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.

Abstract-This paper introduces the multi-robot boundary coverage problem, wherein a group of k robots must inspect every point on the boundary of a 2-dimensional test environment. Using a simplified sensor model, this inspection problem is converted to an equivalent graph representation. In this representation, the coverage problem can be posed as the kRural Postman Problem (kRPP). We present a constructive heuristic which finds a solution to the kRPP, then use that solution to plan the robots' inspection routes. These routes provide complete coverage of the boundary and also balance the inspection load across the k robots. Simulations illustrate the algorithm's performance and characteristics.

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.

Abstract. In this paper, we discuss strengths and limitations of different abstraction levels for distributed robotics experiments. We support the discussion with a concrete case study which has been investigated at four different levels: real robots, embodied simulations, microscopic modeling, and macroscopic modeling. Both modeling methodologies presented represent the collective dynamics of the experiment as a set of stochastic events based on simple geometrical considerations and systematic tests with one or two real robots instead of computing trajectories and sensory information like an embodied simulator would do. The case study we describe is concerned with pulling sticks out of the ground -an action which requires the collaboration of two robots to be successful. Experiments were carried out with teams consisting of two to 24 individuals endowed with simple reactive controllers. In addition to showing that models can deliver both qualitatively and quantitatively correct predictions in time lapses that are three or four orders of magnitude smaller than those required by embodied simulations, we discuss differences, assumptions, and subtle numerical effects of the current modeling methodologies.

This paper presents the investigation of three communication schemes which may be used in a distributed robotic system, two based on implicit forms of communication (mechanical interaction and vision) and one based on an explicit form of communication (infrared signaling). To support the discussion and comparison between the three forms, we have chosen a concrete case study concerned with locating and pulling sticks out of an arena floor, a task successfully achieved only through collaboration between two robots. Communication schemes, among other system features, heavily influence the rate of successful collaborations, the metric adopted in this paper in order to evaluate the performance of the robotic team. Results collected using an embodied simulator show that, as a function of the system constraints (e.g., number of robots, hardware and behavioral parameters) solutions based on more complex individuals do not necessarily lead to an improved team performance. Although the stick pulling is a simple case study without any practical application, it presents all the main difficulties of designing and controlling scalable, distributed robotic systems, characterized by subtle, nested effects between individual and group behavior or hardware and software parameters. We believe that embodied simulations are a key level of implementation in helping us understand these subtle mechanisms, achieve further abstraction, and optimize the system before any real hardware solution is implemented.