Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Distributed MPC for Self-Organized Cooperation of Multiagent Systems -- Extended Version

Matthias Köhler, Matthias A. Müller, Frank Allgöwer

TL;DR

This paper tackles the problem of self-organized cooperation in heterogeneous nonlinear multiagent systems with constraints. It introduces a sequential distributed MPC approach where each agent tracks an artificial cooperation output and communicates only this quantity to neighbors, with a convex, separable cooperation cost V^c encoding the cooperative goal. Under standard terminal conditions and Lipschitz-gradient assumptions, the closed-loop is proven to be asymptotically stable with respect to the cooperative output set, ensuring convergence to the intended cooperative behavior. The framework is demonstrated on consensus and formation control tasks, including a quadrotor formation example, highlighting scalability, robustness, and the practical viability of self-organized cooperation through distributed optimization techniques.

Abstract

We present a sequential distributed model predictive control (MPC) scheme for cooperative control of multi-agent systems with dynamically decoupled heterogeneous nonlinear agents subject to individual constraints. In the scheme, we explore the idea of using tracking MPC with artificial references to let agents coordinate their cooperation without external guidance. Each agent combines a tracking MPC with artificial references, the latter penalized by a suitable coupling cost. They solve an individual optimization problem for this artificial reference and an input that tracks it, only communicating the former to its neighbors in a communication graph. This puts the cooperative problem on a different layer than the handling of the dynamics and constraints, loosening the connection between the two. We provide sufficient conditions on the formulation of the cooperative problem and the coupling cost for the closed-loop system to asymptotically achieve it. Since the dynamics and the cooperative problem are only loosely connected, classical results from distributed optimization can be used to this end. We illustrate the scheme's application to consensus and formation control.

Distributed MPC for Self-Organized Cooperation of Multiagent Systems -- Extended Version

TL;DR

This paper tackles the problem of self-organized cooperation in heterogeneous nonlinear multiagent systems with constraints. It introduces a sequential distributed MPC approach where each agent tracks an artificial cooperation output and communicates only this quantity to neighbors, with a convex, separable cooperation cost V^c encoding the cooperative goal. Under standard terminal conditions and Lipschitz-gradient assumptions, the closed-loop is proven to be asymptotically stable with respect to the cooperative output set, ensuring convergence to the intended cooperative behavior. The framework is demonstrated on consensus and formation control tasks, including a quadrotor formation example, highlighting scalability, robustness, and the practical viability of self-organized cooperation through distributed optimization techniques.

Abstract

We present a sequential distributed model predictive control (MPC) scheme for cooperative control of multi-agent systems with dynamically decoupled heterogeneous nonlinear agents subject to individual constraints. In the scheme, we explore the idea of using tracking MPC with artificial references to let agents coordinate their cooperation without external guidance. Each agent combines a tracking MPC with artificial references, the latter penalized by a suitable coupling cost. They solve an individual optimization problem for this artificial reference and an input that tracks it, only communicating the former to its neighbors in a communication graph. This puts the cooperative problem on a different layer than the handling of the dynamics and constraints, loosening the connection between the two. We provide sufficient conditions on the formulation of the cooperative problem and the coupling cost for the closed-loop system to asymptotically achieve it. Since the dynamics and the cooperative problem are only loosely connected, classical results from distributed optimization can be used to this end. We illustrate the scheme's application to consensus and formation control.
Paper Structure (13 sections, 6 theorems, 40 equations, 7 figures, 1 algorithm)

This paper contains 13 sections, 6 theorems, 40 equations, 7 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Notation
  3. Nonlinear multiagent system
  4. Distributed MPC for cooperation
  5. Analysis of the closed-loop system
  6. Consensus and formation control
  7. Consensus
  8. Formation control
  9. Conclusion
  10. Appendix
  11. Proof of Lemma \ref{['lm:value_function_upper_bound']}
  12. Consensus: Numerical example
  13. Formation control with perturbed initial conditions

Key Result

Theorem 1

Let Assumptions asm:reference and asm:stabilising_terminal_ingredients hold. Then, if Algorithm alg:sequential_MPC is applied for any initial condition $x_0$ for which eq:MPC_for_cooperation is feasible, the optimization problem eq:MPC_for_cooperation in Step 1 of Algorithm alg:sequential_MPC is rec

Figures (7)

  • Figure 1: Evolution over time of the first three states (the outputs) of the quadcopters in Section \ref{['ssec:formation']}.
  • Figure 2: Evolution of the first three states of the quadcopters in Section \ref{['ssec:formation']} into an equilateral triangle. The initial condition of each trajectory is marked by a point and the final value by an X.
  • Figure 3: Communication topologies of the multiagent system in Section \ref{['ssec:consensus_appendix']}. After some time, an agent joins the system and the topology changes from the one on the left-hand side to the other one.
  • Figure 4: Evolution over time of the first two states (the outputs) of the multiagent system in Section \ref{['ssec:consensus_appendix']}. The eventual consensus value changes after an additional agent joins the system.
  • Figure 5: Evolution of the first two states (the outputs) of the multiagent system in Section \ref{['ssec:consensus_appendix']}. The eventual consensus value (black X) changes after an additional agent joins the system. In addition, the output constraint sets are depicted.
  • ...and 2 more figures

Theorems & Definitions (14)

  • Definition 1
  • Remark 1
  • Theorem 1
  • Proof 1
  • Lemma 1
  • Proof 2
  • Lemma 2
  • Proof 3
  • Lemma 3
  • Proof 4
  • ...and 4 more