@inproceedings{894f2b3b6f7d434cbedb1efe57e5909e,

title = "Geometry of 3D environments and sum of squares polynomials",

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 nearly-convex 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.",

author = "Ahmadi, {Amir Ali} and Georgina Hall and Ameesh Makadia and Vikas Sindhwani",

note = "Funding Information: 1Dept. of Operations Research and Financial Engineering, Princeton University, Princeton NJ, USA. Partially supported by a Google Faculty Research Award. a_a_a@princeton.edu, gh4@princeton.edu 2Google, New York, USA makadia@google.com 2Google Brain, New York, USA sindhwani@google.com Publisher Copyright: {\textcopyright} 2017 MIT Press Journals. All rights reserved.; 2017 Robotics: Science and Systems, RSS 2017 ; Conference date: 12-07-2017 Through 16-07-2017",

year = "2017",

language = "English (US)",

series = "Robotics: Science and Systems",

publisher = "MIT Press Journals",

editor = "Siddhartha Srinivasa and Nora Ayanian and Nancy Amato and Scott Kuindersma",

booktitle = "Robotics",

address = "United States",

}