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 Voronoi corridor to further improve the search efficiency, along with a Voronoi potential field constructed to make the searched path keep a reasonable distance from obstacles to provide sufficient optimization margin for the subsequent path smoothing; 2) an efficient quadratic programming-based path smoothing approach is presented, wherein the clearance to obstacles is considered in the form of the penalty of the deviation from the safe reference path 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 25.3 times faster than an advanced sparse-banded structure-based path smoothing approach.

翻译：本文针对移动机器人提出了一种基于栅格广义Voronoi图（G$ \mathbf{^2} $VD）的高效运动规划新方法。与现有方法不同，本文创新点体现在两方面：1）提出了一种新的基于状态格网的路径搜索方法，通过将搜索空间缩减为Voronoi走廊以进一步提高搜索效率，同时构建了Voronoi势场，使搜索路径与障碍物保持合理距离，为后续路径平滑提供充足优化余量；2）提出了一种基于二次规划的高效路径平滑方法，其中通过惩罚偏离安全参考路径的方式考虑障碍物净空距离，从而改善硬约束路径平滑方法的路径通行能力。我们在多种具有挑战性的仿真场景和室外环境中验证了该方法的效率与平滑性。结果表明，在路径搜索阶段计算效率提升17.1%，且采用所提方法的路径平滑速度比基于先进稀疏带状结构的路径平滑方法快25.3倍。