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To improve safety and energy efficiency, autonomous vehicles are expected to drive smoothly in most situations, while maintaining their velocity below a predetermined speed limit. However, some scenarios such as low road adherence or inadequate speed limit may require vehicles to automatically adapt their velocity without external input, while nearing the limits of their dynamic capacities. Many of the existing trajectory planning approaches are incapable of making such adjustments, since they assume a feasible velocity reference is given. Moreover, near-limits trajectory planning often implies high-complexity dynamic vehicle models, making computations difficult. In this article, we use a simple dynamic model derived from numerical simulations to design a trajectory planner for high-speed driving of an autonomous vehicle based on model predictive control. Unlike existing techniques, our formulation includes the selection of a feasible velocity to track a predetermined path while avoiding obstacles. Simulation results on a highly precise vehicle model show that our approach can be used in real-time to provide feasible trajectories that can be tracked using a simple control architecture. Moreover, the use of our simplified model makes the planner more robust and yields better trajectories compared to kinematic models commonly used in trajectory planning.

Abstract-In normal on-road situations, autonomous vehicles will be expected to have smooth trajectories with relatively little demand on the vehicle dynamics to ensure passenger comfort and driving safety. However, the occurrence of unexpected events may require vehicles to perform aggressive maneuvers, near the limits of their dynamic capacities. In order to ensure the occupant's safety in these situations, the ability to plan controllable but near-limits trajectories will be of very high importance. One of the main issues in planning aggressive maneuvers lies in the high complexity of the vehicle dynamics near the handling limits, which effectively makes state-of-theart methods such as Model Predictive Control difficult to use. This article studies a highly precise model of the vehicle body to derive a simpler, constrained second-order integrator dynamic model which remains precise even near the handling limits of the vehicle. Preliminary simulation results indicate that our model provides better accuracy without increasing computation time compared to a more classical kinematic bicycle model. The proposed model can find applications for contingency planning, which may require aggressive maneuvers, or for trajectory planning at high speed, for instance in racing applications.

This paper explores the capability of deep neural networks to capture key characteristics of vehicle dynamics, and their ability to perform coupled longitudinal and lateral control of a vehicle. To this extent, two different artificial neural networks are trained to compute vehicle controls corresponding to a reference trajectory, using a dataset based on high-fidelity simulations of vehicle dynamics. In this study, control inputs are chosen as the steering angle of the front wheels, and the applied torque on each wheel. The performance of both models, namely a Multi-Layer Perceptron (MLP) and a Convolutional Neural Network (CNN), is evaluated based on their ability to drive the vehicle on a challenging test track, shifting between long straight lines and tight curves. A comparison to conventional decoupled controllers on the same track is also provided.In this section, we present the 9 Degrees of Freedom (9 DoF) vehicle model which is used both to generate the training and testing dataset, and as a simulation model to evaluate the performance of the deep-learning-based controllers.The Degrees of Freedom comprise 3 DoF for the vehicle's motion in a plane (V x ,V y ,ψ), 2 DoF for the carbody's rotation (θ ,φ ) and 4 DoF for the rotational speed of each wheel (ω f l , ω f r , ω rl , ω rr ). The model takes into account both the coupling of longitudinal and lateral slips and the load transfer between tires. The control inputs of the model are the torques T ω i applied at each wheel i and the steering angle δ of the front wheel. The low-level dynamics of the engine and brakes are not considered here. The notations are given in Table 1 and illustrated in Figure 1.Remark: the subscript i = 1..4 refers respectively to the front left ( f l), front right ( f r), rear left (rl) and rear right (rr) wheels.Several assumptions were made for the model:• Only the front wheels are steerable.• The roll and pitch rotations happen around the center of gravity.