanism was validated through simulations of multi-agent robot navigation and drone navigation tasks involving prescribed-time RAS specifications and collision avoidance.

Reach-Avoid-Stay-Collision-Avoidance Negotiation Framework for Multi-Agent Systems via Spatiotemporal Tubes

TL;DR

This work tackles safe, time-constrained navigation for multiple agents with unknown dynamics by formulating a prescribed-time Reach-Avoid-Stay with Collision Avoidance () problem. It introduces a distributed, abstraction-free method built on Spatiotemporal Tubes (STTs) and a negotiation mechanism that assigns parameterized tubes to agents, ensuring collision-free corridors and adherence to prescribed times for all . A three-segment, negotiation-enhanced tube framework paired with a dynamics-agnostic controller provides robustness to disturbances and unknown dynamics, with theoretical guarantees of collision avoidance via the NEGOTIATECOLLISION algorithm and practical validation in robot and drone simulations. The approach demonstrates scalable, distributed coordination in dense environments and points to future work on game-theoretic prioritization to further mitigate potential negotiation deadlocks.

Abstract

This study presents a multi-agent negotiation-based framework to obtain collision-free paths while performing prescribed-time reach-avoid-stay (RAS) tasks for agents with unknown dynamics and bounded disturbance. By employing spatiotemporal tubes to generate time-varying state constraints, we ensure that all agents adhere to RAS specifications using synthesized controllers. To prevent inter-agent collisions, a negotiation mechanism is proposed where successful negotiations result in spatiotemporal tubes for each agent fulfilling desired tasks. This approach results in a completely distributed, approximation-free control law for each agent. The effectiveness of this mechanism was validated through simulations of multi-agent robot navigation and drone navigation tasks involving prescribed-time RAS specifications and collision avoidance.

Paper Structure

This paper contains 12 sections, 2 theorems, 17 equations, 4 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Notation and Preliminaries
  3. System and Topology
  4. Problem Formulation
  5. Spatiotemporal Tubes (STT)
  6. Negotiation using parameterized tubes
  7. Controller synthesis
  8. Simulations
  9. Case Study-1: Robot Navigation
  10. Case Study-2: Drone Navigation
  11. Comparison
  12. Conclusion and Future Work

Key Result

Theorem IV.3

Given the multi-agent system $\Sigma$ satisfying Assumption assum0 and assum1, the state space X, communication graph $G = \lbrace \mathcal{I}, \mathcal{E} \rbrace$, set of initial sets $S=\lbrace S_i \rbrace_{i\in \mathcal{I}}$ and set of target sets $T=\lbrace T_i \rbrace_{i\in \mathcal{I}}$, the which ensures that the parameterized tubes are collision-free.

Figures (4)

  • Figure 1: Negotiation Sequence: Iteration-1
  • Figure 2: RASCA task in a 2D arena for Robotic navigation and respective temporal tubes (T-Col-S and T-Col-E are tube collision $\textit{Start}$ and $\textit{End}$ instances and O-Col-S and O-Col-E are obstacle collision $\textit{Start}$ and $\textit{End}$ instances respectively)
  • Figure 3: 3 Agents navigation: RASCA task
  • Figure 4: Drone Navigation: Collision Avoidance

Theorems & Definitions (10)

  • Remark II.1
  • Definition II.2: Prescribed time RASCA task
  • Remark II.3
  • Definition III.1: Spatiotemporal Tubes for PT-RASCA
  • Definition IV.1: Collision Interval for an Agent
  • Definition IV.2
  • Theorem IV.3
  • proof
  • Theorem V.1
  • Remark V.2