This paper presents a novel and efficient collision checking approach called Updating and Collision Check Skipping Quad-tree (USQ) for multi-robot motion planning. USQ extends the standard quad-tree data structure through a time-efficient update mechanism, which significantly reduces the total number of collision checks and the collision checking time. In addition, it handles transitions at the quad-tree quadrant boundaries based on worst-case trajectories of agents. These extensions make quad-trees suitable for efficient collision checking in multi-robot motion planning of large robot teams. We evaluate the efficiency of USQ in comparison with Regenerating Quad-tree (RQ) from scratch at each timestep and naive pairwise collision checking across a variety of randomized environments. The results indicate that USQ significantly reduces the number of collision checks and the collision checking time compared to other baselines for different numbers of robots and map sizes. In a 50-robot experiment, USQ accurately detected all collisions, outperforming RQ which has longer run-times and/or misses up to 25% of collisions.

翻译：本文提出了一种新颖且高效的碰撞检测方法——更新与碰撞检测跳越四叉树 (USQ)，用于多机器人运动规划。USQ 通过一种高时效性的更新机制扩展了标准四叉树数据结构，显著减少了碰撞检测的总次数及检测时间。此外，该方法基于智能体的最坏情况轨迹来处理四叉树象限边界处的过渡问题。这些扩展使得四叉树适用于大规模机器人团队的多机器人运动规划中的高效碰撞检测。我们在多种随机化环境中将USQ的效率与每时间步从头生成四叉树 (RQ) 及朴素成对碰撞检测进行了比较。结果表明，在不同机器人数量和地图尺寸下，USQ相较于其他基线方法显著减少了碰撞检测次数和检测时间。在一项50个机器人的实验中，USQ准确检测了所有碰撞，优于运行时间更长且漏检率高达25%的RQ方法。