The fundamental goal assignment problem for a multi-robot application aims to assign a unique goal to each robot while ensuring collision-free paths, minimizing the total movement cost. A plausible algorithmic solution to this NP-hard problem involves an iterative process that integrates a task planner to compute the goal assignment while ignoring the collision possibilities among the robots and a multi-agent path-finding algorithm to find the collision-free trajectories for a given assignment. This procedure involves a method for computing the next best assignment given the current best assignment. A naive way of computing the next best assignment, as done in the state-of-the-art solutions, becomes a roadblock to achieving scalability in solving the overall problem. To obviate this bottleneck, we propose an efficient conflict-guided method to compute the next best assignment. Additionally, we introduce two more optimizations to the algorithm -- first for avoiding the unconstrained path computations between robot-goal pairs wherever possible, and the second to prevent duplicate constrained path computations for multiple robot-goal pairs. We extensively evaluate our algorithm for up to a hundred robots on several benchmark workspaces. The results demonstrate that the proposed algorithm achieves nearly an order of magnitude speedup over the state-of-the-art algorithm, showcasing its efficacy in real-world scenarios.

翻译：多机器人应用中的基本目标分配问题旨在为每个机器人分配唯一目标，同时确保无碰撞路径并最小化总移动成本。针对这一NP难题，一种可行的算法解决方案采用迭代过程：任务规划器忽略机器人间的碰撞可能性计算目标分配，多智能体路径规划算法则为给定分配寻找无碰撞轨迹。该过程需根据当前最优分配计算下一个最优分配。现有方案中，计算下一个最优分配的朴素方法成为规模化求解整体问题的瓶颈。为突破这一局限，我们提出高效的冲突引导型方法计算下一个最优分配。此外，我们引入两项算法优化——其一在可行时避免计算机器人-目标对之间的无约束路径，其二防止对多个机器人-目标对重复计算有约束路径。我们在多个基准工作空间中针对多达百台机器人进行了广泛评估。结果表明，所提算法相较于现有最优方案实现近一个数量级的加速，验证了其在真实场景中的有效性。