A framework of space–time continuous models for algorithm design in swarm robotics

Abstract

Designing and analyzing self-organizing systems such as robotic swarms is a challenging task even though we have complete knowledge about the robot's interior. It is difficult to determine the individual robot's behavior based on the swarm behavior and vice versa due to the high number of agent-agent interactions. A step towards a solution of this problem is the development of appropriate models, which accurately predict the swarm behavior based on a specified control algorithm. Such models would reduce the necessary number of time-consuming simulations and experiments during the design process of an algorithm. In this paper we propose a model with focus on an explicit representation of space because the effectiveness of many swarm robotic scenarios depends on spatial inhomogeneity. We use methods of statistical physics to address spatiality. Starting from a description of a single robot we derive an abstract model of swarm motion. The model is then extended to a generic model framework of communicating robots. In two examples we validate models against simulation results. Our experience shows that qualitative correctness is easily achieved while quantitative correctness is disproportionately more difficult but still possible.

Swarm robotics: a review from the swarm engineering perspective

“…A recent advancement in macroscopic modeling based on differential equations is due to Hamann and Wörn (2008). Their models include noise, stochasticity, and spatiality.…”

“…The derivation of the Fokker-Planck equation starting from the Langevin equation is possible using tools of statistical mechanics plus some problem-dependent intuition. Hamann and Wörn (2008) applied this modeling method to analyze coordinated motion (which they call collective taxis), aggregation (which they call collective perception) and foraging. Recently, the authors modeled aggregation in presence of a temperature gradient in the environment, and provided a comparison with another model called Stock & Flow (Schmickl et al 2009).…”

The impact of agent density on scalability in collective systems: noise-induced versus majority-based bistability

“…Consequently, the variance in the swarm density becomes relevant. If the swarm density variance is high, which is often the case in swarm systems (e.g., see [35,15]), then there are areas of both high and low density. The fraction of the swarm N h /N operating in an area of high density d h is probably effective, but the fraction of the swarm N l /N operating in an area of low density d l is probably ineffective or even obstructive with respect to the swarm capacity of making a collective decision.…”

Performance Bounds on Spatial Coverage Tasks by Stochastic Robotic Swarms

“…Toward this end, we employ a methodology that is based on models of the robots' decision making and motion at multiple levels of abstraction. The multilevel modeling framework is adopted from the disciplines of stochastic chemical kinetics and fluid dynamics, and it has been used by the authors and others, e.g., in [13], [17], [27], to describe the population dynamics of large numbers of robots. This framework has also been used to model collective behaviors in biological swarms, such as flocking, schooling, chemotaxis, pattern formation, and predator-prey interactions [24].…”