Distributed Model Predictive Control for Dynamic Cooperation of Multi-Agent Systems

TL;DR

This work addresses the challenge of coordinating heterogeneous nonlinear multi-agent systems under both individual and coupling constraints by introducing a distributed model predictive control framework that optimizes over artificial cooperation outputs. The central idea is to decouple local agent behavior from the global cooperative task via cooperation outputs, enabling scalable, decentralized optimization while ensuring recursive feasibility and asymptotic stability. The authors establish transient and asymptotic performance guarantees, including a turnpike-like behavior and, under quadratic bounds, exponential stability, with an emergent cooperative solution rather than a pre-specified target. The framework is demonstrated through satellite constellation reconfiguration, deadlock avoidance in narrow-path traversal, and coordinated quadrotor flight with dynamic task switching, illustrating flexibility to topology changes and external references. Overall, the approach offers a practical, scalable path to dynamic cooperation in complex multi-agent systems with nonlinear dynamics and constraints.

Abstract

We propose a distributed model predictive control (MPC) framework for coordinating heterogeneous, nonlinear multi-agent systems under individual and coupling constraints. The cooperative task is encoded as a shared objective function minimized collectively by the agents. Each agent optimizes an artificial reference as an intermediate step towards the cooperative objective, along with a control input to track it. We establish recursive feasibility, asymptotic stability, and transient performance bounds under suitable assumptions. The solution to the cooperative task is not predetermined but emerges from the optimized interactions of the agents. We demonstrate the framework on numerical examples inspired by satellite constellation control, collision-free narrow-passage traversal, and coordinated quadrotor flight.

Figures (5)

• Figure 1: Relative angular positions of the satellites. From the top: $\vartheta_1 - \vartheta_3$, $\vartheta_2 - \vartheta_3$, $\vartheta_3 - \vartheta_3$, $\vartheta_4 - \vartheta_3$, and $\vartheta_5 - \vartheta_3$.
• Figure 2: Orbital radii of the satellites. A grey dotted line marks the initial radius of the satellites. At $t=282$ from the top: $r_1$, $r_2$, $r_3$, $r_4$, and $r_5$.
• Figure 3: Two agents exchanging positions through a narrow pathway that they cannot cross simultaneously due to collision avoidance constraints. The shaded area indicates the boundary of the narrow pathway. The triangles indicate the direction of travel and velocity. The agents slow down while the collision avoidance constraint is active due to a suboptimal solution returned by the employed decentralized optimization algorithm.
• Figure 4: Positions of the quadrotors during the first phase of the cooperative task from $t=0$ to $t=350$. The agents converge to a circular trajectory with a common centre and radius, but follow it with different phase, as was desired.
• Figure 5: Positions of the quadrotors during the second phase of the cooperative task from $t=350$ to $t=700$. The first agent follows a reference, whereas the rest follow it without colliding.

Theorems & Definitions (36)

• Definition 1
• Definition 2
• Remark 1
• Remark 2
• Remark 3
• Theorem 1
• Proof 1
• Lemma 1
• Proof 2
• Theorem 2