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Distributed MPC For Coordinated Path-Following

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

Abstract

In this paper, we consider a distributed model predictive control (MPC) algorithm for coordinated path-following. Relying on the time-critical cooperative path-following framework, which decouples space and time and reduces the coordination problem to a one-dimensional setting, we formulate a distributed MPC scheme for time coordination. Leveraging properties of the normalized Laplacian, we decouple the MPC dynamics into independent modes and derive a recursive relation linking current and predicted states. Using this structure, we prove that, for prediction horizon $K=1$ and a fixed connected communication network, the system is exponentially stable even in the presence of path-following errors. This provides a first result on the convergence analysis of discrete-time distributed MPC schemes within this framework. The proposed approach enables scalable and efficient real-time implementation with low communication overhead. Moreover, in contrast to the time-critical cooperative path-following framework, the optimization-based structure relaxes the reliance on preplanning by allowing the incorporation of mission-specific requirements, such as vehicle limitations, collision avoidance, and conflict resolution. Simulation results demonstrate applicability to complex scenarios, highlighting agility and exponential convergence under communication failures.

Distributed MPC For Coordinated Path-Following

Abstract

In this paper, we consider a distributed model predictive control (MPC) algorithm for coordinated path-following. Relying on the time-critical cooperative path-following framework, which decouples space and time and reduces the coordination problem to a one-dimensional setting, we formulate a distributed MPC scheme for time coordination. Leveraging properties of the normalized Laplacian, we decouple the MPC dynamics into independent modes and derive a recursive relation linking current and predicted states. Using this structure, we prove that, for prediction horizon and a fixed connected communication network, the system is exponentially stable even in the presence of path-following errors. This provides a first result on the convergence analysis of discrete-time distributed MPC schemes within this framework. The proposed approach enables scalable and efficient real-time implementation with low communication overhead. Moreover, in contrast to the time-critical cooperative path-following framework, the optimization-based structure relaxes the reliance on preplanning by allowing the incorporation of mission-specific requirements, such as vehicle limitations, collision avoidance, and conflict resolution. Simulation results demonstrate applicability to complex scenarios, highlighting agility and exponential convergence under communication failures.

Paper Structure

This paper contains 14 sections, 4 theorems, 144 equations, 4 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Virtual Time
  4. Time-Coordination
  5. Main Approach
  6. Convergence Proof
  7. Unconstrained Case
  8. Original Problem
  9. Simulations
  10. MPC Horizon
  11. Corridor Navigation: Predefined and Autonomous Passage Ordering
  12. Offline Ordering via Predefined Priority
  13. Autonomous Ordering via Agent Competition/Game
  14. Conclusion and Future Work

Key Result

Lemma 1

For every eigenvalue $\lambda_i>0$ of $D^{-1}L$, there exists $h_i>0$ such that, for all $h\in(0,h_i)$, where $\rho(Q_i^h)$ denotes the spectral radius of $Q_i^h$.

Figures (4)

  • Figure 1: Cooperative path-following control framework of multi-agent UAV systems.
  • Figure 2: Agent trajectories. UAV icons represent the initial positions of the agents.
  • Figure 3: Consensus parameter $\gamma$ over time. (a) simulation under the cost function \ref{['eq:Fi1']}; (b) simulation under the cost function \ref{['eq:Fi2']}.
  • Figure 4: Minimum distance maintained between any two UAVs over time: (a) simulation under the cost function \ref{['eq:Fi1']}; (b) simulation under the cost function \ref{['eq:Fi2']}.

Theorems & Definitions (4)

  • Lemma 1
  • Theorem 1
  • Lemma 2
  • Theorem 2