论文标题
多项式时间近时间最佳的多机器人路径在三个维度上计划，并应用于大规模无人机协调
Polynomial Time Near-Time-Optimal Multi-Robot Path Planning in Three Dimensions with Applications to Large-Scale UAV Coordination
论文作者
论文摘要
为了在标记的设置下实现无人驾驶汽车（UAV）的高效，大规模的协调，在这项工作中，我们开发了第一种多项式时间算法，用于在三维空间中重新配置许多移动物体，并在三维的空间中使用Provable $ 1.x $ 1.x $ 1.x $ ASMPTOTOIT $ 1.X $ ASMPTOTOIT MAKEPATOTIOT MAKEP PATIC PRINSTICATION PLINSTICATION PLINSTICATION PLINSTICAL PRICTATIOTION高度robrot dentife high Robrot Dentife high Robot Dentife high Robot dentife。更准确地说，在$ m_1 \ times m_2 \ times m_3 $ grid，$ m_1 \ ge m_2 \ ge m_2 \ ge m_3 $，我们的方法计算解决方案最多可路由$ \ frac {m_1m_2m_3} {3} {3} {3} {3} $ instry of in in n y Importial nourpliped n in n in n in n in n in n in STENT和2 +2m_3 +o（M_1）$，具有高概率。因为此类实例的MakePAN下限为$ M_1+M_2+M_3 -O（M_1）$，也很高，因为$ M_1 \ to \ infty $，$ \ frac {m_1+2m_2+2m_2+2m_3} {m_1+m_1+m_1+m_2+m_2+m_3} $最佳保证。 $\frac{m_1+2m_2+2m_3}{m_1+m_2+m_3} \in (1, \frac{5}{3}]$, yielding $1.x$ optimality. In contrast, it is well-known that multi-robot path planning is NP-hard to optimally solve. In numerical evaluations, our method readily scales to support the motion planning of over $ 100,000 $ 3D的机器人同时实现$ 1.x $最优性。
For enabling efficient, large-scale coordination of unmanned aerial vehicles (UAVs) under the labeled setting, in this work, we develop the first polynomial time algorithm for the reconfiguration of many moving bodies in three-dimensional spaces, with provable $1.x$ asymptotic makespan optimality guarantee under high robot density. More precisely, on an $m_1\times m_2 \times m_3$ grid, $m_1\ge m_2\ge m_3$, our method computes solutions for routing up to $\frac{m_1m_2m_3}{3}$ uniquely labeled robots with uniformly randomly distributed start and goal configurations within a makespan of $m_1 + 2m_2 +2m_3+o(m_1)$, with high probability. Because the makespan lower bound for such instances is $m_1 + m_2+m_3 - o(m_1)$, also with high probability, as $m_1 \to \infty$, $\frac{m_1+2m_2+2m_3}{m_1+m_2+m_3}$ optimality guarantee is achieved. $\frac{m_1+2m_2+2m_3}{m_1+m_2+m_3} \in (1, \frac{5}{3}]$, yielding $1.x$ optimality. In contrast, it is well-known that multi-robot path planning is NP-hard to optimally solve. In numerical evaluations, our method readily scales to support the motion planning of over $100,000$ robots in 3D while simultaneously achieving $1.x$ optimality. We demonstrate the application of our method in coordinating many quadcopters in both simulation and hardware experiments.
