Alternating Direction Method of Multipliers-Based Parallel Optimization for Multi-Agent Collision-Free Model Predictive Control

TL;DR

This work addresses collision-free control for multi-agent systems by recasting the centralized MPC problem with collision-avoidance constraints into a parallelizable ADMM framework. It decomposes the problem into per-agent subproblems and a coupling subproblem for collision avoidance, providing a dual-formulation solution to the per-agent subproblems, an integer-augmented subproblem for collision constraints, an initialization strategy, and rigorous convergence proofs. The approach is validated on a 21-UAV formation, showing substantial reductions in computation time and improved endpoint tracking accuracy compared with baseline methods, while maintaining safety distances. The results demonstrate practical scalability and effectiveness of parallel ADMM in solving non-convex multi-agent MPC with non-convex collision constraints, with potential robustness enhancements and scaling extensions for larger teams in real-world deployments.

Abstract

This paper investigates the collision-free control problem for multi-agent systems. For such multi-agent systems, it is the typical situation where conventional methods using either the usual centralized model predictive control (MPC), or even the distributed counterpart, would suffer from substantial difficulty in balancing optimality and computational efficiency. Additionally, the non-convex characteristics that invariably arise in such collision-free control and optimization problems render it difficult to effectively derive a reliable solution (and also to thoroughly analyze the associated convergence properties). To overcome these challenging issues, this work establishes a suitably novel parallel computation framework through an innovative mathematical problem formulation; and then with this framework and formulation, a parallel algorithm based on alternating direction method of multipliers (ADMM) is presented to solve the sub-problems arising from the resulting parallel structure. Furthermore, an efficient and intuitive initialization procedure is developed to accelerate the optimization process, and the optimum is thus determined with significantly improved computational efficiency. As supported by rigorous proofs, the convergence of the proposed ADMM iterations for this non-convex optimization problem is analyzed and discussed in detail. Finally, a simulation with a group of unmanned aerial vehicles (UAVs) serves as an illustrative example here to demonstrate the effectiveness and efficiency of the proposed approach. Also, the simulation results verify significant improvements in accuracy and computational efficiency compared to other baselines, including primal quadratic mixed integer programming (PQ-MIP), non-convex quadratic mixed integer programming (NC-MIP), and non-convex quadratically constrained quadratic programming (NC-QCQP).

Figures (5)

• Figure 1: Trajectories of the agents in the 3D view.
• Figure 2: Trajectories of the agents in the 2D view without disturbance (left) and with disturbance (right).
• Figure 3: Control inputs of the agents.
• Figure 4: Distances between each pair of agents.
• Figure 5: Distances between each pair of agents with the smaller duality gap.

Theorems & Definitions (22)

• Definition 1
• Remark 1
• Remark 2
• Definition 2
• Remark 3
• Remark 4
• Remark 5
• Remark 6
• Definition 3
• Lemma 1