G$ \mathbf{^2} $VD Planner: Efficient Motion Planning With Grid-based Generalized Voronoi Diagrams

TL;DR

The paper introduces the G^2VD planner, a three-layer motion planning framework for mobile robots that leverages grid-based generalized Voronoi diagrams to expedite path searching within a Voronoi corridor and a fast QP-based path smoothing that implicitly accounts for obstacle clearance. By constructing an incrementally updatable G^2VD and biasing search with a Voronoi field, the planner provides a safe, clearance-aware reference path that enables rapid, convex optimization for smoothing and efficient velocity profiling. The approach yields notable gains in computational efficiency—e.g., reduced search effort and significantly faster smoothing compared with soft/hard-constrained baselines—and demonstrates robust performance in both simulations and outdoor experiments, including static and dynamic obstacle scenarios. Overall, G^2VD offers a practical, real-time capable solution that balances efficiency, safety, and smoothness for autonomous navigation in complex environments.

Abstract

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.

Figures (13)

• Figure 1: Flow chart of the proposed three-layer motion planning framework.
• Figure 2: G$^2$VD of an office-like environment. The Voronoi edge pixels are colored in blue and red, and the shortest Voronoi path is colored in red. The gray region surrounding the Voronoi path denotes the Voronoi corridor.
• Figure 3: Illustration of the Voronoi field of the office-like environment shown in Fig. \ref{['fig:voronoi']}. The light yellow regions are obstacle areas.
• Figure 4: Illustration of path searching results.
• Figure 5: Illustration of path smoothing formulation. $\mathbf{x}_{i-1}$, $\mathbf{x}_i$, and $\mathbf{x}_{i+1}$ denote three successive path vertices. $d_{i+1}$ is the distance from $\mathbf{x}_{i+1}$ to the closest obstacle. The black blocks represent obstacles.