Ádám M. Halász

Optimized Stochastic Policies for Task Allocation in Swarms of Robots

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.

Stochastic Modeling and Control of Biological Systems: The Lactose Regulation System of Escherichia Coli

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.

Quantitative understanding of cell signaling: the importance of membrane organization.

Systems biology modeling of signal transduction pathways traditionally employs ordinary differential equations, deterministic models based on the assumptions of spatial homogeneity. However, this can be a poor approximation for certain aspects of signal transduction, especially its initial steps: the cell membrane exhibits significant spatial organization, with diffusion rates approximately two orders of magnitude slower than those in the cytosol. Thus, to unravel the complexities of signaling pathways, quantitative models must consider spatial organization as an important feature of cell signaling. Furthermore, spatial separation limits the number of molecules that can physically interact, requiring stochastic simulation methods that account for individual molecules. Herein, we discuss the need for mathematical models and experiments that appreciate the importance of spatial organization in the membrane.

Mathematical Simulation of Membrane Protein Clustering for Efficient Signal Transduction

Initiation and propagation of cell signaling depend on productive interactions among signaling proteins at the plasma membrane. These diffusion-limited interactions can be influenced by features of the membrane that introduce barriers, such as cytoskeletal corrals, or microdomains that transiently confine both transmembrane receptors and membrane-tethered peripheral proteins. Membrane topographical features can lead to clustering of receptors and other membrane components, even under very dynamic conditions. This review considers the experimental and mathematical evidence that protein clustering impacts cell signaling in complex ways. Simulation approaches used to consider these stochastic processes are discussed.

Specialization as an optimal strategy under varying external conditions

We present an investigation of specialization when considering the execution of collaborative tasks by a robot swarm. Specifically, we consider the stick-pulling problem first proposed by Martinoli et al. [1], [2] and develop a macroscopic analytical model for the swarm executing a set of tasks that require the collaboration of two robots. We show, for constant external conditions, maximum productivity can be achieved by a single species swarm with carefully chosen operational parameters. While the same applies for a two species swarm, we show how specialization is a strategy best employed for changing external conditions.

Navigation-based optimization of stochastic strategies for allocating a robot swarm among multiple sites

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, 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.

Algorithms for the analysis and synthesis of a bio-inspired swarm robotic system

We present a methodology for characterizing, analyzing, and synthesizing swarm behaviors using both a macroscopic continuous model that represents a swarm as a continuum and a macroscopic discrete model that enumerates individual agents. Our methodology is applied to a dynamical model of ant house hunting, a decentralized process in which a colony attempts to emigrate to the best site among several alternatives. The model is hybrid because the colony switches between different sets of behaviors, or modes, during this process. Using the model in [1], we investigate the relation of site population growth to initial system state with an algorithm called Multi-Affine Reachability analysis using Conical Overapproximations (Marco) [2]. We then derive a microscopic hybrid dynamical model of an agent that respects the specifications of the global behavior at the continuous level. Our multi-level simulations demonstrate that we have produced a rigorously correct microscopic model from the macroscopic descriptions.

Optimization of stochastic strategies for spatially inhomogeneous robot swarms: A case study in commercial pollination

We present a scalable approach to optimizing robot control policies for a target collective behavior in a spatially inhomogeneous robotic swarm. The approach can incorporate robot feedback to maintain system performance in an unknown environmental flow field. We consider systems in which the robots follow both deterministic and random motion and transition stochastically between tasks. Our methodology is based on an abstraction of the swarm to a macroscopic continuous model, whose dimensionality is independent of the population size, that describes the expected time evolution of swarm subpopulations over a discretization of the environment. We incorporate this model into a stochastic optimization method and map the optimized model parameters onto the robot motion and task transition control policies to achieve a desired global objective. We illustrate our methodology with a scenario in which the behaviors of a swarm of robotic bees are optimized for both uniform and nonuniform pollination of a blueberry field, including in the presence of an unknown wind.

Towards A Fully Automated High-Throughput Phototransfection System.

We have designed and implemented a framework for creating a fully automated high-throughput phototransfection system. Integrated image processing, laser target position calculation, and stage movements show a throughput increase of >23x over the current manual phototransfection method although the potential for even greater throughput improvements (>110x) is described. A software tool for automated off-line single-cell morphological measurements, as well as real-time image segmentation analysis, has also been constructed and shown to be able to quantify changes in the cell before and after the process, successfully characterizing them, using metrics such as cell perimeter, area, major and minor axis length, and eccentricity values.

Orchestration of ErbB3 signaling through heterointeractions and homointeractions.

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.