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Incorporating Social Awareness into Control of Unknown Multi-Agent Systems: A Real-Time Spatiotemporal Tubes Approach

Siddhartha Upadhyay, Ratnangshu Das, Pushpak Jagtap

TL;DR

The paper addresses safe, coordinated control of multiple agents with unknown dynamics, aiming for prescribed-time reach-avoid-stay (TRAS) tasks in dynamic environments. It introduces a decentralized real-time spatiotemporal tube (STT) framework that jointly synthesizes per-agent tubes and a socially aware interaction policy, encoded by a Social Interaction Function and a Social Awareness Index, to handle heterogeneous cooperation. A closed-form, approximation-free controller is derived to keep each agent's output within its evolving STT while avoiding dynamic obstacles and inter-agent collisions, with formal guarantees on safety and timing. The approach is demonstrated through 2D hardware and simulations with omnidirectional robots and a 3D UAV scenario, showing real-time computation, model-free robustness to disturbances, and scalability to larger teams while respecting diverse social behaviors.

Abstract

This paper presents a decentralized control framework that incorporates social awareness into multi-agent systems with unknown dynamics to achieve prescribed-time reach-avoid-stay tasks in dynamic environments. Each agent is assigned a social awareness index that quantifies its level of cooperation or self-interest, allowing heterogeneous social behaviors within the system. Building on the spatiotemporal tube (STT) framework, we propose a real-time STT framework that synthesizes tubes online for each agent while capturing its social interactions with others. A closed-form, approximation-free control law is derived to ensure that each agent remains within its evolving STT, thereby avoiding dynamic obstacles while also preventing inter-agent collisions in a socially aware manner, and reaching the target within a prescribed time. The proposed approach provides formal guarantees on safety and timing, and is computationally lightweight, model-free, and robust to unknown disturbances. The effectiveness and scalability of the framework are validated through simulation and hardware experiments on a 2D omnidirectional

Incorporating Social Awareness into Control of Unknown Multi-Agent Systems: A Real-Time Spatiotemporal Tubes Approach

TL;DR

The paper addresses safe, coordinated control of multiple agents with unknown dynamics, aiming for prescribed-time reach-avoid-stay (TRAS) tasks in dynamic environments. It introduces a decentralized real-time spatiotemporal tube (STT) framework that jointly synthesizes per-agent tubes and a socially aware interaction policy, encoded by a Social Interaction Function and a Social Awareness Index, to handle heterogeneous cooperation. A closed-form, approximation-free controller is derived to keep each agent's output within its evolving STT while avoiding dynamic obstacles and inter-agent collisions, with formal guarantees on safety and timing. The approach is demonstrated through 2D hardware and simulations with omnidirectional robots and a 3D UAV scenario, showing real-time computation, model-free robustness to disturbances, and scalability to larger teams while respecting diverse social behaviors.

Abstract

This paper presents a decentralized control framework that incorporates social awareness into multi-agent systems with unknown dynamics to achieve prescribed-time reach-avoid-stay tasks in dynamic environments. Each agent is assigned a social awareness index that quantifies its level of cooperation or self-interest, allowing heterogeneous social behaviors within the system. Building on the spatiotemporal tube (STT) framework, we propose a real-time STT framework that synthesizes tubes online for each agent while capturing its social interactions with others. A closed-form, approximation-free control law is derived to ensure that each agent remains within its evolving STT, thereby avoiding dynamic obstacles while also preventing inter-agent collisions in a socially aware manner, and reaching the target within a prescribed time. The proposed approach provides formal guarantees on safety and timing, and is computationally lightweight, model-free, and robust to unknown disturbances. The effectiveness and scalability of the framework are validated through simulation and hardware experiments on a 2D omnidirectional

Paper Structure

This paper contains 20 sections, 3 theorems, 54 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Formulation
  3. Notation
  4. System Definition
  5. Socially Aware Multi-Agent System (SA-MAS)
  6. Problem Formulation
  7. Designing Spatiotemporal Tubes (STTs)
  8. Preliminaries of STT Design
  9. STT Centre Dynamics
  10. STT Radius Dynamics
  11. Social Interaction Function (SIF)
  12. Theoretical Guarantee of TRAS Satisfaction
  13. Controller Synthesis
  14. Case Studies
  15. 2D Omnidirectional Robot
  16. ...and 5 more sections

Key Result

Theorem 3.1

The STT $\Gamma^{(k)}(t),\forall k \in {\mathcal{A}}$ in eqn:stt_ball meets the following to ensure satisfaction of the TRAS specification:

Figures (4)

  • Figure 1: Interaction between an egoistic (high-priority) fire truck and an altruistic (collision-avoiding) grocery vehicle.
  • Figure 2: Hardware demonstration of two omnidirectional robots in a cluttered dynamic environment,https://www.youtube.com/watch?v=oDo6Qs9vw7s.
  • Figure 3: Simulation of eight omnidirectional mobile robots in a 2D environment with different prescribed times. Two egoistic agents (${s}_a^{(1)} = {s}_a^{(5)} = 0.1$, yellow) interact with six altruistic agents (${s}_a^{(2)} = {s}_a^{(3)} = {s}_a^{(4)} = {s}_a^{(6)} = {s}_a^{(7)} = {s}_a^{(8)} = 0.99$), demonstrating scalability to multiple agents, https://www.youtube.com/watch?v=oDo6Qs9vw7s.
  • Figure 4: Simulation of eight UAVs in a 3D environment with different prescribed times. Two egoistic agents (${s}_a^{(1)} = {s}_a^{(5)} = 0.1$, yellow) and six altruistic agents (${s}_a^{(2)} = {s}_a^{(3)} = {s}_a^{(4)} = {s}_a^{(6)} = {s}_a^{(7)} = {s}_a^{(8)} = 0.99$) coordinate safely, showing scalability from ground robots to aerial systems, https://www.youtube.com/watch?v=oDo6Qs9vw7s.

Theorems & Definitions (8)

  • Definition 2.1: Temporal Reach Avoid Stay (TRAS)
  • Definition 2.3: STT for TRAS
  • Theorem 3.1
  • Proof 3.2
  • Lemma 3.3
  • Proof 3.4
  • Theorem 4.1
  • Proof 4.2