Stéphane Gaubert (CMAP, École Polytechnique)

Stéphane Gaubert
École Polytechnique

21 Juin 2018, 14.00
salle des commissions, bât Polytech
Campus de St. Jérôme


Tropical analysis of timed Petri nets with priorities and application to performance evaluation of an emergency call center

We analyze a timed Petri net model of an emergency call center which processes calls with different levels of priority. The counter variables of the Petri net represent the cumulated number of events as a function of time. We show that these variables are determined by a piecewise linear dynamical system. We also prove that computing the stationary regimes of the associated uid dynamics reduces to the problem of computing a tropical prevariety, i.e., to solving a polynomial system over a tropical (min-plus) semifield. This leads to explicit formulae expressing the throughput of the uid system as a piecewise linear function of the resources, revealing the existence of different congestion phases. Numerical experiments show that the analysis of the fluid dynamics yields a good approximation of the real throughput. In this way, tropical geometry allows one to identify bottleneck resources. This works originates from a case study, concerning the analysis of the new organization of reception of the 17-18-112 emergency calls in the Paris area, currently deployed by Préfecture de Police. This is a joint work with Xavier Allamigeon and Vianney Boeuf.

Ahmed Chemori (LIRMM – CNRS University of Montpellier, France)

Ahmed Chemori
Université de Montpellier

24 Mai 2018, 14.00
salle des commissions, bât Polytech
Campus de St. Jérôme


Control of Complex Robotic Systems:
Challenges, Design and Experiments

Robotics was initially and for a long time guided by needs in industry. Indeed, the early years of robotics was largely focused on robot manipulators, used mainly for simple and repetitive automation tasks. The first industrial robot manipulator appeared in 1961 in the assembly lines of General Motors. The early control systems for robot manipulators were designed to control independently each axis of the robot as a Single-Input-Single-Output (SISO) linear system. Linear automatic control theory was then extensively used in this basic solution, where the coupling dynamics between the different axes of the robot were often neglected and the robot model significantly simplified. Beyond these issues, the main barriers to progress were the high cost of computation, the lack of good sensors, and the lack of fundamental understanding of robot dynamics. However, the progress of robotics and automation as well as their associated innovative applications has required the consideration of more and more complex tasks needing high performances. These challenging tasks required a deeply understanding of complex nonlinear dynamics of robots. Besides, it has also motivated the development of new theoretical advances in different control fields (robust, adaptive, etc.), which has consequently enabled more sophisticated applications. Nowadays, robotic control systems are highly advanced, including manipulation robotics, underwater robotics, aerial robotics, mobile robotics, medical robotics, parallel robotics, wearable robotics, humanoid robotics and more others. In this lecture the main challenges related to control of robotic systems will be emphasized, and illustrated through different applications in robotics. For each of these fields, the motivations and the need of developing advanced control schemes will be first highlighted. Then some proposed advanced control solutions will be introduced and illustrated through real-time experiments.