Fundamental Diagrams of 1D-Traffic Flow by Optimal Control Models

Traffic on a circular road is described by dynamic programming equations associated to optimal control problems. By solving the equations analytically, we derive the relation between the average car density and the average car flow, known as the fundamental diagram of traffic. First, we present a model based on min-plus algebra, then we extend it to a stochastic dynamic programming model, then to a stochastic game model. The average car flow is derived as the average cost per time unit of optimal control problems, obtained in terms of the average car density. The models presented in this article can also be seen as developed versions of the car-following model. The derivations proposed here can be used to approximate, understand and interprete fundamental diagrams derived from real measurements.Comment: 17 pages

Deep Generative Modeling of LiDAR Data

Building models capable of generating structured output is a key challenge for AI and robotics. While generative models have been explored on many types of data, little work has been done on synthesizing lidar scans, which play a key role in robot mapping and localization. In this work, we show that one can adapt deep generative models for this task by unravelling lidar scans into a 2D point map. Our approach can generate high quality samples, while simultaneously learning a meaningful latent representation of the data. We demonstrate significant improvements against state-of-the-art point cloud generation methods. Furthermore, we propose a novel data representation that augments the 2D signal with absolute positional information. We show that this helps robustness to noisy and imputed input; the learned model can recover the underlying lidar scan from seemingly uninformative dataComment: Presented at IROS 201

Dynamic Congestion and Tolls with Mobile Source Emission

This paper proposes a dynamic congestion pricing model that takes into account mobile source emissions. We consider a tollable vehicular network where the users selfishly minimize their own travel costs, including travel time, early/late arrival penalties and tolls. On top of that, we assume that part of the network can be tolled by a central authority, whose objective is to minimize both total travel costs of road users and total emission on a network-wide level. The model is formulated as a mathematical program with equilibrium constraints (MPEC) problem and then reformulated as a mathematical program with complementarity constraints (MPCC). The MPCC is solved using a quadratic penalty-based gradient projection algorithm. A numerical study on a toy network illustrates the effectiveness of the tolling strategy and reveals a Braess-type paradox in the context of traffic-derived emission.Comment: 23 pages, 9 figures, 5 tables. Current version to appear in the Proceedings of the 20th International Symposium on Transportation and Traffic Theory, 2013, the Netherland

Symplectic integrators for index one constraints

We show that symplectic Runge-Kutta methods provide effective symplectic integrators for Hamiltonian systems with index one constraints. These include the Hamiltonian description of variational problems subject to position and velocity constraints nondegenerate in the velocities, such as those arising in sub-Riemannian geometry and control theory.Comment: 13 pages, accepted in SIAM J Sci Compu

Extended Object Tracking: Introduction, Overview and Applications

This article provides an elaborate overview of current research in extended object tracking. We provide a clear definition of the extended object tracking problem and discuss its delimitation to other types of object tracking. Next, different aspects of extended object modelling are extensively discussed. Subsequently, we give a tutorial introduction to two basic and well used extended object tracking approaches - the random matrix approach and the Kalman filter-based approach for star-convex shapes. The next part treats the tracking of multiple extended objects and elaborates how the large number of feasible association hypotheses can be tackled using both Random Finite Set (RFS) and Non-RFS multi-object trackers. The article concludes with a summary of current applications, where four example applications involving camera, X-band radar, light detection and ranging (lidar), red-green-blue-depth (RGB-D) sensors are highlighted.Comment: 30 pages, 19 figure

Car collision avoidance with velocity obstacle approach

The obstacle avoidance maneuver is required for an autonomous vehicle. It is essential to define the system's performance by evaluating the minimum reaction times of the vehicle and analyzing the probability of success of the avoiding operation. This paper presents a collision avoidance algorithm based on the velocity bstacle approach that guarantees collision-free maneuvers. The vehicle is controlled by an optimal feedback control named FLOP, designed to produce the best performance in terms of safety and minimum kinetic collision energy. Dimensionless accident evaluation parameters are proposed to compare different crash scenarios