In order to drive safely and efficiently on public roads, autonomous vehicles will have to understand the intentions of surrounding vehicles, and adapt their own behavior accordingly. If experienced human drivers are generally good at inferring other vehicles' motion up to a few seconds in the future, most current Advanced Driving Assistance Systems (ADAS) are unable to perform such medium-term forecasts, and are usually limited to high-likelihood situations such as emergency braking. In this article, we present a first step towards consistent trajectory prediction by introducing a long short-term memory (LSTM) neural network, which is capable of accurately predicting future longitudinal and lateral trajectories for vehicles on highway. Unlike previous work focusing on a low number of trajectories collected from a few drivers, our network was trained and validated on the NGSIM US-101 dataset, which contains a total of 800 hours of recorded trajectories in various traffic densities, representing more than 6000 individual drivers.

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This paper considers the problem of optimal trajectory generation for autonomous driving under both continuous and logical constraints. Classical approaches based on continuous optimization formulate the trajectory generation problem as a nonlinear program, in which vehicle dynamics and obstacle avoidance requirements are enforced as nonlinear equality and inequality constraints. In general, gradientbased optimization methods are then used to find the optimal trajectory. However, these methods are ill-suited for logical constraints such as those raised by traffic rules, presence of obstacles and, more generally, to the existence of multiple maneuver variants. We propose a new formulation of the trajectory planning problem as a Mixed-Integer Quadratic Program. This formulation can be solved efficiently using widely available solvers, and the resulting trajectory is guaranteed to be globally optimal. We apply our framework to several scenarios that are still widely considered as challenging for autonomous driving, such as obstacle avoidance with multiple maneuver choices, overtaking with oncoming traffic or optimal lane-change decision making. Simulation results demonstrate the effectiveness of our approach and its real-time applicability.