  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.
