Micro-Aerial Vehicles (MAVs) have the advantage of moving freely in 3D space. However, creating compact and sparse map representations that can be efficiently used for planning for such robots is still an open problem. In this paper, we take maps built from noisy sensor data and construct a sparse graph containing topological information that can be used for 3D planning. We use a Euclidean Signed Distance Field, extract a 3D Generalized Voronoi Diagram (GVD), and obtain a thin skeleton diagram representing the topological structure of the environment. We then convert this skeleton diagram into a sparse graph, which we show is resistant to noise and changes in resolution. We demonstrate global planning over this graph, and the orders of magnitude speed-up it offers over other common planning methods. We validate our planning algorithm in real maps built onboard an MAV, using RGB-D sensing.
Hoff al presented a 2D but 3D-applicable method for building GVDs and then planning using potential fields in them. 3D is done with multiple 2D slices, and computed using graphics hardware @cite_9 . The obstacles are from a labelled CAD model, and obstacles are defined per-object for the purposes of Voronoi boundaries (that is, a point belongs on the GVD if it is equidistant to two distinct , rather than any surface boundaries). Foskey al extended @cite_9 to use a GVD for path planning directly in the graph, and if no solution through the GVD is found, use Probabilistic Roadmaps with sampling informed by the GVD.
@cite_9
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We present techniques for fast motion planning by using discrete approximations of generalized Voronoi diagrams, computed with graphics hardware. Approaches based on this diagram computation are applicable to both static and dynamic environments of fairly high complexity. We compute a discrete Voronoi diagram by rendering a 3D distance mesh for each Voronoi site. The sites can be points, line segments, polygons, polyhedra, curves and surfaces. The computation of the generalized Voronoi diagram provides fast proximity query toolkits for motion planning. The tools provide the distance to the nearest obstacle stored in the Z-buffer, as well as the Voronoi boundaries, Voronoi vertices and weighted Voronoi graphs extracted from the frame buffer using continuation methods. We have implemented these algorithms and demonstrated their performance for path planning in a complex dynamic environment composed of more than 140,000 polygons.