chapter  5
44 Pages

BEECLUST: A Swarm Algorithm Derived from Honeybees: Derivation of the Algorithm, Analysis by Mathematical Models, and Implementation on a Robot Swarm

WithTHOMAS SCHMICKL, HEIKO HAMANN

Contents 5.1 Motivation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

5.1.1 From Swarm Intelligence to Swarm Robotics. . . . . . . . . . . . . . . . . . . . . 96 5.1.2 From Biological Inspirations to Robotic Algorithms . . . . . . . . . . . . . 99 5.1.3 Modeling the Swarm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

5.2 Our Biological Inspiration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 5.3 Analyzing Some Basic Results of the Observed Features of the Bee’s

Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

5.4 The Robotic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 5.4.1 The Swarm Robot “Jasmine” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 5.4.2 The Swarm Robot “I-SWARM” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 5.4.3 Shared and Different Properties of These Two Robots . . . . . . . . . . . 109 5.4.4 The Algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

5.5 Swarm Experiments Using a Multi-Agent Simulation of the Robots . . . . 111 5.5.1 Simulating the Swarm Robot “Jasmine” . . . . . . . . . . . . . . . . . . . . . . . . . . 112 5.5.2 Simulating the Swarm Robot “I-SWARM” . . . . . . . . . . . . . . . . . . . . . . . 112

5.6 Preliminary Robotic Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.7 Macroscopic Model of the Robots’ Collective Behavior . . . . . . . . . . . . . . . . . . 116 5.8 The Compartment Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 5.9 Macroscopic Model-Step 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

5.9.1 Macroscopic, Space-Continuous Models for Robot Swarms . . . . . 123 5.9.2 Modeling the Collision-Based Adaptive Swarm Aggregation in

Continuous Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 5.10 Results of Our Two Different Modeling Approaches . . . . . . . . . . . . . . . . . . . . 126 5.11 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 5.12 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

We demonstrate the derivation of a powerful and simple as well as robust and flexible algorithm for a swarm robotic system derived from observations of honeybees’ collective behavior. We show how such observations made in a natural system can be translated into an abstract representation of behavior (algorithm) working in the sensor-actor world of small autonomous robots. By developing several mathematical models of varying complexity, the global features of the swarm system are investigated. These models support us in interpreting the ultimate reasons of the observed collective swarm behavior, and they allow us to predict the swarm’s behavior in novel environmental conditions. In turn, these predictions serve as inspiration for new experimental setups with both the natural system (honeybees and other social insects) and the robotic swarm. In this way, a deeper understanding of the complex properties of the collective algorithm, taking place in the bees and in the robots, is achieved.