A Lexicographic Search Method for Multi-Objective Motion Planning

We consider multi-objective motion planning problems in which two competing resources are penalized hierarchically. The highest-priority resource takes on non-negative values over robot paths, and is frequently zero-valued. This is intended to capture problems in which robots must manage a resource such as collision risk, exposure to threats, or access to valuable measurements, whose consideration is critical in some regions of the environment, and unimportant in others. This leaves freedom for tie-breaking with respect to a secondary resource, which we assume to be a strictly positive quantity consumed by the robot, such as distance traveled, energy expended or time elapsed. We leverage the paradigm of lexicographic optimization and apply it for the first time to graph search over roadmaps. Specifically, our "lexicographic search" is employed in concert with probabilistic roadmaps to solve motion planning problems under various non-negative cost functions motivated by real-world applications.