Elsevier

Robotics and Autonomous Systems

Volume 57, Issue 9, 30 September 2009, Pages 913-921
Robotics and Autonomous Systems

Two different approaches to a macroscopic model of a bio-inspired robotic swarm

https://doi.org/10.1016/j.robot.2009.06.002Get rights and content

Abstract

By compiling macroscopic models we analyze the adaptive behavior in a swarm of autonomous robots generated by a bio-inspired, distributed control algorithm. We developed two macroscopic models by taking two different perspectives: A Stock & Flow model, which is simple to implement and fast to simulate, and a spatially resolved model based on diffusion processes. These two models were compared concerning their prediction quality and their analytical power: One model allowed easy identification of the major feedback loops governing the swarm behavior. The other model allowed analysis of the expected shapes and positions of observable robot clusters. We found a high correlation in the challenges posed by both modeling techniques and we highlighted the inherent problems of inferring emergent macroscopic rules from a microscopic description of swarm behavior.

Introduction

Swarm robotics [1], [2], which is the robotic application of swarm intelligence [3], [4], [5], is an emerging field of science characterized by a high degree of interdisciplinarity. An ever-increasing variety of projects tries to solve the major key problems of autonomously interacting moving machines (robots), which are: complexity, noise tolerance, adaptability and predictability of collective behavior. Most of these projects are performed by interdisciplinary teams to tackle these problems from several scientific directions simultaneously and cooperatively [6], [7]. These teams often include engineering scientists, mathematicians, physicists and biologists. The approaches pursued to develop the robot controllers are also manifold. Evolutionary Algorithms [8], potential field methods [9], and hand-coded bio-inspired algorithms [10] are applied. The idea of investigating bio-inspired control algorithms is based on the fact that interacting groups of organisms (swarms, herds, flocks) are frequently found in nature [11]. These forms of collective behavior emerged by natural selection [12] during millions of years of biological evolution and can, therefore, be assumed to be well shaped and well adapted to the ecological constraints of the animals that show these behaviors. By translating these behavioral principles to robotic control programs, stable and efficient robotic swarms can be formed. Whereas these control programs act in environments that are comparable to the environment of the focal real-world organisms. Additionally, the robotic swarm can also serve as a sort of a hardware simulation of the biological source of inspiration. In this way, it can be used as a valuable tool to investigate and to understand biological swarm systems. For both of these approaches, the identification and the understanding of key factors shaping the swarm behavior and other global swarm properties are crucial for achieving valuable scientific results. As these systems are multi-component systems consisting of many cooperating agents, the basic key factors reside within the agent-to-agent interactions. It is the composition of distributed feedback loops (negative and positive) being responsible for the resulting collective swarm behaviors.

Often bottom-up simulation (individual-based or embodied simulation) is used to simulate swarm behavior on a computer. These microscopic models have frequently turned out to be an imperfect tool for identifying and analyzing these feedbacks: Such simulations are often too much focused on mimicking the overall collective behaviors instead of incorporating all relevant proximate mechanisms. Unfortunately, the predicted collective swarm behavior might result from simulation artifacts, hidden behind the high complexity of these individual-based simulations. Additionally, bottom-up simulations suffer from computational complexity, not allowing decent and exhaustive parameter sweeps within reasonable time.

In contrast, macroscopic models involving a higher level of abstraction, are easier to understand, easier to analyze (parameter sweeps, sensitivity analysis) and can possibly reveal a few intrinsic parameters of the system strongly affecting or even governing the swarm behavior.

In general, the purpose of macroscopic models in swarm robotics is to support the algorithm design phase as the design of individual-/micro-level algorithms, that result in the desired swarm/macrobehavior, has proven to be challenging [13], [14]. One option to overcome this problem is the modeling approach. In swarm robotics there is only a small variety in mature state-of-the-art models that are ready to support the algorithm design phase. The presumably mostly used approach is based on rate equations (e.g., see [14], [15]). A drawback of these rate equation approaches is the limited representation of space — either homogeneous space is assumed or a rough discretization by states is done (nevertheless, in [16] a conceptual approach is reported showing a generalization of the rate equation approach to continuous space). In addition to the rate equation approaches, several other preliminary and rather specialized models were proposed: In [17] a formal method using temporal logic to specify emergent swarm behavior is presented. In [18] a model for a special aggregation behavior is analytically derived by applying combinatorics and linear algebra. In [19] a model for a special case of a collective motion algorithm [20] is presented. For a more detailed review of swarm models with focus on swarm robotics see [13].

