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.
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 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.