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In this thesis we study a mathematical model that describes task partitioning in a colony of ants. This process of self-organization is modeled by a nonlinear coupled system of rst order autonomous ordinary dierential equations. We discuss how this system of equations can be derived based on the behavior of ants in a colony. We use GNU Octave (a high-level programming language) to solve the system of equations numerically for dierent sets of parameters and show how the solutions respond to changes in the parameter values. Finally, we prove that the model is well-posed locally in time. We rewrite the system of ordinary dierential equations in terms of a system of coupled Volterra integral equations and look at the right-hand side of the system as a nonlinear operator on a Banach space. By doing so, we have transformed the problem of showing existence and uniqueness of solutions to a system of ordinary dierential equations into a problem of showing existence and uniqueness of a xed point to the corresponding integral operator. Additionally, we use Gronwall's inequality to prove the stability of solutions with respect to data and parameters.

Task allocation, and task switching have an important effect on the efficiency of distributed, locally controlled systems such as social insect colonies. Both efficiency and workload distribution are global features of the system which are not directly accessible to workers and can only be sampled locally by an individual in a distributed system. To investigate how the cost of task switching affects global performance we use social wasp societies as a metaphor to construct a simple model system with four interconnected tasks. Our goal is not the accurate description of the behavior of a given species, but to seek general conclusions on the effect of noise and time delay on a behavior that is partitioned into subtasks. In our model a nest structure needs to be constructed by the cooperation of individuals that carry out different tasks: builders, pulp and water foragers, and individuals storing water. We report a simulation study based on a model using delay-differential equations to analyze the trade-off between task switching costs and keeping a high degree of adaptivity in a dynamic, noisy environment. Combining the methods of time-delayed equations and stochastic processes we are able to represent the influence of swarm size and task switching sensitivity. We find that the system is stable for reasonable choices of parameters but shows oscillations for extreme choices of parameters and we find that the system is resilient to perturbations. We identify a trade-off between reaching equilibria of high performance and having short transients.

Task allocation, and task switching have an important effect on the efficiency of distributed, locally controlled systems such as social insect colonies. Both efficiency and workload distribution are global features of the system which are not directly accessible to workers and can only be sampled locally by an individual in a distributed system. To investigate how the cost of task switching affects global performance we use social wasp societies as a metaphor to construct a simple model system with four interconnected tasks. Our goal is not the accurate description of the behavior of a given species, but to seek general conclusions on the effect of noise and time delay on a behavior that is partitioned into subtasks. In our model a nest structure needs to be constructed by the cooperation of individuals that carry out different tasks: builders, pulp and water foragers, and individuals storing water. We report a simulation study based on a model using delay-differential equations to analyze the trade-off between task switching costs and keeping a high degree of adaptivity in a dynamic, noisy environment. Combining the methods of time-delayed equations and stochastic processes we are able to represent the influence of swarm size and task switching sensitivity. We find that the system is stable for reasonable choices of parameters but shows oscillations for extreme choices of parameters and we find that the system is resilient to perturbations. We identify a trade-off between reaching equilibria of high performance and having short transients.

In this thesis, we propose an approach to achieve autonomous task partitioning in swarms of robots. Task partitioning is the process by which tasks are decomposed into sub-tasks and it is often an advantageous way of organizing work in groups of individuals. Therefore, it is interesting to study its application to swarm robotics, in which groups of robots are deployed to collectively carry out a mission. The capability of partitioning tasks autonomously can enhance the flexibility of swarm robotics systems because the robots can adapt the way they decompose and perform their work depending on specific environmental conditions and goals. So far, few studies have been presented on the topic of task partitioning in the context of swarm robotics. Additionally, in all the existing studies, there is no separation between the task partitioning methods and the behavior of the robots and often task partitioning relies on characteristics of the environments in which the robots operate.<p>This limits the applicability of these methods to the specific contexts for which they have been built. The work presented in this thesis represents the first steps towards a general framework for autonomous task partitioning in swarms of robots. We study task partitioning in foraging, since foraging abstracts practical real-world problems. The approach we propose in this thesis is therefore studied in experiments in which the goal is to achieve autonomous task partitioning in foraging. However, in the proposed approach, the task partitioning process relies upon general, task-independent concepts and we are therefore confident that it is applicable in other contexts. We identify two main capabilities that the robots should have: i) being capable of selecting whether to employ task partitioning and ii) defining the sub-tasks of a given task. We propose and study algorithms that endow a swarm of robots with these capabilities. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

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