Paul Liu

Papers

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About

Paul Liu is a leading researcher in algorithmic robotics and computational geometry, with a primary focus on coordinated motion planning for multi-agent systems. His work addresses the fundamental challenge of determining optimal, collision-free paths for multiple robots operating in shared environments. Liu’s most cited paper, "Characterizing minimum-length coordinated motions for two discs" (2016, 10 citations), provides an exact mathematical characterization of the shortest collision-avoiding motion for two disc robots, a foundational contribution to the theory of optimal multi-robot coordination. This analytical result offers a rigorous benchmark for evaluating heuristic and approximation algorithms in the field. Liu’s impact is further demonstrated by his first-place victory in the CG:SHOP 2021 challenge, detailed in "Coordinated Motion Planning Through Randomized k-Opt" (5 citations). For this competition, he and his team developed a winning algorithm that minimized total distance traveled and makespan for square robots, showcasing the practical power of randomized k-opt optimization. This achievement highlights Liu’s ability to translate complex geometric theory into high-performance, real-world solutions, making him a notable figure in both theoretical and applied motion planning research.