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Game-Theoretic Coordination For Time-Critical Missions of UAV Systems

Mikayel Aramyan, Anna Manucharyan, Lusine Poghosyan, Rohith Madhavan, Tigran Bakaryan, Naira Hovakimyan

TL;DR

This work addresses time-critical coordination of UAV swarms by formulating a distributed game-theoretic framework in which agents minimize a time-synchronization based cost over a one-dimensional consensus parameter, the virtual time $\gamma_i(t)$. The authors prove the existence and exponential stability of a Nash equilibrium under ideal conditions and extend the approach with a model predictive control (MPC) scheme to handle non-ideal networks, path-following errors, and disturbances. They validate the method through high-fidelity simulations and real flight experiments, demonstrating rapid synchronization, collision avoidance, and robustness to communication failures and wind. The proposed approach is scalable, computationally efficient, and suitable for real-time deployment in dynamic UAV missions, enabling agile and reliable swarm operations in complex environments.

Abstract

Cooperative missions involving Unmanned Aerial Vehicles (UAVs) in dynamic environments pose significant challenges in ensuring both coordination and agility. In this paper, we introduce a novel game-theoretic approach for time-critical missions, where each UAV optimizes a cost function that incorporates temporal and mission-specific constraints. The optimization is performed within a one-dimensional domain, significantly reducing the computational cost and enabling real-time application to complex and dynamic scenarios. The framework is distributed in structure, allowing to achieve global, system-wide coordination (a Nash equilibrium) by using only local information. For ideal systems, we prove the existence and exponential stability of the Nash equilibrium. Furthermore, we invoke model predictive control (MPC) for non-ideal scenarios. In particular, we propose a discrete-time optimization approach that tackles path-following errors and communication failures, ensuring reliable and agile performance in dynamic and uncertain environments. Simulation results demonstrate the effectiveness and agility of the approach in ensuring successful mission execution across diverse scenarios. Experiments using a motion capture system provide further validation under realistic conditions.

Game-Theoretic Coordination For Time-Critical Missions of UAV Systems

TL;DR

This work addresses time-critical coordination of UAV swarms by formulating a distributed game-theoretic framework in which agents minimize a time-synchronization based cost over a one-dimensional consensus parameter, the virtual time . The authors prove the existence and exponential stability of a Nash equilibrium under ideal conditions and extend the approach with a model predictive control (MPC) scheme to handle non-ideal networks, path-following errors, and disturbances. They validate the method through high-fidelity simulations and real flight experiments, demonstrating rapid synchronization, collision avoidance, and robustness to communication failures and wind. The proposed approach is scalable, computationally efficient, and suitable for real-time deployment in dynamic UAV missions, enabling agile and reliable swarm operations in complex environments.

Abstract

Cooperative missions involving Unmanned Aerial Vehicles (UAVs) in dynamic environments pose significant challenges in ensuring both coordination and agility. In this paper, we introduce a novel game-theoretic approach for time-critical missions, where each UAV optimizes a cost function that incorporates temporal and mission-specific constraints. The optimization is performed within a one-dimensional domain, significantly reducing the computational cost and enabling real-time application to complex and dynamic scenarios. The framework is distributed in structure, allowing to achieve global, system-wide coordination (a Nash equilibrium) by using only local information. For ideal systems, we prove the existence and exponential stability of the Nash equilibrium. Furthermore, we invoke model predictive control (MPC) for non-ideal scenarios. In particular, we propose a discrete-time optimization approach that tackles path-following errors and communication failures, ensuring reliable and agile performance in dynamic and uncertain environments. Simulation results demonstrate the effectiveness and agility of the approach in ensuring successful mission execution across diverse scenarios. Experiments using a motion capture system provide further validation under realistic conditions.

Paper Structure

This paper contains 25 sections, 2 theorems, 76 equations, 9 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Path Planning and Following
  4. Time Coordination for Simultaneous Arrival
  5. Problem Formulation
  6. Main Approach
  7. Existence of Solution and Exponential Stability
  8. Algorithm
  9. Simulations
  10. Simulation Framework
  11. Ideal Communication and Ideal Path-Following
  12. Non-Ideal Communication and Ideal Path-Following
  13. Non-Ideal Communication and Non-Ideal Path-Following
  14. Collision Avoidance
  15. Flight Experiments
  16. ...and 10 more sections

Key Result

Proposition 2

Let $\alpha>0$. Then, there exists $\bm{\gamma}^*=(\gamma_1^*,\dots,\gamma_N^*)\in \prod_{j=1}^{N}\mathcal{B}^{0}_j$ solving Problem prob-exp-stab. Moreover, the solution has the following explicit form where $\mu_1,\mu_3<0$, and the constants $H^1_i,H_i^3, C_i^1, \nu_1, C_i^2$ only depend on $\alpha$ and initial conditions.

Figures (9)

  • Figure 1: Snapshot of the flight experiment demonstrating four UAVs coordinating and avoiding collisions in the presence of non-ideal communication. The added trail effect highlights the flight path of UAVs, a circular symbol representing the balance between two opposing forces, yin and yang.
  • Figure 2: Game-theoretic cooperative path-following of a system of UAVs: the block on Optimal Temporal Coordination uses a game-theoretic formulation and ensures existence and convergence of Nash equilibrium.
  • Figure 3: Ideal communication, ideal path following: (a) A top view of the actual trajectories followed by the UAVs under ideal conditions, with red circles marking the starting points and stars indicating the final positions; (b) $\gamma_i$ over time; (c) $\dot{\gamma_i}$ over time.
  • Figure 4: (a) Ideal communication, ideal path following, $\ddot{\gamma_i}$ over time, (b) Non-ideal communication, ideal path following, $\gamma_i$ over time, (c) Non-ideal communication, ideal path following, $\ddot{\gamma_i}$ over time.
  • Figure 5: Non-ideal communication, non-ideal path following: (a) A top view of the trajectories influenced by wind disturbance, with red circles marking the starting points and stars indicating the final positions; (b) $\gamma_i$ over time; (c) $\ddot{\gamma_i}$ over time.
  • ...and 4 more figures

Theorems & Definitions (9)

  • Definition 1
  • Proposition 2
  • proof
  • Theorem 3
  • proof
  • Definition 4
  • Definition 5
  • proof
  • proof