The call of duty: Self-organised task allocation in a population of up to twelve mobile robots

Abstract

Teams with up to 12 real robots were given the mission to maintain the energy stocked in their nest by collecting food-items. To achieve this mission efficiently, we implemented a simple and decentralised task allocation mechanism based on individual activation-thresholds, i.e. the energy level of the nest under which a given robot decides to go collect food-items. The experiments show that such a mechanism — already studied among social insects — results in an efficient dynamical task allocation even under the noisy conditions prevailing in real experiments. Experiments with different team sizes were carried out to investigate the effect of team size on performance and risk of mission failure.

Introduction

In human and other social groups with advanced labour division, life is organised around a series of concurrent activities. For a society to function efficiently, the number of individuals (team size) involved in these activities has to be continuously adjusted such as to satisfy its changing needs. The process regulating team size — and thus modulating labour division — is called task allocation. It can be evident when centralised and embodied in a special agency (like a foreman dispatching men on a working site) or it can be less visible when decentralised (as with neighbours providing unsupervised help after an earthquake). Behind the diversity of possible task allocation mechanisms lays a common structure: they all act at the individual level, prompting individuals either to continue or to change their activities (Fig. 1). The condition that triggers the change to another activity may be a simple rule of thumb or a complex decision-making procedure.

Task or role³ allocation has been extensively studied in social insects (e.g. [6], [10], [13], [15], [26], [27], [28], [32], [33]). The study of task allocation in social insects is particularly interesting since their labour division and its regulation are organised by surprisingly simple and robust means. Task allocation within insect colonies was considered a rigid process. The different activities were associated with different castes and caste polymorphism was related to genetic or internal factors [11]. At the same time, other observations indicated that individuals could change activity during their life span [27], [32], suggesting other than genetic factors being relevant for task allocation. These findings have let to reformulate the caste definition based purely on morphological or genetic criteria to incorporate age or simple behavioral differences [13], [27]. Thus, recent research on task allocation in social insects concentrates on behavioral flexibility and stresses the importance of external and decentralised factors like pheromones or individual encounters [5], [25]. One of the most inspiring models to explain this decentralised and flexible task allocation found in social insects is the activation-threshold model.

In the activation-threshold model, individuals react to stimuli that are intrinsically bound to the task to be accomplished. For instance, neglected brood or the corpse of dead ants diffuse an odour of increasing strength. When this stimulus reaches an individual’s threshold value, the individual reacts by adopting the relevant activity (in our example: grooming the brood or carrying the corpse out of the nest) or by increasing its likelihood to do so. This is a proximal mechanism: individuals closer to the work to be done are most likely to be recruited. Moreover, if the individuals do not have the same threshold value, the recruitment is gradual, which may allow regulation of the teams’ sizes [6], [26], [27]. Indeed, Bonabeau et al. [4] have shown that such a simple activation-threshold model “… can account for the workers’ behavioral flexibility”.⁴ Similarly, models in sociology have shown that simple reaction-threshold differences among individuals may lead to complex social dynamics [9], [30]. The purpose of the experiments described below was to test the efficiency of the activation-threshold mechanism for task allocation in practical robotics.

The regulation of a group of robots engaged in several concurrent activities involves regulating the team members’ activity in real time (dynamical task allocation). A variety of mechanisms may achieve task allocation, however, when working with real mobile robots whose perceptions, communication and actions are reckoned to be limited, it is advisable to select a mechanism for its simplicity and its robustness. A good candidate for a robust and simple task allocation mechanism is the activation-threshold mechanism described above [6], [26], [27]. Its task-related recruiting stimuli increase when the tasks to be accomplished are neglected, acting as a feed-back. In a team of N agents whose choice of activities is limited to two, neglecting the first activity (because too many individuals are engaged in the second activity) causes the stimulus for the first activity to increase, prompting individuals to change from the second to the first activity; and conversely (Fig. 2). Choosing appropriate activation-thresholds is crucial for the performance of the robot team since individuals with the same activation-thresholds and exposed to the same stimuli switch activity at the same time, yielding generally a poor regulation. Hence, one of our objectives was to show that simply implementing different activation-thresholds is sufficient for an effective task allocation mechanism in robotic experiments.

From the biologist’s point of view, the purpose of these experiments is to contribute a piece of heuristic evidence that complex social systems may be organised on decentralised organisation principles. Central to sociality is labour division, with its correlates of specialisation, cooperation and task allocation. As we have seen above, social insects are thought to organise an important aspect of labour division, i.e. task allocation, in a decentralised manner where each individual’s decision is made according to a simple set of rules based on local information only. Many complex patterns and collective behaviours observed at the colony (macroscopic) level emerge as the aggregated result of the decentralised interactions at the individual (microscopic) level. This mode of organisation, termed self-organisation [19], could account for many collective phenomena found in social insects [8]. Other authors used successfully mathematical models of self-organisation to model either specific behaviours (e.g. [35], [37]) or whole insect colonies [3], [20], [21]. Yet it is difficult to prove unequivocally that self-organisation is the main mechanism operating in social insect societies and that all complex collective behaviours emerge from interactions among individuals with simple stereotyped behaviours.

Our experiments intend to bring heuristic evidence, and thus shed some light on two questions: first, can we imagine plausible mechanisms of automatic and decentralised control for insect societies; and secondly, do these mechanisms account for or lend themselves to the gradual evolution from a solitary individual systems to sociality? Such a gradual evolution implies that the transition from the ancestral, solitary state to a social system is beneficial. Hence, individuals in simple aggregations have to have a better pay-off than solitary individuals, and individuals in groups with cooperative interactions have to outperform individuals in aggregations. Since not all animals live in social systems it follows that these conditions are not always given. One element which has proven to influence social organisation are environmental factors. Among them, the distribution of food and its availability was identified as one of the key features [1], [7], [17], [29]. Therefore, we also examined the influence of different food distributions on social organisation. However, it should be stressed that our robots do not mimic any specific social insect species and therefore, no binding conclusion can be obtained by the comparative study of our robots’ behaviour and the behaviour of social insects.