# MAREVA

MAREVA: Applied Mathematics: Robotics, Vision, Control systems theory

MAREVA brings together skills in three different areas of Applied Mathematics: Robotics, Vision and Automation. Indeed, to develop increasingly complex projects, for example in multidisciplinary fields such as surgical robotics or autonomous vehicles, it is important to master the concepts of control theory, filtering, vision, robotics and artificial learning.

Control Systems Theory is an engineering science that analyzes the properties of dynamic systems to estimate and control them. The apparent diversity of the dynamic systems studied (linear or non-linear differential systems, recurrent systems, discrete event systems, deterministic or random systems), the diversity of their application fields (mechanical, electrical, hydraulic, aerodynamic, physico-chemical, biological economical phenomena ...) and the diversity of control objectives (following reference trajectories, working at the lowest cost, making the system insensitive to certain disturbances and poorly known environments...)  explain the wide range of mathematical tools required for their study (algebra, analysis, differential geometry, topology, probabilities, optimisation...). Faced with this multiple reality, the fundamental concepts of modeling, input/output relationship, controllability and observability, stability, robustness... make the unit of automatic control.

A Robotic system is a mechanism with means of perception, reasoning and action that allow it to interact with its environment. Robotics was initially developed in the manufacturing field (manipulator arms for welding, painting, handling, assembly) where it allowed a significant increase in productivity. Beyond the manufacturing activity, robotics has spread to many other fields where the environment is not well known, uncertain or even hostile. This is the case, for example, in agricultural robotics, but also in the fields of nuclear power, autonomous vehicles, space and underwater robotics, not forgetting humanoid robotics. Virtual reality is also addressed, particularly in the framework of man-machine collaboration.

Artificial vision is now experiencing a great expansion. On the one hand, we are witnessing the appearance of increasingly sophisticated acquisition systems, producing images of increasing resolution, hyper-spectral data and unstructured 3D point clouds among others. On the other hand, the success of deep learning has opened up new methodological and application perspectives. These methods are combined with so-called "classical" techniques, such as mathematical morphology, offering better interpretability, and which remain necessary in situations where annotated data are scarce. The fields of application of vision are extremely broad: genomics, biomedicine, industrial control, materials, multimedia, robotics ... Examples from these wide application domains illustrate the studied concepts and allow a full understanding of the notions introduced in class.

The MAREVA option thus brings together the main scientific fields of engineering sciences: mechanics and more generally physics for the modelling of the studied systems, automation for trajectory planning and open or closed loop control, electronics for the implementation of real-time controllers and instrumentation, computer science for the processing of sensor data and programming languages, computer vision and learning techniques for interpreting reality.