TY - JOUR
T1 - PDE-based optimization for stochastic mapping and coverage strategies using robotic ensembles
AU - Elamvazhuthi, Karthik
AU - Kuiper, Hendrik
AU - Berman, Spring
N1 - Funding Information:
Spring Berman (M07) received the B.S.E. degree in mechanical and aerospace engineering from Princeton University, Princeton, NJ, in 2005 and the M.S.E. and Ph.D. degrees in mechanical engineering and applied mechanics from the University of Pennsylvania, Philadelphia, PA, in 2008 and 2010, respectively. From 2010 to 2012, she was a Postdoctoral Researcher in Computer Science at Harvard University, Cambridge, MA. Since 2012, she has been an Assistant Professor of Mechanical and Aerospace Engineering with the School for Engineering of Matter, Transport and Energy (SEMTE), Arizona State University, Tempe, AZ. Her research focuses on the modeling and analysis of behaviors in biological and engineered collectives and the synthesis of control strategies for robotic swarms. Prof. Berman is a recipient of the 2014 Defense Advanced Research Projects Agency Young Faculty Award and the 2016 Office of Naval Research Young Investigator Award.
Funding Information:
This work was supported by National Science Foundation (NSF) award no. CMMI-1436960. The material in this paper was partially presented at the IEEE Robotics and Automation Society Conference (ICRA), May 25–30, 2015, Seattle, Washington, USA. This paper was recommended for publication in revised form by Associate Editor Thomas Meurer under the direction of Editor Miroslav Krstic.
Publisher Copyright:
© 2018 Elsevier Ltd
PY - 2018/9
Y1 - 2018/9
N2 - This paper presents a novel partial differential equation (PDE)-based framework for controlling an ensemble of robots, which have limited sensing and actuation capabilities and exhibit stochastic behaviors, to perform mapping and coverage tasks. We model the ensemble population dynamics as an advection–diffusion–reaction PDE model and formulate the mapping and coverage tasks as identification and control problems for this model. In the mapping task, robots are deployed over a closed domain to gather data, which is unlocalized and independent of robot identities, for reconstructing the unknown spatial distribution of a region of interest. We frame this task as a convex optimization problem whose solution represents the region as a spatially-dependent coefficient in the PDE model. We then consider a coverage problem in which the robots must perform a desired activity at a programmable probability rate to achieve a target spatial distribution of activity over the reconstructed region of interest. We formulate this task as an optimal control problem in which the PDE model is expressed as a bilinear control system, with the robots’ coverage activity rate and velocity field defined as the control inputs. We validate our approach with simulations of a combined mapping and coverage scenario in two environments with three target coverage distributions.
AB - This paper presents a novel partial differential equation (PDE)-based framework for controlling an ensemble of robots, which have limited sensing and actuation capabilities and exhibit stochastic behaviors, to perform mapping and coverage tasks. We model the ensemble population dynamics as an advection–diffusion–reaction PDE model and formulate the mapping and coverage tasks as identification and control problems for this model. In the mapping task, robots are deployed over a closed domain to gather data, which is unlocalized and independent of robot identities, for reconstructing the unknown spatial distribution of a region of interest. We frame this task as a convex optimization problem whose solution represents the region as a spatially-dependent coefficient in the PDE model. We then consider a coverage problem in which the robots must perform a desired activity at a programmable probability rate to achieve a target spatial distribution of activity over the reconstructed region of interest. We formulate this task as an optimal control problem in which the PDE model is expressed as a bilinear control system, with the robots’ coverage activity rate and velocity field defined as the control inputs. We validate our approach with simulations of a combined mapping and coverage scenario in two environments with three target coverage distributions.
KW - Autonomous mobile robots
KW - Bilinear control systems
KW - Decentralized systems
KW - Distributed-parameter systems
KW - Optimal control
KW - Partial differential equations
KW - Stochastic systems
KW - Swarm robotics
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U2 - 10.1016/j.automatica.2018.06.007
DO - 10.1016/j.automatica.2018.06.007
M3 - Article
AN - SCOPUS:85048731805
SN - 0005-1098
VL - 95
SP - 356
EP - 367
JO - Automatica
JF - Automatica
ER -