In this paper, we present a time-discrete, incremental methodology for modeling, at the microscopic and macroscopic level, the dynamics of distributed manipulation experiments using swarms of autonomous robots endowed with reactive controllers. The methodology is well-suited for nonspatial metrics since it does not take into account robots' trajectories or the spatial distribution of objects in the environment. The strength of the methodology lies in the fact that it has been generated by considering incremental abstraction steps, from real robots to macroscopic models, each with well-defined mappings between successive implementation levels. Precise heuristic criteria based on geometrical considerations and systematic tests with one or two real robots prevent the introduction of free parameters in the calibration procedure of models. As a consequence, we are able to generate highly abstracted macroscopic models that can capture the dynamics of a swarm of robots at the behavioral level while still being closely anchored to the characteristics of the physical set-up. Although this methodology has been and can be applied to other experiments in distributed manipulation (e.g., object aggregation and segregation, foraging), in this paper we focus on a strictly collaborative case study concerned with pulling sticks out of the ground, an action that requires the collaboration of two robots to be successful. Experiments were carried out with teams consisting of two to 600 individuals at different levels of implementation (real robots, embodied simulations, microscopic and macroscopic models). Results show that models can deliver both qualitatively and quantitatively correct predictions in time lapses that are at least four orders of magnitude smaller than those required by embodied simulations and that they represent a useful tool for generalizing the dynamics of these highly stochastic, asynchronous, nonlinear systems, often outperforming intuitive reasoning. Finally, in addition to discussing subtle numerical effects, small prediction discrepancies, and difficulties in generating the mapping between different abstractions levels, we conclude the paper by reviewing the intrinsic limitations of the current modeling methodology and by proposing a few suggestions for future work.

In this paper, we present discrete-time, nonspatial, macroscopic models able to capture the dynamics of collective aggregation experiments using groups of embodied agents endowed with reactive controllers. The strength of the proposed models is that they have been built up incrementally, with matching between models and embodied simulations verified at each step as new complexity was added. Precise heuristic criteria based on geometrical considerations and systematic tests with one or two embodied agents prevent the introduction of free parameters into the models. The collective aggregation experiments presented in this paper are concerned with the gathering and clustering of small objects initially scattered in an enclosed arena. Experiments were carried out with teams consisting of one to ten individuals, using groups of both constant and time-varying sizes. In the latter case, the number of active workers was controlled by a simple, fully distributed, thresholdbased algorithm whose aim was to allocate an appropriate number of individuals to a time-evolving aggregation demand. To this purpose, agents exclusively used their local perception to estimate the availability of work. Results show that models can deliver both qualitatively and quantitatively correct predictions and they represent a useful tool for generalizing the dynamics of these highly stochastic, asynchronous, nonlinear systems, often outperforming intuitive reasoning. Finally, in addition to discussions of small prediction discrepancies and difficulties in generating quantitatively correct macroscopic models, we conclude the paper by reviewing the intrinsic limitations of the current modeling methodology and by proposing a few suggestions for future work.

In this paper we present three scalable, fully distributed, threshold-based algorithms for allocating autonomous embodied workers to a given task whose demand evolves dynamically over time. Individuals estimate the availability of work based solely on local perceptions. The differences among the algorithms lie in the threshold distribution among teammates (homogeneous or heterogeneous team), in the mechanism used for establishing threshold values (fixed, parameter-based or variable, rule-based), and in the sharing (public) or not sharing (private) of demand estimations through local peer-to-peer communication. We tested the algorithms' efficiency and robustness in a collective manipulation case study concerned with the clustering of initially scattered small objects. The aggregation experiment has been studied at two different experimental levels using a microscopic model and embodied simulations. Results show that teams using a number of active workers dynamically controlled by one of the allocation algorithms achieve similar or better performances in aggregation than those characterized by a constant team size while using on average a considerably reduced number of agents over the whole aggregation process. While differences in efficiency among the algorithms are small, differences in robustness are much more apparent. Threshold variability and peer-to-peer communication appear to be two key mechanisms for improving worker allocation robustness against environmental perturbations.

This paper presents a scalable threshold-based algorithm for allocating workers to a given task whose demand evolves dynamically over time. The algorithm is fully distributed and solely based on the local perceptions of the individuals. Each agent decides autonomously and deterministically to work only when it "feels" that some work needs to be done based on its sensory inputs. In this paper, we applied the worker allocation algorithm to a collective manipulation case study concerned with the gathering and clustering of initially scattered small objects. The aggregation experiment has been studied at three different experimental levels by using macroscopic and microscopic probabilistic models, and embodied simulations. Results show that teams using a number of active workers dynamically controlled by the allocation algorithm achieve similar or better performances in aggregation than those characterized by a constant team size, while using a considerably reduced number of agents over the whole aggregation process. Since this algorithm does not imply any form of explicit communication among agents, it represents a cost-effective solution for controlling the number of active workers in embedded systems consisting of a few to thousands of units.

In this paper, we present a mathematical model of an aggregation experiment carried out using multiple embodied agents in teams of time-varying sizes The aggregation experiment is concerned with the gathering and the clustering of small objects initially scattered in an enclosed arena. The number of active agents engaged in the aggregation task is varying according to a local, distributed stimulus-response law, similar to the behavior observed in ant colonies. We use a set of differential equations to describe the dynamics of the system at the macroscopic level. We validate the predictions of this model by comparing them to experimental data obtained using a sensor-based embodied simulator. Results show that the proposed approach delivers accurate predictions and constitutes a computationally efficient tool for studying aggregation experiments with groups of constant or variable sues. The simplicity of the model suggests that it is easily applicable to other aggregation or segregation experiments characterized by different agent capabilities and individual control algorithms.