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.
Fang al use 2D GVDs to inform sampling in 3D space for MAV navigation in indoor environments @cite_23 . They build a 2D GVD from a down-projection of the environment, and use this to overcome the difficulties that sampling-based methods have with narrow corridors and openings. In contrast, our method actually builds a 3D GVD, fully capturing the geometry of the space.
@cite_23
2587596550
Path planning in complicated 3D environments with narrow passages and rooms is a challenging problem, which is usually time consuming for geometric searching methods or incomplete for sampling-based methods. Focusing on these issues, this paper presents a new algorithm named 2D Voronoi-based Random Tree which combines the completeness of the voronoi diagram based 2D path searching methods and the efficiency of sampling based path planning methods. In this method, 2D voronoi diagram is created and used to guide the growth of random trees in complicated 3D environments. In each iteration of random trees growth, a new node on voronoi edges is selected by moving forward to the target with a fix step length along edges. And then, the 3D particles are distributed locally around this node and be selected according to a cost function for the random trees growth. By doing so, this method can find a valid path in complicated 3D environments with narrow passages and rooms while improving its efficiency and completeness. To demonstrate its effectiveness, efficiency and robustness, the proposed method is examined and compared with RRT algorithm in various practical complex 3D environments.