An Enzyme-Inspired Approach to Stochastic Allocation of Robotic Swarms Around Boundaries

Pavlic, Theodore P.; Wilson, Sean; Kumar, Ganesh P.; Berman, Spring

doi:10.1007/978-3-319-28872-7_36

Cited by 7 publications

(19 citation statements)

References 23 publications

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“…The unordered points t i , which were picked uniformly randomly on the unit interval I , are called the parent variables; the i th ordered point t i is called the i th order statistic of the parent. An approach based on order statistics not only confirms Equation (19) [21, pp.133-135] but also yields the pdf's of t i and s i . To simplify notation, we define the indicator function 1 X : X → {0, 1} of an arbitrary set X to be 1 X (x) := 1 iff x ∈ X, and 1 X (x) := 0 otherwise.…”

Section: Statistics Of Robot Positions and Slacksmentioning

confidence: 98%

“…(6) An immediate consequence of Equation (19) is that we can now evaluate the integral in Equation (6) as |E | = p sat |Ω| = p sat /(n − 1)! Let Σ denote the sum on the right side of Equation (19). Given n, d, and s = 1, this sum Σ Equation (19) takes K steps in all to evaluate in a loop.…”

Section: Geometric Interpretation Of P Satmentioning

confidence: 99%

“…Let Σ denote the sum on the right side of Equation (19). Given n, d, and s = 1, this sum Σ Equation (19) takes K steps in all to evaluate in a loop. For efficiency, the k-th step computes n k recursively from …”

Section: Geometric Interpretation Of P Satmentioning

confidence: 99%

“…Snapshot of a simulation in which a swarm of randomly-moving robots (green circles) with only local information must allocate themselves in groups of target sizes (red circles) around the perimeters of two types of circular regions (yellow and blue). We have developed an approach to designing stochastic robot control policies that produce the target allocations with probabilistic guarantees on performance [19].…”

Section: Introductionmentioning

confidence: 99%

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Statistical analysis of stochastic multi-robot boundary coverage

Kumar

Berman

2014

2014 IEEE International Conference on Robotics and Automation (ICRA)

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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 InclusionExclusion 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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Section: Statistics Of Robot Positions and Slacksmentioning

confidence: 98%

Section: Geometric Interpretation Of P Satmentioning

confidence: 99%

Section: Geometric Interpretation Of P Satmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Statistical analysis of stochastic multi-robot boundary coverage

Kumar

Berman

2014

2014 IEEE International Conference on Robotics and Automation (ICRA)

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“…Some research focuses on coating objects as an independent task under the name of target surrounding or boundary coverage. The techniques used in this context include stochastic robot behaviors [13,14], rule-based control mechanisms [15] and potential field-based approaches [16]. While the analytic techniques developed in swarm robotics are somewhat relevant to this work, many such systems assume more computational power and movement capabilities than the model studied in this work does.…”

Section: Related Workmentioning

confidence: 99%

On the Runtime of Universal Coating for Programmable Matter

Derakhshandeh

Gmyr

Porter

et al. 2016

Lecture Notes in Computer Science

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Abstract. Imagine coating buildings and bridges with smart particles (also coined smart paint) that monitor structural integrity and sense and report on traffic and wind loads, leading to technology that could do such inspection jobs faster and cheaper and increase safety at the same time. In this paper, we study the problem of uniformly coating objects of arbitrary shape in the context of self-organizing programmable matter, i.e., programmable matter which consists of simple computational elements called particles that can establish and release bonds and can actively move in a self-organized way. Particles are anonymous, have constant-size memory, and utilize only local interactions in order to coat an object. We continue the study of our Universal Coating algorithm by focusing on its runtime analysis, showing that our algorithm terminates within a linear number of rounds with high probability. We also present a matching linear lower bound that holds with high probability. We use this lower bound to show a linear lower bound on the competitive gap between fully local coating algorithms and coating algorithms that rely on global information, which implies that our algorithm is also optimal in a competitive sense. Simulation results show that the competitive ratio of our algorithm may be better than linear in practice.

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Universal coating for programmable matter

Derakhshandeh

Gmyr

Richa

et al. 2017

Theoretical Computer Science

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The idea behind universal coating is to have a thin layer of a specific substance covering an object of any shape so that one can measure a certain condition (like temperature or cracks) at any spot on the surface of the object without requiring direct access to that spot. We study the universal coating problem in the context of self-organizing programmable matter consisting of simple computational elements, called particles, that can establish and release bonds and can actively move in a self-organized way. Based on that matter, we present a worst-case work-optimal universal coating algorithm that uniformly coats any object of arbitrary shape and size that allows a uniform coating. Our particles are anonymous, do not have any global information, have constant-size memory, and utilize only local interactions.

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An Enzyme-Inspired Approach to Stochastic Allocation of Robotic Swarms Around Boundaries

Cited by 7 publications

References 23 publications

Statistical analysis of stochastic multi-robot boundary coverage

Statistical analysis of stochastic multi-robot boundary coverage

On the Runtime of Universal Coating for Programmable Matter

Universal coating for programmable matter

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