Concurrent-Allocation Task Execution for Multi-Robot Path-Crossing-Minimal Navigation in Obstacle Environments

TL;DR

This work tackles the problem of concurrent allocation and path-crossing-minimal navigation for multiple robots in obstacle-laden environments. It introduces the concurrent-allocation task execution (CATE) framework, which encodes robot allocation, desired-point convergence, and collision/obstacle avoidance as integer and control barrier function (CBF) constraints, solved online as a constrained optimization problem. The method guarantees feasibility and asymptotic convergence, directly computing the optimal allocation and control input without explicit path planning, and extends to dynamic obstacles and higher-dimensional spaces. Extensive simulations and two AMR experiments validate that CATE reduces trajectory length and path crossings while ensuring stable, deadlock-free operation in complex environments. The approach offers a reactive, efficient alternative to traditional fixed-ordering or decoupled plans, with practical implications for scalable, reliable multi-robot navigation in cluttered spaces.

Abstract

Reducing undesirable path crossings among trajectories of different robots is vital in multi-robot navigation missions, which not only reduces detours and conflict scenarios, but also enhances navigation efficiency and boosts productivity. Despite recent progress in multi-robot path-crossing-minimal (MPCM) navigation, the majority of approaches depend on the minimal squared-distance reassignment of suitable desired points to robots directly. However, if obstacles occupy the passing space, calculating the actual robot-point distances becomes complex or intractable, which may render the MPCM navigation in obstacle environments inefficient or even infeasible. In this paper, the concurrent-allocation task execution (CATE) algorithm is presented to address this problem (i.e., MPCM navigation in obstacle environments). First, the path-crossing-related elements in terms of (i) robot allocation, (ii) desired-point convergence, and (iii) collision and obstacle avoidance are encoded into integer and control barrier function (CBF) constraints. Then, the proposed constraints are used in an online constrained optimization framework, which implicitly yet effectively minimizes the possible path crossings and trajectory length in obstacle environments by minimizing the desired point allocation cost and slack variables in CBF constraints simultaneously. In this way, the MPCM navigation in obstacle environments can be achieved with flexible spatial orderings. Note that the feasibility of solutions and the asymptotic convergence property of the proposed CATE algorithm in obstacle environments are both guaranteed, and the calculation burden is also reduced by concurrently calculating the optimal allocation and the control input directly without the path planning process.

Figures (18)

• Figure 1: Top-down view of the three-robot navigation with fixed-ordering strategies to illustrate the undesirable path crossings.
• Figure 2: Simple interpretation of a 2D disk covering complex irregular obstacles.
• Figure 3: Two existing methods for achieving navigation with non-intersecting paths. (a, b) Decoupled execution of the minimal squared-distance assignment, preferred-velocity calculation, and inter-robot collision avoidance in order alonso2012image. (a, c) Concurrent execution of the minimal squared-distance assignment and collision-free trajectory planning turpin2014captsabattini2017optimized. The blue and yellow circles denote the initial positions of robots and the final positions of desired points, respectively. The black and red arrows denote the non-selected and optimal robot-point pairs, respectively. $\alpha_{i,k}^{\ast}=1$ the correspondence between robot $i$ and desired point $k$ in \ref{['eq_con_a_poi_a_rob']}.
• Figure 4: Failure of the minimal squared-distance assignment between robots and desired points in Fig. \ref{['previous_PCM']} when encountering obstacles occupying the space.
• Figure 5: Illustration of the core idea of the CATE optimization for the MPCM navigation in obstacle environments.

Theorems & Definitions (22)

• Remark 1
• Remark 2
• Definition 1
• Definition 2
• Remark 4
• Remark 5
• Lemma 1
• proof
• Lemma 2
• proof