Both models, that are presented in this paper, are macroscopic and have potential to be generalizable. The idea of this modeling approach is to predict the macroscopic behavior based on the control algorithm, which is a microscopic description. The most relevant quantity, that is predicted by the models, is number of robots (or robot density) at areas of interest.

Section snippets

The robotic swarm — empiric experiments

The focal scenario of our modeling approach was a series of empiric experiments performed with a swarm of 15 mobile and autonomous Jasmine robots [21]. These robots were controlled by a bio-inspired algorithm, that is called ‘BEECLUST’ and that was derived from honeybees’ navigation behavior in a temperature gradient. For details of this study, please see [22], [23], [24]. For transferring the honeybees’ behavior to a robotic swarm, the temperature gradient was translated into a light gradient

The stock & flow model

To investigate the basic properties of the focal swarm robotic system, we constructed a very abstract macroscopic model of a swarm of 15 robots. The model depicts the control algorithm described above and was parameterized in a way to reflect the empiric experiments performed with the real robot hardware. We carefully incorporated all hardware parameters of the Jasmine robot (sensory radius, velocity, etc.) as well as all environmental parameters (arena dimensions, luminance on both sides of

Spatial model of self-propelled particles

In this approach we followed the concept of Brownian agents as a model for swarm robots, that is, robots are seen as self-propelled particles showing random motion [27], [13], [28]. This approach is based on the idea that a microscopic description of the motion of a single robot can be set up: a stochastic differential equation — a Langevin equation. Based on the Langevin equation a macroscopic description of the particle density of the whole swarm is mathematically derived: a partial

Results and discussion

In Fig. 4 we present the sensory input spatially resolved as perceived by a robot according to our model (see Eqs. (5), (7)). Note the plateaus at values of 180 which are caused by the min-function in Eq. (5).

In Fig. 5 the number of aggregated robots below the two lamps is given over time in all four consecutive phases of different environmental conditions (lamp configurations). The prediction of the Stock & Flow model closely follows the median aggregation levels observed with real robotic

Conclusion

Our analysis showed that the focal swarm robotic system can be well described by different macroscopic model approaches. Both offered high prediction quality without extensive fitting procedures. The Stock & Flow model was not systematically fitted to the empiric data, it was just parameterized with obvious and measurable parameters like robot speed, sensory radius and arena dimensions. The advantage of the suggested macroscopic models is that they allow exhaustive parameter sweeps with low

Acknowledgments

All authors are supported by the EU-IST-FET project ‘SYMBRION’, no. 216342 and the EU-ICT project ‘REPLICATOR’, no. 216240. Hamann is supported by the German Research Foundation (DFG) within the Research Training Group GRK 1194 Self-organizing Sensor-Actuator Networks. Schmickl is supported by the following grants: EU-IST FET project I-SWARM, no. 507006 and the FWF research grant Temperature-induced aggregation of young honeybees, no. P19478-B16.

Thomas Schmickl has a Ph.D. in Biology and works currently as an Assistant Professor in the Department for Zoology and supervises the “Artificial Life Lab” at at the Karl-Franzens-University in Graz, Austria. His scientific interests include evolutionary robotics, swarm robotics, swarm intelligence, behavioral ecology and biological modeling. He is currently engaged in four research projects: one is focusing on the self-organization in honeybee groups and three projects are focusing on swarms

References (31)

  • E. Şahin

    Swarm robotics: From sources of inspiration to domains of application

  • A.J.C. Sharkey

    Swarm robotics and minimalism

    Connection Science

    (2007)
  • G. Beni, From swarm intelligence to swarm robotics, in: E. Şahin, W.M. Spears (Eds.), Swarm Robotics — SAB 2004...
  • J. Kennedy et al.

    Swarm Intelligence

    (2001)
  • E. Bonabeau et al.

