Minimizing Localization Travel Distance (regular paper)

Localization — determining one’s location in a known environment — is a fundamental task for an autonomous robot. We analyze worst-case behavior in terms of performance ratio and travel cost. We assume no actuator or sensory uncertainty, and we consider both tactile and long range sensors in both discrete grid graphs and continuous polygonal domains. We show that it is NP-hard to find localization plans whose worst-case travel cost is within a certain logarithmic factor of optimal. Applying our performance measures to a localization algorithm originating in the Delayed Planning Architecture [4],[9], [8], we find that its performance ratio is poor, ranging between and , depending on sensor and domain type. In contrast, the algorithm’s performance is good when measured in terms of travel cost, on discretized domains such as grid graphs. On graphs with vertices, the algorithm’s worst-case travel cost is between and . As a corollary we find that the total distance traveled by the greedy mapping algorithm is also