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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 sucharXiv:1909.02184v2 fatcat:ry44ljkmc5g57dicp67yfstdke