We present a scalable approach to dynamically allocating a swarm of homogeneous robots to multiple tasks, which are to be performed in parallel, following a desired distribution. We employ a decentralized strategy that requires no communication among robots. It is based on the development of a continuous abstraction of the swarm obtained by modeling population fractions and defining the task allocation problem as the selection of rates of robot ingress and egress to and from each task. These rates are used to determine probabilities that define stochastic control policies for individual robots, which, in turn, produce the desired collective behavior. We address the problem of computing rates to achieve fast redistribution of the swarm subject to constraint(s) on switching between tasks at equilibrium. We present several formulations of this optimization problem that vary in the precedence constraints between tasks and in their dependence on the initial robot distribution. We use each formulation to optimize the rates for a scenario with four tasks and compare the resulting control policies using a simulation in which 250 robots redistribute themselves among four buildings to survey the perimeters. KeywordsMarkov processes, distributed control, multi-robot systems, optimisation, stochastic systems, Markov processes, decentralized strategy, distributed control, homogeneous swarm robots, optimization problem, optimized stochastic policies, stochastic systems, task allocation, Distributed control, Markov processes, optimization, stochastic systems, swarm robotics, task allocation This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it. Abstract-We present a scalable approach to dynamically allocating a swarm of homogeneous robots to multiple tasks, which are to be performed in parallel, following a desired distribution. We employ a decentralized strategy that requires no communication among robots. It is based on the development of a continuous abstraction of the swarm obtained by modeling population fractions and defining the task allocation problem as the selection of rates of robot ingress and egress to and from each task. These rates are used to determine probabilities that define stochastic control policies for individual robots, which, in turn, produce the desired collective behavior. We address the problem of computing rates to achieve fast redistribution of the swarm subject to constraint(s) on switching between tasks at equilibrium. We present several formulations of this optimizatio...

We present a biologically inspired approach to the dynamic assignment and reassignment of a homogeneous swarm of robots to multiple locations, which is relevant to applications like search and rescue, environmental monitoring, and task allocation. Our work is inspired by experimental studies of ant house hunting and empirical models that predict the behavior of the colony that is faced with a choice between multiple candidate nests. We design quorum based stochastic control policies that enable the team of agents to distribute themselves among multiple candidate sites in a specified ratio, and compare our results to the linear stochastic policies described in (Halasz et al.We show how our quorum model consistently performs better than the linear models while minimizing computational requirements and now it can be implemented without the use of inter-agent wireless communication.

Abstract-In this paper, we present a comprehensive framework for stochastic modeling, model abstraction, and controller design for a biological system. The first half of the paper concerns modeling and model abstraction of the system. Most models in systems biology are deterministic models with ordinary differential equations in the concentration variables. We present a stochastic hybrid model of the lactose regulation system of E. coli bacteria that capture important phenomena which cannot be described by continuous deterministic models. We then show that the resulting stochastic hybrid model can be abstracted into a much simpler model, a two-state continuous-time Markov chain. The second half of the paper discusses controller design for a specific architecture. The architecture consists of measurement of a global quantity in a colony of bacteria as an output feedback and manipulation of global environmental variables as control actuation. We show that controller design can be performed on the abstracted (Markov chain) model and implementation on the real model yields the desired result.

We present an approach for the dynamic assignment and reassignment of a large team of homogeneous robotic agents to multiple locations with applications to search and rescue, reconnaissance and exploration missions. Our work is inspired by experimental studies of ant house hunting and empirical models that predict the behavior of the colony that is faced with a choice between multiple candidate nests. We design stochastic control policies that enable the team of agents to distribute themselves between multiple candidate sites in a specified ratio. Additionally, we present an extension to our model to enable fast convergence via switching behaviors based on quorum sensing. The stability and convergence properties of these control policies are analyzed and simulation results are presented.

We present a decentralized, communication-less approach to the dynamic allocation of a swarm of homogeneous robots to a target distribution among multiple sites. Building on our work in [1], we optimize stochastic control policies for the robots that cause the population to quickly redistribute among the sites while adhering to a limit on inter-site traffic at equilibrium. We propose a way to account for delays due to navigation between sites in our controller synthesis procedure. Control policies that are designed with and without the use of delay statistics are compared for a simulation in which 240 robots distribute themselves among four buildings.

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A biochemical species is called producible in a constraints-based metabolic model if a feasible steady-state flux configuration exists that sustains its nonzero concentration during growth. Extreme semipositive conservation relations (ESCRs) are the simplest semipositive linear combinations of species concentrations that are invariant to all metabolic flux configurations. In this article, we outline a fundamental relationship between the ESCRs of a metabolic network and the producibility of a biochemical species under a nutrient media. We exploit this relationship in an algorithm that systematically enumerates all minimal nutrient sets that render an objective species weakly producible (i.e., producible in the absence of thermodynamic constraints) through a simple traversal of ESCRs. We apply our results to a recent genome scale model of Escherichia coli metabolism, in which we traverse the 51 anhydrous ESCRs of the metabolic network to determine all 928 minimal aqueous nutrient media that render biomass weakly producible. Applying irreversibility constraints, we find 287 of these 928 nutrient sets to be thermodynamically feasible. We also find that an additional 365 of these nutrient sets are thermodynamically feasible in the presence of oxygen. Since biomass producibility is commonly used as a surrogate for growth in genome scale metabolic models, our results represent testable hypotheses of alternate growth media derived from in silico analysis of the E. coli genome scale metabolic network.

ErbB receptors form homodimers and heterodimers between family members. To model ErbB2/ErbB3 signaling, single-particle tracking data are used to create a simulation space with overlapping receptor domains. Stochastic modeling of receptor dimerization and phosphorylation reveals the complexity of ErbB2-3 interactions.