In this paper, an efficient motion planning approach with grid-based generalized Voronoi diagrams (G$ \mathbf{^2} $VD) is newly proposed for mobile robots. Different from existing approaches, the novelty of this work is twofold: 1) a new state lattice-based path searching approach is proposed, in which the search space is reduced to a novel Voronoi corridor to further improve the search efficiency; 2) an efficient quadratic programming-based path smoothing approach is presented, wherein the clearance to obstacles is considered to improve the path clearance of hard-constrained path smoothing approaches. We validate the efficiency and smoothness of our approach in various challenging simulation scenarios and outdoor environments. It is shown that the computational efficiency is improved by 17.1% in the path searching stage, and path smoothing with the proposed approach is 6.6 times faster than an advanced sparse-banded structure-based path smoothing approach and 53.3 times faster than the popular timed-elastic-band planner. A video showing outdoor navigation on our campus is available at https://youtu.be/iMXGthgvp58.

翻译：本文针对移动机器人提出了一种基于网格广义Voronoi图（G$ \mathbf{^2} $VD）的高效运动规划方法。与现有方法不同，本文的创新点体现在两个方面：1）提出一种基于状态晶格的新路径搜索方法，将搜索空间缩减为新型Voronoi走廊以进一步提升搜索效率；2）提出一种基于二次规划的高效路径平滑方法，该方法考虑障碍物间隙以改善硬约束路径平滑方法的路径通过性。我们在多种具有挑战性的仿真场景和室外环境中验证了所提方法的效率和平滑性。结果表明，路径搜索阶段计算效率提升17.1%，所提路径平滑方法相比先进的稀疏带状结构路径平滑方法提速6.6倍，相比流行的定时弹性带规划器提速53.3倍。展示校园室外导航的视频可访问https://youtu.be/iMXGthgvp58。