Polynomial Time Near-Time-Optimal Multi-Robot Path Planning in Three Dimensions with Applications to Large-Scale UAV Coordination
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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× m_2 × m_3 grid, m_1≥ m_2≥ m_3, our method computes solutions for routing up to 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 →∞, m_1+2m_2+2m_3/m_1+m_2+m_3 optimality guarantee is achieved. m_1+2m_2+2m_3/m_1+m_2+m_3∈ (1, 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.
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