Toward SLAM on graphs

We present an algorithm for SLAM on planar graphs. We assume that a robot moves from node to node on the graph using odometry to measure the distance between consecutive landmark observations. At each node, the robot follows a branch chosen at random, without reporting which branch it follows. A low-level process detects (with some uncertainty) the presence of landmarks, such as corners, branches, and bumps, but only triggers a binary flag for landmark detection (i.e., the robot is oblivious to the details or "appearance" of the landmark). Under uncertainties of the robot's odometry, landmark detection, and the current landmark position of the robot, we present an E-M-based SLAM algorithm for two cases: (1) known, arbitrary topology with unknown edge lengths and (2) unknown topology, but restricted to "elementary" 1- and 2-cycle graphs. In the latter case, the algorithm (flexibly and reversibly) closes loops and allows for dynamic environments (adding and deleting nodes).