Name: Kensen Shi High School: A&M Consolidated High School Mentor: Dr. Nancy Amato

1. Name: Kensen Shi High School: A&M Consolidated High School Mentor: Dr. Nancy Amato Project Title: Lazy Toggle PRM: A Single-Query Approach to Motion Planning The motion planning problem involves finding a valid path for a moveable object among obstacles (e.g., planning safe motions for assembly-line robots in a factory setting). Probabilistic RoadMaps (PRMs) are quite successful in solving complex motion planning problems. While particularly suited for multiple-query scenarios (i.e., those where multiple paths must be planned in the same environment), they lack efficiency in both solving single-query scenarios and mapping narrow passages (e.g., doorways between rooms). Two PRM variants separately tackle these gaps. Lazy PRM reduces the computational cost of roadmap construction for single-query scenarios by delaying roadmap validation until query time. Toggle PRM is well suited for mapping narrow spaces by mapping both the free space and the obstacle space, which gives certain theoretical benefits. However, fully validating the two roadmaps can be costly. In this paper, we present a cohesive strategy, Lazy Toggle PRM, for integrating these two approaches into a method which is suited for both narrow passages and efficient single-query calculations. We demonstrate the effectiveness of Lazy Toggle PRM in a wide range of scenarios, including those with narrow passages and highly complex environments, concluding that it is more effective than contemporary methods in solving difficult queries.