A Lexicographic Search Method for Multi-Objective Motion Planning

Abstract: We propose a novel method for multi-objective motion planning problems by leveraging the paradigm of lexicographic optimization and applying it for the first time to graph search over probabilistic roadmaps. The competing resources of interest are penalized hierarchically during the search. Higher-ranked resources cause a robot to incur non-negative costs over the paths traveled, which are occasionally zero-valued. This is intended to capture problems in which a robot must manage resources such as visibility of threats, availability of communications, and access to valuable measurements. This leaves freedom for tie-breaking with respect to lower-priority resources; at the bottom of the hierarchy is a strictly positive quantity consumed by the robot, such as distance traveled, energy expended or time elapsed. We compare our method with two other multi-objective approaches, a naive weighted sum method and an expanded graph search method, demonstrating that a lexicographic search can solve such planning problems efficiently without a need for parameter-tuning in unintuitive units. The proposed method is also demonstrated on hardware using a laser-equipped ground robot.