A macroscopic model for high intensity radiofrequency signal detection in swarm robotics systems

Abstract

In recent years, there has been a growing interest in resource location in unknown environments for robotic systems, which are composed of multiple simple robots rather than one highly capable robot [M. Sempere, F. Aznar, M. Pujol, and R. Rizo, On cooperative swarm foraging for simple, non explicitly connected, agents, 2010]. This tradeoff reduces the design and hardware complexity of the robots and removes single point failures, but adds complexity in algorithm design. The challenge is to programme a swarm of simple robots, with minimal intercommunication and individual capability, to perform a useful task as a group. This paper is focused on finding the highest intensity area of a radiofrequency (RF) signal in urban environments. These signals are usually more intense near the city centre and its proximity, since in these zones the risk of signal saturation is high. RF radiation (RFR) is boosted or blocked mainly depending on orography or building structures. RF providers need to supply enough coverage, setting up different antennas to be able to provide a minimum quality of service. We will define a micro/macroscopic mathematical model to efficiently study a swarm robotic system, predict their long-term behaviour and gain insight into the system design. The macroscopic model will be obtained from Rate Equations, describing the dynamics of the swarm collective behaviour. In our experimental section, the Campus of the University of Alicante will be used to simulate our model. Three RFR antennas will be taken into account, one inside our Campus and the other two in its perimeter. Several tests, that show the convergence of the swarm towards the RFR, will be presented. In addition, the obtained RFR maps and the macroscopic behaviour of the swarm will be discussed.

Keywords:

• macroscopic mathematical model
• swarm robotic system
• resource location

1999 AMS Subject Classifications:

• 68T01
• 68T40
• 68T05

Acknowledgements

This work has been supported by the Spanish Ministerio de Ciencia e Innovacin, project TIN2009-10581.

Notes

1 Although the rules that define the operation of the agents are extremely simple, this not the case with the operation of the swarm. As discussed in [13], the design and evaluation of the behaviours that generate self-organization of swarm systems is a complex problem that depends on many factors, including the initial position of agents, the distribution of the environment\ldots.

2 The simplest way to calculate this vector requires to know the current position of the robot pos_i and the position of its pair pos_mi so that the repulsion vector can be defined as and the attraction vector is . Nevertheless, the attraction or repulsion vectors can be also calculated without knowing the current position of the robot, by using only indirect location methods.