Geometry of 3D environments and sum of squares polynomials

Amir Ali Ahmadi, Georgina Hall, Ameesh Makadia, Vikas Sindhwani

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

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.

Original languageEnglish (US)
Title of host publicationRobotics
Subtitle of host publicationScience and Systems XIII, RSS 2017
EditorsSiddhartha Srinivasa, Nora Ayanian, Nancy Amato, Scott Kuindersma
PublisherMIT Press Journals
ISBN (Electronic)9780992374730
StatePublished - Jan 1 2017
Event2017 Robotics: Science and Systems, RSS 2017 - Cambridge, United States
Duration: Jul 12 2017Jul 16 2017

Publication series

NameRobotics: Science and Systems
Volume13
ISSN (Electronic)2330-765X

Other

Other2017 Robotics: Science and Systems, RSS 2017
CountryUnited States
CityCambridge
Period7/12/177/16/17

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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