Design of an advanced control algorithm for Urbanloop capsules

Urban transportation in France faces ever-growing environmental, social, and economic challenges. Statistics show that over 50\% of the French population relies on private cars daily due to a lack of viable alternatives. To address this issue and offer a compelling choice for urban mobility, the Nancy metropolis, the Grand Est region, and the University of Lorraine are collaboratively developing a novel urban transport system: Urbanloop. It features a new on-rail system, fully electric, that avoids intermediate stops and waiting time, potentially serving as a new option for public transport in medium-sized cities. The aim of this work is to enhance the performance of the control law used to move the pods along the circuit, focusing on improving speed and passenger comfort. This effort involves constructing a mathematical model based on physical laws and validating this model. Such validation is crucial for building and running simulations for the proposed new control law. Specifically, the problem is divided into two parts: the generation of the reference trajectory by solving an optimization problem, and the application of the LQR method on the linearized system obtained near the reference trajectory. Furthermore, this paper compares the heuristic law proposed by Urbanloop with the newly proposed control law.