Modeling Swarm Robotic Systems: a Case Study in Collaborative Distributed Manipulation

Abstract

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.

System Identification of Self-Organizing Robotic Swarms

“…As more extensively detailed in [9] we abstract the robots' behavior as an arbitrary Probabilistic Finite State Machine (PFSM), whose states are chosen according to the metric of interest. Interactions among the robots or with the environment are represented by state transitions and abstracted to encountering probabilities, whereas the time spent in a certain state is captured by the average interaction time.…”

“…Calibration of Model Parameters: Following [4,9], we calculate the geometric probability of encountering an object from the ratio of the object's detection area (the area in that it can be detected by another robot), and the total area of the arena. The (unit less) geometric probability can then be converted into the object's encountering probability per time-step, using a simple heuristic based on the area that a robot sweeps with its sensors in this period (based on the characteristics of its sensors and its speed).…”

“…System modeling and identification [6,8] is the process of deriving a mathematical model for a metric of interest from observed data. For swarm-robotic systems, probabilistic models have been successfully applied to several case studies (see for instance [9] or [7,11]), and lead to good quantitative agreement between reality and the prediction of the model. In this contribution, we take a step forwards and show how the identification process can be complemented by optimization procedures for improving the quantitative agreement between model prediction and experimental data.…”

“…Such improved models can then serve as a baseline for exploring other aspects of the system without performing additional experiments. As a case study we consider a homogeneous swarm engaged in the inspection of a regular structure [5], where modeling assumptions (homogeneous distribution of robots and objects, see [9] for more details) are only partially fulfilled. In this case, optimization of model parameters allows us not only to achieve accurate prediction in the model, but also yields valuable insight into improving the structure of the model.…”

Communication in a Swarm of Miniature Robots: The e-Puck as an Educational Tool for Swarm Robotics

“…Taking this logic one step further, we can actually formalize the varying degrees of complexity possible; ranging from realistic simulation to mathematical macroscopic models [15]. Further details and examples of this multi-level approach can be found in [9,2].…”