Landmark selection strategies for path execution

A mobile robot often executes a planned path by measuring its position relative to visible landmarks at known positions and then using this information to estimate its own absolute position. The minimum number of landmarks k required for self-location depends on the types of measurements the robot can perform, such as visual angles using a video camera on a pan-tilt unit, distances using a laser range finder, or absolute orientation using a compass. The problem we address is how to find which k landmarks the robot should detect and track over which segments of a path, so that the cost of sensing (detection and tracking) is minimized. We assume that there are more landmarks visible from each point of the robot's path than the minimum necessary, and that their positions are known relative to the path. We present several formulations of this problem in graph-theoretic terms, with different amounts of flexibility, generality and complexity, which can be solved by known graph-theoretic algorithms. We present uniform-cost algorithms (all landmarks have equal cost of detection and tracking), and weighted-cost algorithms (each landmark has different cost). The complexity of these algorithms is low-order polynomial in the number of landmarks k that must be simultaneously tracked at each point of the robot's path. We also present an algorithm that can incorporate not only the sensing cost for each landmark, but the suitability of the landmark configurations relative to the robot. The resulting complexity is, in this case, exponential in the number of landmarks k tracked at each point of the robot path. The algorithm is still practical, since k is typically a fixed small integer.