TY - GEN
T1 - Statistical analysis of stochastic multi-robot boundary coverage
AU - Kumar, Ganesh P.
AU - Berman, Spring
N1 - Publisher Copyright:
© 2014 IEEE.
PY - 2014/9/22
Y1 - 2014/9/22
N2 - We present a novel analytical approach to computing the population and geometric parameters of a multi-robot system that will provably produce specified boundary coverage statistics. We consider scenarios in which robots with no global position information, communication, or prior environmental data have arrived at uniformly random locations along a simple closed or open boundary. This type of scenario can arise in a variety of multi-robot tasks, including surveillance, collective transport, disaster response, and therapeutic and imaging applications in nanomedicine. We derive the probability that a given point robot configuration is saturated, meaning that all pairs of adjacent robots are no farther apart than a specified distance. This derivation relies on a geometric interpretation of the saturation probability and an application of the Inclusion-Exclusion Principle, and it is easily extended to finite-sized robots. In the process, we obtain formulas for (a) an integral that is in general computationally expensive to compute directly, and (b) the volume of the intersection of a regular simplex with a hypercube. In addition, we use results from order statistics to compute the probability distributions of the robot positions along the boundary and the distances between adjacent robots. We validate our derivations of these probability distributions and the saturation probability using Monte Carlo simulations of scenarios with both point robots and finite-sized robots.
AB - We present a novel analytical approach to computing the population and geometric parameters of a multi-robot system that will provably produce specified boundary coverage statistics. We consider scenarios in which robots with no global position information, communication, or prior environmental data have arrived at uniformly random locations along a simple closed or open boundary. This type of scenario can arise in a variety of multi-robot tasks, including surveillance, collective transport, disaster response, and therapeutic and imaging applications in nanomedicine. We derive the probability that a given point robot configuration is saturated, meaning that all pairs of adjacent robots are no farther apart than a specified distance. This derivation relies on a geometric interpretation of the saturation probability and an application of the Inclusion-Exclusion Principle, and it is easily extended to finite-sized robots. In the process, we obtain formulas for (a) an integral that is in general computationally expensive to compute directly, and (b) the volume of the intersection of a regular simplex with a hypercube. In addition, we use results from order statistics to compute the probability distributions of the robot positions along the boundary and the distances between adjacent robots. We validate our derivations of these probability distributions and the saturation probability using Monte Carlo simulations of scenarios with both point robots and finite-sized robots.
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U2 - 10.1109/ICRA.2014.6906592
DO - 10.1109/ICRA.2014.6906592
M3 - Conference contribution
AN - SCOPUS:84929177954
T3 - Proceedings - IEEE International Conference on Robotics and Automation
SP - 74
EP - 81
BT - Proceedings - IEEE International Conference on Robotics and Automation
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2014 IEEE International Conference on Robotics and Automation, ICRA 2014
Y2 - 31 May 2014 through 7 June 2014
ER -