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Multi-Agent Feedback Motion Planning using Probably Approximately Correct Nonlinear Model Predictive Control

Mark Gonzales, Adam Polevoy, Marin Kobilarov, Joseph Moore

TL;DR

The paper tackles the challenge of coordinating multiple robots with nonlinear stochastic dynamics in cluttered environments by introducing a distributed receding-horizon PAC-NMPC framework that accounts for model and state measurement uncertainty. A gyroscopic obstacle-avoidance-inspired terminal cost and a policy-sharing scheme enable probabilistically-safe formation control, with simulations showing performance comparable to centralized methods and improved robustness to measurement noise. Key contributions include: (1) a scalable distributed PAC-NMPC formulation for multi-agent formation in obstacle fields, (2) a gyroscopic terminal cost to mitigate local minima, and (3) comprehensive simulations demonstrating robustness, scalability to higher dimensions, and favorable trade-offs against RA-MPPI. The approach holds practical potential for robust, scalable multi-robot collaboration in uncertain, real-world settings.

Abstract

For many tasks, multi-robot teams often provide greater efficiency, robustness, and resiliency. However, multi-robot collaboration in real-world scenarios poses a number of major challenges, especially when dynamic robots must balance competing objectives like formation control and obstacle avoidance in the presence of stochastic dynamics and sensor uncertainty. In this paper, we propose a distributed, multi-agent receding-horizon feedback motion planning approach using Probably Approximately Correct Nonlinear Model Predictive Control (PAC-NMPC) that is able to reason about both model and measurement uncertainty to achieve robust multi-agent formation control while navigating cluttered obstacle fields and avoiding inter-robot collisions. Our approach relies not only on the underlying PAC-NMPC algorithm but also on a terminal cost-function derived from gyroscopic obstacle avoidance. Through numerical simulation, we show that our distributed approach performs on par with a centralized formulation, that it offers improved performance in the case of significant measurement noise, and that it can scale to more complex dynamical systems.

Multi-Agent Feedback Motion Planning using Probably Approximately Correct Nonlinear Model Predictive Control

TL;DR

The paper tackles the challenge of coordinating multiple robots with nonlinear stochastic dynamics in cluttered environments by introducing a distributed receding-horizon PAC-NMPC framework that accounts for model and state measurement uncertainty. A gyroscopic obstacle-avoidance-inspired terminal cost and a policy-sharing scheme enable probabilistically-safe formation control, with simulations showing performance comparable to centralized methods and improved robustness to measurement noise. Key contributions include: (1) a scalable distributed PAC-NMPC formulation for multi-agent formation in obstacle fields, (2) a gyroscopic terminal cost to mitigate local minima, and (3) comprehensive simulations demonstrating robustness, scalability to higher dimensions, and favorable trade-offs against RA-MPPI. The approach holds practical potential for robust, scalable multi-robot collaboration in uncertain, real-world settings.

Abstract

For many tasks, multi-robot teams often provide greater efficiency, robustness, and resiliency. However, multi-robot collaboration in real-world scenarios poses a number of major challenges, especially when dynamic robots must balance competing objectives like formation control and obstacle avoidance in the presence of stochastic dynamics and sensor uncertainty. In this paper, we propose a distributed, multi-agent receding-horizon feedback motion planning approach using Probably Approximately Correct Nonlinear Model Predictive Control (PAC-NMPC) that is able to reason about both model and measurement uncertainty to achieve robust multi-agent formation control while navigating cluttered obstacle fields and avoiding inter-robot collisions. Our approach relies not only on the underlying PAC-NMPC algorithm but also on a terminal cost-function derived from gyroscopic obstacle avoidance. Through numerical simulation, we show that our distributed approach performs on par with a centralized formulation, that it offers improved performance in the case of significant measurement noise, and that it can scale to more complex dynamical systems.
Paper Structure (17 sections, 10 equations, 12 figures, 1 table)

This paper contains 17 sections, 10 equations, 12 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Probably Approximately Correct Nonlinear Model Predictive Control (PAC-NMPC)
  4. PAC-NMPC for Multi-Agent Control
  5. Problem Formulation
  6. Cost Function
  7. Distributed Multi-Agent PAC-NMPC
  8. State Measurement Error
  9. Simulation Experiments
  10. Centralized Model
  11. Distributed Model
  12. PAC-NMPC and RA-MPPI
  13. Impact of State Measurement Uncertainty
  14. Formation Points
  15. Symmetric Antipodal Under State Uncertainty
  16. ...and 2 more sections

Figures (12)

  • Figure 1: A five-agent team in a wedge formation in an obstacle field.
  • Figure 2: Symmetric Antipodal Experiment with Trajectory Deconflicting using Terminal Gyroscopic Obstacle Avoidance Cost
  • Figure 3: Trial Outcomes: With RA-MPPI, the followers struggled to keep up with the constantly changing cost function and collided with obstacles. The centralized model ran 19 Trials, and the antipodal test ran 10 trials; the rest ran 50 trials
  • Figure 4: Centralized vs Distributed Formation Error: The centralized approach (green) held the best formation before the obstacles. As the agents encounter obstacles, the centralized approach exhibits a higher formation error due to frequent agent trapping.
  • Figure 5: PAC-NMPC Formation
  • ...and 7 more figures