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Distributed Stochastic Search for Multi-Agent Model Predictive Control

Taehyun Yoon, Augustinos D. Saravanos, Evangelos A. Theodorou

TL;DR

The paper addresses scalability and nonconvexity in nonlinear multi-agent MPC with inter-agent couplings. It proposes distributed stochastic search (SS), a generalized sampling-based optimization framework, and uses ADMM for consensus in distributed DMPC. SS unifies multiple optimization strategies via a shape function S, recovering variational optimization, cross-entropy, variational inference, and Tsallis variational inference, with update rules such as q*(û) = Z^{-1} exp(-J(state)(X_{û})/η) p(û). Experiments on multi-robot navigation, including a 64-agent formation, show that distributed SS can outperform distributed IPOPT, achieving high task completion and low collisions, demonstrating scalable, nonconvex optimization for real-time control.

Abstract

Many real-world multi-agent systems exhibit nonlinear dynamics and complex inter-agent interactions. As these systems increase in scale, the main challenges arise from achieving scalability and handling nonconvexity. To address these challenges, this paper presents a distributed sampling-based optimization framework for multi-agent model predictive control (MPC). We first introduce stochastic search, a generalized sampling-based optimization method, as an effective approach to solving nonconvex MPC problems because of its exploration capabilities. Nevertheless, optimizing the multi-agent systems in a centralized fashion is not scalable as the computational complexity grows intractably as the number of agents increases. To achieve scalability, we formulate a distributed MPC problem and employ the alternating direction method of multipliers (ADMM) to leverage the distributed approach. In multi-robot navigation simulations, the proposed method shows a remarkable capability to navigate through nonconvex environments, outperforming a distributed optimization baseline using the interior point optimizer (IPOPT). In a 64-agent multi-car formation task with a challenging configuration, our method achieves 100% task completion with zero collisions, whereas distributed IPOPT fails to find a feasible solution.

Distributed Stochastic Search for Multi-Agent Model Predictive Control

TL;DR

The paper addresses scalability and nonconvexity in nonlinear multi-agent MPC with inter-agent couplings. It proposes distributed stochastic search (SS), a generalized sampling-based optimization framework, and uses ADMM for consensus in distributed DMPC. SS unifies multiple optimization strategies via a shape function S, recovering variational optimization, cross-entropy, variational inference, and Tsallis variational inference, with update rules such as q*(û) = Z^{-1} exp(-J(state)(X_{û})/η) p(û). Experiments on multi-robot navigation, including a 64-agent formation, show that distributed SS can outperform distributed IPOPT, achieving high task completion and low collisions, demonstrating scalable, nonconvex optimization for real-time control.

Abstract

Many real-world multi-agent systems exhibit nonlinear dynamics and complex inter-agent interactions. As these systems increase in scale, the main challenges arise from achieving scalability and handling nonconvexity. To address these challenges, this paper presents a distributed sampling-based optimization framework for multi-agent model predictive control (MPC). We first introduce stochastic search, a generalized sampling-based optimization method, as an effective approach to solving nonconvex MPC problems because of its exploration capabilities. Nevertheless, optimizing the multi-agent systems in a centralized fashion is not scalable as the computational complexity grows intractably as the number of agents increases. To achieve scalability, we formulate a distributed MPC problem and employ the alternating direction method of multipliers (ADMM) to leverage the distributed approach. In multi-robot navigation simulations, the proposed method shows a remarkable capability to navigate through nonconvex environments, outperforming a distributed optimization baseline using the interior point optimizer (IPOPT). In a 64-agent multi-car formation task with a challenging configuration, our method achieves 100% task completion with zero collisions, whereas distributed IPOPT fails to find a feasible solution.
Paper Structure (20 sections, 35 equations, 2 figures, 1 table)

This paper contains 20 sections, 35 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Sampling-based optimization
  3. Variational optimization
  4. Cross-entropy method
  5. Variational inference
  6. Tsallis variational inference
  7. Stochastic search
  8. Distributed stochastic search for multi-agent MPC
  9. Problem formulation
  10. Centralized multi-agent MPC problem
  11. Distributed multi-agent MPC problem
  12. Consensus optimization using ADMM
  13. Local stochastic search update
  14. Global and dual updates
  15. Simulation results
  16. ...and 5 more sections

Figures (2)

  • Figure 1: 64-agent Dubins car formation task visualization: "$\times$" for target positions, "$\bullet$" for initial positions, black circles for obstacles, real lines for final trajectories, and dashed lines for the sampled trajectories. (\ref{['fig:dubins-formation-hard1-ipopt']}), (\ref{['fig:dubins-formation-hard1-ipopt-snapshot']}): Distributed IPOPT converges to the local minimum. (\ref{['fig:dubins-formation-hard1-ss']}), (\ref{['fig:dubins-formation-hard1-ss-snapshot']}): Distributed SS avoids the local minimum by sampling trajectories and completes the task.
  • Figure 2: Distributed stochastic search (proposed method) trajectories on 24-agent quadcopter formation task: "$\times$" for target positions, "$\bullet$" for initial positions, red purple columns for obstacles, and real lines for trajectories.