Exploratory Digraph Navigation Using A

We describe Exploratory Digraph Navigation as a fundamental problem of graph theory concerned with using a graph with incomplete edge and vertex information for navigation in a partially unknown environment. We then introduce EDNA*, a simple A* extension which provably solves the problem and give worst-case bounds on the number of edges explored by said algorithm. We compare the performance of this algorithm to a non-exploratory strategy using A* and discuss its relation to existing algorithms such as D* Lite, PHA* with early stopping, EWP or exploration algorithms. 1 Exploratory Digraph Navigation (EDN) 1.1 Exploratory Digraph Navigation problems Imagine a mobile robot navigating in a physical world W whose representation is a directed graph (digraph) G as sketched on Figure 1. Dotted lines on the figure represents data not available in the robot’s internal map G, also called currently known graph [Felner et al., 2004], of the world at planning time. G\G represents space not explored yet. From its current position, the robot wants to reach a goal position with minimal effort. While planning its path to the goal on G, it realizes that it essentially has two choices: using a known (safe) path, which may be quite long, or trying to find a shortcut thanks to places whose knowledge is incomplete (think of rooms containing doors not yet opened). However, taking a shortcut is risky since the expected shortcut may actually be a dead end, forcing the robot to turn back and replan its path. The said shortcut may also actually be longer than the safe path. Depending on its internal state (battery level, mission, . . . ), the robot may want to privilege the safe path or hope for luck and try an exploratory path which may lead to a decrease of traveled distance relative to the safe path while increasing the robot’s knowledge of its environment. The typical use of Exploratory Navigation is together with robotic Simultaneous Localization And Mapping (SLAM) where a robot models its environment as a graph [Choset and Nagatani, 2001; Bosse et al., 2004] or as an occupancy grid [Elfes, 1989] (where each pixel can be considered as ∗This research was supported by a DGA-MRIS scholarship G