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Conflict-Based Model Predictive Control for Scalable Multi-Robot Motion Planning

Ardalan Tajbakhsh, Lorenz T. Biegler, Aaron M. Johnson

TL;DR

This work targets scalable multi-robot motion planning in continuous time under kinodynamic constraints. It introduces CB-MPC, which combines a CBS-style conflict-tree high-level planner with MPC-based low-level planning to produce collision-free, executable trajectories in a receding-horizon framework. The key contributions are the CB-MPC algorithm, a definition of inter-agent conflicts over time-ranges, and empirical evidence showing superior success rates, lower solve times, and better scalability than Vanilla-MPC, Joint-MPC, Pr-MPC, and D-MPC across multiple environments; and the ability to replace full-horizon kinodynamic planners with a CB-MPC plus high-level planner. The results support practical deployment in dense and dynamic settings and highlight avenues for incorporating uncertainty and multi-modal behavior in future work.

Abstract

This paper presents a scalable multi-robot motion planning algorithm called Conflict-Based Model Predictive Control (CB-MPC). Inspired by Conflict-Based Search (CBS), the planner leverages a similar high-level conflict tree to efficiently resolve robot-robot conflicts in the continuous space, while reasoning about each agent's kinematic and dynamic constraints and actuation limits using MPC as the low-level planner. We show that tracking high-level multi-robot plans with a vanilla MPC controller is insufficient, and results in unexpected collisions in tight navigation scenarios. Compared to other variations of multi-robot MPC like joint, prioritized, and distributed, we demonstrate that CB-MPC improves the executability and success rate, allows for closer robot-robot interactions, and reduces the computational cost significantly without compromising the solution quality across a variety of environments. Furthermore, we show that CB-MPC combined with a high-level path planner can effectively substitute computationally expensive full-horizon multi-robot kinodynamic planners.

Conflict-Based Model Predictive Control for Scalable Multi-Robot Motion Planning

TL;DR

This work targets scalable multi-robot motion planning in continuous time under kinodynamic constraints. It introduces CB-MPC, which combines a CBS-style conflict-tree high-level planner with MPC-based low-level planning to produce collision-free, executable trajectories in a receding-horizon framework. The key contributions are the CB-MPC algorithm, a definition of inter-agent conflicts over time-ranges, and empirical evidence showing superior success rates, lower solve times, and better scalability than Vanilla-MPC, Joint-MPC, Pr-MPC, and D-MPC across multiple environments; and the ability to replace full-horizon kinodynamic planners with a CB-MPC plus high-level planner. The results support practical deployment in dense and dynamic settings and highlight avenues for incorporating uncertainty and multi-modal behavior in future work.

Abstract

This paper presents a scalable multi-robot motion planning algorithm called Conflict-Based Model Predictive Control (CB-MPC). Inspired by Conflict-Based Search (CBS), the planner leverages a similar high-level conflict tree to efficiently resolve robot-robot conflicts in the continuous space, while reasoning about each agent's kinematic and dynamic constraints and actuation limits using MPC as the low-level planner. We show that tracking high-level multi-robot plans with a vanilla MPC controller is insufficient, and results in unexpected collisions in tight navigation scenarios. Compared to other variations of multi-robot MPC like joint, prioritized, and distributed, we demonstrate that CB-MPC improves the executability and success rate, allows for closer robot-robot interactions, and reduces the computational cost significantly without compromising the solution quality across a variety of environments. Furthermore, we show that CB-MPC combined with a high-level path planner can effectively substitute computationally expensive full-horizon multi-robot kinodynamic planners.
Paper Structure (16 sections, 4 equations, 5 figures, 3 tables, 1 algorithm)

This paper contains 16 sections, 4 equations, 5 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related works
  3. Preliminaries
  4. Conflict Based Search (CBS)
  5. Model Predictive Control Planner (MPC)
  6. Conflict-Based Model Predictive Control
  7. Conflicts in CB-MPC
  8. CB-MPC Algorithm
  9. Experiments
  10. Baseline Comparisons
  11. Experimental Setup
  12. Results
  13. Narrow Environment
  14. Open Environment
  15. Randomized Environment
  16. ...and 1 more sections

Figures (5)

  • Figure 1: (a) Tracking a conflict-based search (CBS) generated plan with a vanilla MPC controller does not guarantee collision-free execution due to tracking error and unaccounted kinematic constraints. (b) CB-MPC allows for closer robot-robot interactions while remaining collision-free in execution.
  • Figure 2: (a) Agents black and blue are tasked to go from their start poses (shown in solid colors) to their goal poses (shown in transparent colors). For a given planning horizon $t_h$, the initial predicted MPC trajectory of the agents has a collision at $t_c$. Collision constraints are added at each timestep between [$t_c$, $t_h$] (shown in red dots) for the black agent since it has a lower total cost. (b,c) The updated MPC solution resolves the prior constraints, but results in a new collision. (d) Collision-free trajectories are generated after collisions are resolved iteratively.
  • Figure 3: Comparison between the Joint-MPC (left) and CB-MPC (right) in the narrow environment. CB-MPC is able to get similar quality of solution with the makespan of 8.35 compared to 8.45 of the Joint-MPC at a significantly lower computation cost. Red dots denote the active constraints.
  • Figure 4: Only CB-MPC can solve: (a) the 12-robot problem in the open environment (b) the 18-robot problem in the randomized environment.
  • Figure 5: Randomized environment results. (a) Success rate (higher is better) (b) Average solve time per robot (lower is better) (c) Max solve time per fleet (lower is better) (d) Makespan (lower is better). CB-MPC results in higher success rate in almost all cases and significantly better average and max solve times compared to D-MPC and Pr-MPC, with similar makespan.