Factor graphs are a very powerful graphical representation, used to model many problems in robotics. They are widely spread in the areas of Simultaneous Localization and Mapping (SLAM), computer vision, and localization. In this paper we describe an approach to fill the gap with other areas, such as optimal control, by presenting an extension of Factor Graph Solvers to constrained optimization. The core idea of our method is to encapsulate the Augmented Lagrangian (AL) method in factors of the graph that can be integrated straightforwardly in existing factor graph solvers.We show the generality of our approach by addressing three applications, arising from different areas: pose estimation, rotation synchronization and Model Predictive Control (MPC) of a pseudo-omnidirectional platform. We implemented our approach using C++ and ROS. Besides the generality of the approach, application results show that we can favorably compare against domain specific approaches.

The paper deals with the modelling and the control of a job market dynamics which considers unemployed individuals and two classes of jobs: a temporary one, characterised by a lower quality of economical treatment and/or long duration assurance for the workers, and a regular one, more stable and economically more satisfactory. For each of the two classes, the active workers as well as the vacancies are considered. Control actions are introduced, representing different government efforts devoted to the quantity and the quality improvements of the work. Choices in the model are discussed and compared with literature. The numerical results of some simulations are reported to better put in evidence the results obtained.