8,057 research outputs found
Hybridization of Nonlinear and Mixed-Integer Linear Programming for Aircraft Separation With Trajectory Recovery
International audienceThe approach presented in this article aims at finding a solution to the problem of conflict-free motion planning for multiple aircraft on the same flight level with trajectory recovery. One contribution of this work is to develop three consistent models, from a continuous-time representation to a discrete-time linear approximation. Each of these models guarantees separation at all times as well as trajectory recovery, but they are not equally difficult to solve. A new hybrid algorithm is thus developed in order to use the optimal solution of a mixed integer linear program as a starting point when solving a nonlinear formulation of the problem. The significance of this process is that it always finds a solution when the linear model is feasible while still taking into account the nonlinear nature of the problem. A test bed containing numerous data sets is then generated from three virtual scenarios. A comparative analysis with three different initialisations of the nonlinear optimisation validates the efficiency of the hybrid method
A path planning and path-following control framework for a general 2-trailer with a car-like tractor
Maneuvering a general 2-trailer with a car-like tractor in backward motion is
a task that requires significant skill to master and is unarguably one of the
most complicated tasks a truck driver has to perform. This paper presents a
path planning and path-following control solution that can be used to
automatically plan and execute difficult parking and obstacle avoidance
maneuvers by combining backward and forward motion. A lattice-based path
planning framework is developed in order to generate kinematically feasible and
collision-free paths and a path-following controller is designed to stabilize
the lateral and angular path-following error states during path execution. To
estimate the vehicle state needed for control, a nonlinear observer is
developed which only utilizes information from sensors that are mounted on the
car-like tractor, making the system independent of additional trailer sensors.
The proposed path planning and path-following control framework is implemented
on a full-scale test vehicle and results from simulations and real-world
experiments are presented.Comment: Preprin
High-order filtered schemes for time-dependent second order HJB equations
In this paper, we present and analyse a class of "filtered" numerical schemes
for second order Hamilton-Jacobi-Bellman equations. Our approach follows the
ideas introduced in B.D. Froese and A.M. Oberman, Convergent filtered schemes
for the Monge-Amp\`ere partial differential equation, SIAM J. Numer. Anal.,
51(1):423--444, 2013, and more recently applied by other authors to stationary
or time-dependent first order Hamilton-Jacobi equations. For high order
approximation schemes (where "high" stands for greater than one), the
inevitable loss of monotonicity prevents the use of the classical theoretical
results for convergence to viscosity solutions. The work introduces a suitable
local modification of these schemes by "filtering" them with a monotone scheme,
such that they can be proven convergent and still show an overall high order
behaviour for smooth enough solutions. We give theoretical proofs of these
claims and illustrate the behaviour with numerical tests from mathematical
finance, focussing also on the use of backward difference formulae (BDF) for
constructing the high order schemes.Comment: 27 pages, 16 figures, 4 table
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