    Swarm Intelligence: From Natural to Artificial Systems

    (1999)
  • F. Mondada et al.

    The cooperation of swarm-bots: Physical interactions in collective robotics

    IEEE Robotics & Automation Magazine

    (2005)
  • J. Seyfried

    The I-SWARM project: Intelligent small world autonomous robots for micro-manipulation

  • V. Trianni

    Evolutionary swarm robotics — Evolving self-organising behaviours in groups of autonomous robots

  • O. Khatib

    Real-time obstacle avoidance for manipulators and mobile robots

    International Journal of Robotics Research

    (1986)
  • D. Payton et al.

    Pheromone robotics

    Autonomous Robots

    (2001)
  • C.W. Reynolds

    Flocks, herds, and schools

    Computer Graphics

    (1987)
  • C. Darwin

    On the Origin of Species By Means of Natural Selection

    (1859)
  • H. Hamann, Space-time continuous models of swarm robotics systems: Supporting global-to-local programming, Ph.D....
  • A. Martinoli, Swarm intelligence in autonomous collective robotics: From tools to the analysis and synthesis of...
  • N. Correll et al.

    System identification of self-organizing robotic swarms

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    Thomas Schmickl has a Ph.D. in Biology and works currently as an Assistant Professor in the Department for Zoology and supervises the “Artificial Life Lab” at at the Karl-Franzens-University in Graz, Austria. His scientific interests include evolutionary robotics, swarm robotics, swarm intelligence, behavioral ecology and biological modeling. He is currently engaged in four research projects: one is focusing on the self-organization in honeybee groups and three projects are focusing on swarms of autonomous and evolving microrobots. He teaches courses on biological modeling, including the topics self-organization, swarm intelligence and ecological models at the Department for Zoology (Graz), at the Department for Environmental System Sciences (Graz), and at the University of Applied Sciences in St. Poelten (Austria) in the course of studies “SimCom: Simulation and Computation”.

    Heiko Hamann is currently a research assistant at the “Artificial Life Lab”, Department for Zoology, Karl-Franzens-University in Graz, Austria. He received a Ph.D. from the Department of Computer Science of the University of Karlsruhe, Germany in 2008 and a masters degree in computer science from the University of Stuttgart, Germany in 2006. He studied abroad at the Oregon State University, Corvallis, USA and was supported by scholarships of the state Baden-Wuerttemberg, Germany and the Landesstiftung Baden-Wuerttemberg gGmbH. His main research interests include swarm robotics and complex systems.

    Heinz Wörn was born in 1948 and studied electronic engineering at the University of Stuttgart. He did his Ph.D. thesis on “Multi-processor control systems”. He is an expert on robotics and automation with 18 years of industrial experience. In 1997 he became Professor at the University of Karlsruhe, Germany for “Complex Systems in Automation and Robotics” and also head the Institute for Process Control and Robotics at the University of Karlsruhe. Prof. Wörn leads a group of about 35 scientists who research in the field of robotics with focus on the areas of industrial robotics, humanoid robotics, medicine robotics, micro and swarm robotics. He has published over 300 peer-reviewed papers.

    Karl Crailsheim has been working for 30 years in the field of the highly organized social systems, especially on bees. He combines ethological studies with energetic studies thus evaluating costs of sociality and costs of certain strategies. One of his main interests is the process of trophallaxis (exchange of food between individuals within a social group) that not only serves as a method to distribute fuels for motion and development, but of special interest for social systems and also swarms of robots also serves as an information channel. The second line of research is the distribution of individuals in gradients (e.g. temperature gradients). Karl Crailsheim and his study group (see below) significantly contributed to the I-Swarm EU project and developed several useful tools within this project especially some bio-inspired control strategies for collective robotics. With the I-Swarm project he was introduced to robot hardware and his interest in artificial life and swarm technology started. He was president of the International Union for the Study of Social Insects (central European section) for 4 years, is the president of the standing Commission of Honeybee Biology in Apimondia at present. He published about 100 peer-reviewed papers and served as co-editor and member of the scientific board of several Entomology journals. He is currently involved in two national research projects, as well as in two EU-funded bio-robotic projects (SYMBRION, REPLICATOR).

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