The AURORA project aims at developing new strategies to take assistive robotics a step further. In order to provide extended services to potential users, engaging a team of simpler robots is often preferable to using a unique, super-capable robot. In such multi-robot systems, the coordination for task execution is one of the major challenges to overcome. The present thesis proposes a solution to the specific issue of multi-robot task allocation within an heterogeneous team of robots, with additional inter-task precedence constraints. The main elements of the state of the art that support this project are reported, including useful taxonomies and existing methods. From the analyzed solutions, the one that better fits with the constraints of the project is an iterated auction-based algorithm able to manage precedence constraints, which has been modified to handle heterogeneity and partial scheduling. The selected solution has been designed and implemented with the particular purpose of being applied to the robotized kitchen setup of the AURORA project; it is however flexible and scalable and can therefore be applied to other use-cases, for instance vehicle-routing problems. Several evaluation scenarios have been tested, that demonstrate the good functioning and characteristics of the system, as well as the possibility to integrate humans into the task assignation process.