An optimal control approach to mapping GPS-denied environments using a stochastic robotic swarm

Ragesh K. Ramachandran, Karthik Elamvazhuthi, Spring Berman

Research output: Chapter in Book/Report/Conference proceedingChapter

15 Scopus citations


This paper presents an approach to mapping a region of interest using observations from a robotic swarm without localization. The robots have local sensing capabilities and no communication, and they exhibit stochasticity in their motion. We model the swarm population dynamics with a set of advection-diffusion-reaction partial differential equations (PDEs). The map of the environment is incorporated into this model using a spatially-dependent indicator function that marks the presence or absence of the region of interest throughout the domain. To estimate this indicator function, we define it as the solution of an optimization problem in which we minimize an objective functional that is based on temporal robot data. The optimization is performed numerically offline using a standard gradient descent algorithm. Simulations show that our approach can produce fairly accurate estimates of the positions and geometries of different types of regions in an unknown environment.

Original languageEnglish (US)
Title of host publicationSpringer Proceedings in Advanced Robotics
PublisherSpringer Science and Business Media B.V.
Number of pages17
StatePublished - 2018

Publication series

NameSpringer Proceedings in Advanced Robotics
ISSN (Print)2511-1256
ISSN (Electronic)2511-1264


  • Distributed robotic systems
  • Mapping gps-denied environments
  • Stochastic robotics
  • Unlocalized robotic swarm

ASJC Scopus subject areas

  • Mechanical Engineering
  • Artificial Intelligence
  • Engineering (miscellaneous)
  • Applied Mathematics
  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Computer Science Applications


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