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Deadlock Resolution and Recursive Feasibility in MPC-based Multi-robot Trajectory Generation

Yuda Chen, Meng Guo, Zhongkui Li

TL;DR

The paper tackles the challenge of online, collision-free multi-robot trajectory generation with guarantees on feasibility and deadlock avoidance. It introduces an infinite-horizon MPC framework (IMPC-DR) built on a modified buffered Voronoi scheme with a velocity-dependent buffer and a terminal warning band, enabling online deadlock detection and smooth, adaptive resolution. A formal deadlock condition framed as a force equilibrium is derived, along with a detection mechanism and a right-hand-rule-inspired resolution that preserves recursive feasibility under distributed, local communication. Extensive simulations and hardware experiments validate the approach, showing superior success rates and livelock avoidance in crowded and high-speed scenarios, with practical viability on nano-quadrotor platforms.

Abstract

Online collision-free trajectory generation within a shared workspace is fundamental for most multi-robot applications. However, many widely-used methods based on model predictive control (MPC) lack theoretical guarantees on the feasibility of underlying optimization. Furthermore, when applied in a distributed manner without a central coordinator, deadlocks often occur where several robots block each other indefinitely. Whereas heuristic methods such as introducing random perturbations exist, no profound analyses are given to validate these measures. Towards this end, we propose a systematic method called infinite-horizon model predictive control with deadlock resolution. The MPC is formulated as a convex optimization over the proposed modified buffered Voronoi with warning band. Based on this formulation, the condition of deadlocks is formally analyzed and proven to be analogous to a force equilibrium. A detection-resolution scheme is proposed, which can effectively detect deadlocks online before they even happen. Once detected, it utilizes an adaptive resolution scheme to resolve deadlocks, under which no stable deadlocks can exist under minor conditions. In addition, the proposed planning algorithm ensures recursive feasibility of the underlying optimization at each time step under both input and model constraints, is concurrent for all robots and requires only local communication. Comprehensive simulation and experiment studies are conducted over large-scale multi-robot systems. Significant improvements on success rate are reported, in comparison with other state-of-the-art methods and especially in crowded and high-speed scenarios.

Deadlock Resolution and Recursive Feasibility in MPC-based Multi-robot Trajectory Generation

TL;DR

The paper tackles the challenge of online, collision-free multi-robot trajectory generation with guarantees on feasibility and deadlock avoidance. It introduces an infinite-horizon MPC framework (IMPC-DR) built on a modified buffered Voronoi scheme with a velocity-dependent buffer and a terminal warning band, enabling online deadlock detection and smooth, adaptive resolution. A formal deadlock condition framed as a force equilibrium is derived, along with a detection mechanism and a right-hand-rule-inspired resolution that preserves recursive feasibility under distributed, local communication. Extensive simulations and hardware experiments validate the approach, showing superior success rates and livelock avoidance in crowded and high-speed scenarios, with practical viability on nano-quadrotor platforms.

Abstract

Online collision-free trajectory generation within a shared workspace is fundamental for most multi-robot applications. However, many widely-used methods based on model predictive control (MPC) lack theoretical guarantees on the feasibility of underlying optimization. Furthermore, when applied in a distributed manner without a central coordinator, deadlocks often occur where several robots block each other indefinitely. Whereas heuristic methods such as introducing random perturbations exist, no profound analyses are given to validate these measures. Towards this end, we propose a systematic method called infinite-horizon model predictive control with deadlock resolution. The MPC is formulated as a convex optimization over the proposed modified buffered Voronoi with warning band. Based on this formulation, the condition of deadlocks is formally analyzed and proven to be analogous to a force equilibrium. A detection-resolution scheme is proposed, which can effectively detect deadlocks online before they even happen. Once detected, it utilizes an adaptive resolution scheme to resolve deadlocks, under which no stable deadlocks can exist under minor conditions. In addition, the proposed planning algorithm ensures recursive feasibility of the underlying optimization at each time step under both input and model constraints, is concurrent for all robots and requires only local communication. Comprehensive simulation and experiment studies are conducted over large-scale multi-robot systems. Significant improvements on success rate are reported, in comparison with other state-of-the-art methods and especially in crowded and high-speed scenarios.
Paper Structure (27 sections, 8 theorems, 52 equations, 15 figures, 4 tables, 1 algorithm)

This paper contains 27 sections, 8 theorems, 52 equations, 15 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Robot Dynamics
  4. Collision Avoidance
  5. MPC-based MATG
  6. Distributed Solution, Recursive Feasibility and Deadlock
  7. Proposed Solution
  8. MBVC-WB
  9. Complete Optimization
  10. Condition for Deadlocks
  11. Deadlock Detection and Resolution
  12. The Complete Algorithm
  13. Property Analyses
  14. Simulation and Experiment
  15. Typical Scenarios
  16. ...and 12 more sections

Key Result

Lemma 1

If $p^i_k \in \mathcal{V}^{i j}_{k}$ holds, $\forall i,j\in \mathcal{N}$ that $i\neq j$, and $\forall k\in \mathcal{K}$, then holds for the same set of $i,j,k$ as above and $p^{ij}_k = {p^i_k-p^j_k}$. Furthermore, assuming that robots $i,\,j$ move at constant velocities from $p^i_{k}$ to $p^i_{k+1}$ and from $p^j_{k}$ to $p^j_{k+1}$, respectively, the planned trajectories $\mathcal{P}^i(t),\, \ma

Figures (15)

  • Figure 1: Illustration of the MBVC-WB. Left: the shared space is split at each step of horizon; Right: a warning band is added for the terminal step of horizon, i.e., $k=K$.
  • Figure 2: Deadlock can be treated as a force equilibrium, where the attractive force from the target (in yellow, red, blue) and the repulsive forces from other robots (in green) are balanced.
  • Figure 3: Illustration of how $\theta^{i j}$ in \ref{['eq: rho^ij']} is computed, given the terminal horizon position (THP) of robots $i,j$ and the target.
  • Figure 4: Left: The condition of deadlocks is a force equilibrium for robot $1$ in which the resulting force $F^1=0$. Right: After introducing the right-hand rule, the repulsive forces to the left side $F^{13}_R$ is increased while the force to the right side $F^{12}_R$ is decreased gradually, yielding the summed force $F^{1}$ nonzero. Thus the condition of deadlocks is falsified.
  • Figure 5: Illustration of three possible cases when two robots form a deadlock.
  • ...and 10 more figures

Theorems & Definitions (31)

  • Remark 1
  • Definition 1: Recursive Feasibility
  • Definition 2: Deadlock
  • Definition 3: Predetermined Trajectory (PT)
  • Remark 2
  • Lemma 1
  • proof
  • Remark 3
  • Theorem 1
  • proof
  • ...and 21 more