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
1979184258 2587596550 2084474153 2111994433
We present an incremental algorithm for constructing and reconstructing Generalized Voronoi Diagrams (GVDs) on grids. Our algorithm, Dynamic Brushfire, uses techniques from the path planning community to efficiently update GVDs when the underlying environment changes or when new information concerning the environment is received. Dynamic Brushfire is an order of magnitude more efficient than current approaches. In this paper we present the algorithm, compare it to current approaches on several experimental domains involving both simulated and real data, and demonstrate its usefulness for multirobot path planning. 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. In robotics, grid maps are often used for solving tasks like collision checking, path planning, and localization. Many approaches to these problems use Euclidean distance maps (DMs), generalized Voronoi diagrams (GVDs), or configuration space (c-space) maps. A key challenge for their application in dynamic environments is the efficient update after potential changes due to moving obstacles or when mapping a previously unknown area. To this end, this paper presents novel algorithms that perform incremental updates that only visit cells affected by changes. Furthermore, we propose incremental update algorithms for DMs and GVDs in the configuration space of non-circular robots. These approaches can be used to implement highly efficient collision checking and holonomic path planning for these platforms. Our c-space representations benefit from parallelization on multi-core CPUs and can also be integrated with other state-of-the-art path planners such as rapidly-exploring random trees. In various experiments using real-world data we show that our update strategies for DMs and GVDs require substantially less cell visits and computation time compared to previous approaches. Furthermore, we demonstrate that our GVD algorithm deals better with non-convex structures, such as indoor areas. All our algorithms consider actual Euclidean distances rather than grid steps and are easy to implement. An open source implementation is available online. 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.