Related papers: Constructing Optimal Highways
A family of plane oriented continuous paths depending on a fixed real positive number $R$ is considered. For any point $x$ on the path, the previous points lie out of any circle of radius $R$ having at $x$ interior normal in a suitable…
This article provides numerical simulation of an optimal transport path from a single source to an atomic measure of equal total mass. We first construct an initial transport path, and then modify the path as much as possible by using both…
Planning trajectories for automated vehicles in urban environments requires methods with high generality, long planning horizons, and fast update rates. Using a path-velocity decomposition, we contribute a novel planning framework, which…
This paper investigates the problem of computing a two-dimensional optimal curvature straight line (CS) shortest path for an unmanned aerial vehicle (UAV) to intercept a moving target, with both the UAV (pursuer) and target travelling at…
Given two points in the plane, and a set of "obstacles" given as curves through the plane with assigned weights, we consider the point-separation problem, which asks for the minimum-weight subset of the obstacles separating the two points.…
Nowadays, methodologies coming from studying physical systems are being applied to the description of a wide variety of complex systems. In particular, one can study thermodynamical methods to describe the overall behavior of many systems,…
Autonomous highway driving involves high-speed safety risks due to limited reaction time, where rare but dangerous events may lead to severe consequences. This places stringent requirements on trajectory planning in terms of both…
We study the optimal scheduling of graph states in measurement-based quantum computation, establishing an equivalence between measurement schedules and path decompositions of graphs. We define the spatial cost of a measurement schedule…
Path planning is a major problem in autonomous vehicles. In recent years, with the increase in applications of Unmanned Aerial Vehicles (UAVs), one of the main challenges is path planning, particularly in adversarial environments. In this…
In this paper, a new fast algorithm for path planning and a collision prediction framework for two dimensional dynamically changing environments are introduced. The method is called Time Distance (TD) and benefits from the space-time space…
We study the problem of planning routes in road networks when certain streets or areas are closed at certain times. For heavy vehicles, such areas may be very large since many European countries impose temporary driving bans during the…
Most optimal routing problems focus on minimizing travel time or distance traveled. Oftentimes, a more useful objective is to maximize the probability of on-time arrival, which requires statistical distributions of travel times, rather than…
Given a set P of n points in the plane, the unit-disk graph G_{r}(P) with respect to a parameter r is an undirected graph whose vertex set is P such that an edge connects two points p, q \in P if the Euclidean distance between p and q is at…
Solving for the minimum time bounded acceleration trajectory with prescribed position and velocity at endpoints is a highly nonlinear problem. The methods and bounds developed in this paper distinguish when there is a continuous…
In this paper we address the speed planning problem for a vehicle over an assigned path with the aim of minimizing a weighted sum of travel time and energy consumption under suitable constraints (maximum allowed speed, maximum traction or…
In this paper, we study the problem of map matching with travel time constraints. Given a sequence of $k$ spatio-temporal measurements and an embedded path graph with travel time costs, the goal is to snap each measurement to a close-by…
This paper is based on a crucial issue in the aviation world: how to optimize the trajectory and controls given to the aircraft in order to optimize flight time and fuel consumption. This study aims to provide elements of a response to this…
This paper analyzes the use of variable speed limits to optimize travel time reliability for commuters. The investigation focuses on a traffic corridor with a bottleneck subject to the capacity drop phenomenon. The optimization criterion is…
In this paper we present an algorithm for optimal processing of time-dependent sequenced route queries in road networks, i.e., given a road network where the travel time over an edge is time-dependent and a given ordered list of categories…
Two multivehicle routing problems are considered in the framework that a visit to a location must take place during a specific time window in order to be counted and all time windows are the same length. In the first problem, the goal is to…