A First Step Toward a Possibilistic Swarm Multi-robot Task Allocation

The task allocation problem is one of the main issues in multi-robot systems. Typical ways to address this problem are based on Swarm Intelligence. One of them is the so-called Response Threshold Method. In the aforementioned method every robot has associated a task response threshold and a task stimuli in such a way that the robot’s probability of executing a certain task depends on both factors. On of the advantage of the aforesaid method is given by the fact that the original problem is treated from a distributed mode which, at the same time, means a very low computational requirements. However, the Response Threshold Method cannot be extended in a natural way to allocate more than two tasks when the theoretical basis is provided by probability theory. Motivated by this fact, this paper leaves the probabilistic approach to the problem and takes a first step towards a possibilistic theoretical approach in order to treat successfully the multi-robot task allocation problem when more than two tasks must be performed. As an example of application, an scenario where each robot task stimuli only depends on the distance between tasks is studied and the convergence of the system to an stable state is shown.