## Section: New Results

### Vehicular transportation systems

#### Traffic estimation and prediction

Participants : C. Canudas de Wit [Contact person] , A. Kibangou, L. Leon Ojeda, F. Morbidi.

Reconstructing densities in portions of the road links
not equipped with sensors constitutes an important task
in traffic estimation, forecasting, and control problems.
Among many other approaches, model-based observers is
one popular technique to build this information. They can
also be understood as *virtual sensors* deployed inside of
the cells not equipped with *true sensors*. They are used
to better track, in real-time, density variations with a fine
degree of granularity in the space, as the *virtual cells* can
be selected as small as desired.
In [30] , a graph constrained-CTM observer was introduced. It allows reconstructing
rather accurately the internal states (densities) of
a road portion not equipped with sensors. This strategy
for real-time density estimation was applied on Grenoble
South Ring. Simulation results exhibit that the measured
densities obtained from the traffic simulator Aimsun and
the estimated densities agree closely. In [69] , this observer has been associated with an adaptive Kalman filtering approach for traffic prediction in terms of travel time. The adaptive Kalman filtering approach was also been used for predicting input flows in [68] .

#### Traffic control

Participants : C. Canudas de Wit [Contact person] , D. Pisarski.

The problem of equilibrium points for the Cell Transmission Model was studied in [42] . The structure of equilibrium sets was analyzed in terms of model parameters and boundary conditions. The goal was to determine constant input flows, so that the resultant steady state of vehicle density was uniformly distributed along a freeway. The necessary and sufficient conditions for the existence of one-to-one relation between input flow and density were derived. The equilibrium sets were described by formulas that allow to design a desired balanced density. A numerical example for the case of a two-cell system was presented. In [41] , the problem of optimal balancing of traffic density distributions was explored. The optimization was carried out over the sets of equilibrium points for the Cell Transmission Traffic Model. The goal was to find the optimal balanced density distribution, that maximizes both the Total Travel Distance and the total input flow. The optimization was executed in two steps. At the first step, a nonlinear problem to find a uniform density distribution that maximizes the Total Travel Distance was solved . The second step was to solve a quadratic problem reflecting the trade-off between density balance and input flow maximization. At both steps, decomposition methods were used. The computational algorithms associated to such a problem were given. Finally, in [71] , the application of the idea of optimal balancing of traffic density distribution was presented. It was implemented to the Grenoble South Ring in the context of the Grenoble Traffic Lab. The traffic on the ring is represented by the Cell Transmission Model that was tuned by using real data and Aimsun micro-simulator. A special attention was paid to the calibration of a flow merging model. A large-scale optimization problem was solved by using advanced combinatorial procedures. The main difficulties in the implementation as well as the limitations of the designed software were highlighted. Finally, the results of different traffic scenarios on the Grenoble South Ring were presented.

#### Vehicle control for disabled people

Participants : C. Canudas de Wit [Contact person] , V. Ciarla, J. Dumon, F. Quaine [UJF] , V. Cahouet [UJF] .

The typical architecture of an Electric Power Assistance Steering (EPAS) system includes a static map to provide the correct amplification to the drivers exerted torque. In literature, it is generally known as booster curve. This work concerns the study of the amplification criteria, that are commonly used to these booster curves. The basic concepts of the Electric Power Steering (EPS) systems with a realistic model for the friction contact, that acts on the wheels are discussed. A relation between the assistance and the driver's torque is provided, under the hypothesis of a position-oriented control of the movement and the Stevens' power law [33] . In current works, we want to modify the general architecture of the EPAS system for people driving with two arms. For this purpose, we insert two additional blocks: the first one provides an estimation of the gravitational torque due to the weight of the driver's arm while the second gets as inputs the total driver's torque and the estimated gravitational torque in order to update the driver's torque with the gravitational torque. The updated measure is then given as input to the booster curve for deriving the correct assistance.

#### Control of communicating vehicles in urban environment

Participants : C. Canudas de Wit [Contact person] , G. de Nunzio.

For a given vehicle there are different ways to travel on a given distance in a given time, corresponding to different levels of energy consumption; therefore, there is an energy-optimal trajectory. Advising the driver via a suitable interface can reduce the energy consumed during the travel, and thus improve the energy efficiency: this is the principle of eco driving. In urban areas, the optimal trajectory of the vehicle depends on interactions with other vehicles, but also on passive signs (panels, priorities, etc.) and active signs (traffic lights); in each case, constraints are imposed on the command (vehicle speed). From the infrastructure perspective, traffic control in urban areas consists in determining the state of traffic signals in order to solve an optimization problem, for example minimizing travel time of vehicles in the road network. If all the vehicles can communicate with one another and with the active infrastructure (traffic lights), we can imagine benefits for each of the two problems which can be considered as a whole: on the one hand, for vehicles, more information is available that can be integrated into the online optimization problem; on the other hand, there are new measures and new commands available to control traffic. Indeed, the estimation of the traffic is no longer necessary, as the position and speed of approaching vehicles is known. More importantly, the traffic manager can send instructions to the vehicle. The aim of the research is to evaluate the potential in terms of energy saving and traffic improvement made possible by communicating vehicle. This work is carried out in collaboration with IFP in the framework of a CIFRE thesis.