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Amir Ali Ahmadi (a_a_aprinceton.edu) Abstract: Motivated by applications in robotics and computer vision, we study problems related to spatial reasoning of a 3D environment using sublevel sets of polynomials. These include: tightly containing a cloud of points (e.g., representing an obstacle) with convex or nearlyconvex basic semialgebraic sets, computation of Euclidean distance between two such sets, separation of two convex basic semalgebraic sets that overlap, and tight containment of the union of several basic semialgebraic sets with a single convex one. We use algebraic techniques from sum of squares optimization that reduce all these tasks to semidefinite programs of small size and present numerical experiments in realistic scenarios. Keywords: Sum of squares optimization, semidefinite programming, bounding volumes, penetration and distance measures Category 1: Linear, Cone and Semidefinite Programming (Semidefinite Programming ) Category 2: Applications  Science and Engineering Citation: Download: [PDF] Entry Submitted: 01/31/2017 Modify/Update this entry  
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