We developed a mathematical model in the form of of a simple differential equation, which allows us to reproduce with bodiless agents all aspects of the motion behaviour observed in individual honeybees. These aspects manifest in the occurrence of four fundamentally different types of motion patterns: In a thermal gradient, goal finders are able to directly walk to place of optimum temperature, while the other two types with high motion activity, random walkersand wall followers, incessantly criss-cross an arena or move along the arena’s wall, respectively. The fourth type, immobile bees, are characterized by very low motion activity.

As an intermediate step towards the embodiment of this model, we created a multi-agent model to simulate swarms of agents in a simplified environment while incorprating all aspects of individual motion behaviour. We used an evolutionary algorithm to optimze the distribution of behavioural types over the individuals composing the swarm with regard to specific optimum finding tasks. These simulation experiments gave an insight as to why swarm heterogeneity, which is found in honeybees and many other social species, is advantageous for the swarm. At the same time, we established the method of programming robotic swarms based on the variability of individual behaviour as the novel swarm level optimization paradigm. This paradigm describes how to control a swarm’s ultimate behaviour by composing it from individuals with different behavioural traits.

For an implementation of the behavioural algorithms under physically realistic conditions we resorted to ePuck robots, which we extended by two temperature sensors located at the ends of two antennae. Similar to the bees observed in the predecessor project, these ThermoBots move in a circular arena, on the ground of which we establish a thermal gradient. Due to the comparable embodiment (antennae), the perception of the thermal gradient is similar to that experienced by the bees. The implementation of the four types of behaviour in this robot swarm led to a novel mechatronically embodied model of honeybee behaviour in temperature fields.

The results of the project and the introduction of the new concept for programming swarms will contribute to the solution of technical problems which robot engineers haven’t been able to solve so far. Additionally, we improved our knowledge about the mechanisms that govern the collective behaviour of biological organisms on the most fundamental level.