Multi-robot systems offer enhanced capability over their monolithic counterparts, but they come at a cost of increased complexity in coordination. To reduce complexity and to make the problem tractable, multi-robot motion planning (MRMP) methods in the literature adopt de-coupled approaches that sacrifice either optimality or dynamic feasibility. In this paper, we present a convexification method, namely "parabolic relaxation", to generate optimal and dynamically feasible trajectories for MRMP in the coupled joint-space of all robots. We leverage upon the proposed relaxation to tackle the problem complexity and to attain computational tractability for planning over one hundred robots in extremely clustered environments. We take a multi-stage optimization approach that consists of i) mathematically formulating MRMP as a non-convex optimization, ii) lifting the problem into a higher dimensional space, iii) convexifying the problem through the proposed computationally efficient parabolic relaxation, and iv) penalizing with iterative search to ensure feasibility and recovery of feasible and near-optimal solutions to the original problem. Our numerical experiments demonstrate that the proposed approach is capable of generating optimal and dynamically feasible trajectories for challenging motion planning problems with higher success rate than the state-of-the-art, yet remain computationally tractable for over one hundred robots in a highly dense environment.

翻译：多机器人系统提高了其单体对等系统的能力,但以协调的复杂程度增加为代价。为了降低复杂性,并使文献中的问题具有可拉动性,多机器人运动规划(MRMP)方法采用非混合方法,牺牲最佳性或动态可行性。在本文件中,我们提出了一个分解方法,即“抛物放松”,为所有机器人合用空间的MRMP创造最佳和动态可行轨迹。我们利用拟议的放松来解决问题复杂性,并实现在极端集群环境中规划100多个机器人的可计算性。我们采取了多阶段优化方法,包括i)用数学方式制定MRMP,作为非电离子优化或动态优化。在本文中,我们提出了一个分解方法,即“抛物放松”,通过拟议的高效的对准抛物放松法,为MRMMP创造最佳和动态的轨迹。我们进行的数字实验表明,在最具有挑战性、最接近性、最强的机率的机器人计算方法上,仍然能够产生最优的机率。