Automatic Conflict Solving using Biharmonic Navigation Functions

Guys, Laureline; Puechmorel, Stéphane; Lapasset, Laurent

doi:10.1016/j.sbspro.2012.09.852

Cited by 5 publications

(8 citation statements)

References 4 publications

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“…Potential fields are also expensively studied, starting from the standard method, to its extension with navigation functions [13], the usage of more complex potential fields [14], or the combination between potential fields and swarming [15]. Those methods have the particularity of providing a proof of convergence.…”

Section: State Of the Artmentioning

confidence: 99%

Dynamic collision avoidance using local cooperative airplanes decisions

et al. 2019

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In the near future, air traffic control (ATC) will have to cope with a radical change in the structure of air transport [1]. Apart from the increase in traffic that will push the system to its limits, the insertion of new aerial vehicles such as drones into the airspace, with different flight performances, will increase its heterogeneity. Current research aims at increasing the level of automation and partial delegation of the control to on-board systems. In this work, we investigate the collision avoidance management problem using a decentralized distributed approach. We propose an autonomous and generic multiagent system to address this complex problem. We validate our system using state-of-the-art benchmarks. The results underline the adequacy of our local and cooperative approaches to efficiently solve the studied problem.

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Section: State Of the Artmentioning

confidence: 99%

Dynamic collision avoidance using local cooperative airplanes decisions

et al. 2019

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“…In practice, the values of  are saved during the computation of the solution v of (12)- (13). We follow the process proposed in the work of Bokanowski et al 27 Thus, once we have solved the HJB equation (12)-(13), we get the reachability function v and we use (14) to reconstruct  from v. A numerical approximation  I of  (ξ I ) is computed as follows. We first set  I equal to a large numerical value everywhere on the domain .…”

Section: Optimal Trajectories Reconstructionmentioning

confidence: 99%

“…Finally, we find the coordinated motion approach, which takes into account the whole set of mobiles simultaneously leading to more complex methods. Among deterministic methods, we can cite some works based on navigation functions (see the work of Guys et al). Moreover, Alton optimized the trajectory of 2 robots without collision.…”

Section: Introductionmentioning

confidence: 99%

On a Hamilton‐Jacobi‐Bellman approach for coordinated optimal aircraft trajectories planning

Parzani

Puechmorel

2017

Optim Control Appl Methods

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Summary In the context of future air traffic management, an increasing importance is given to environmental considerations and especially fuel consumption. It is thus advisable to make an optimal use of external conditions knowledge, like wind or temperature, to reduce the total fuel needed to complete a flight. On the other hand, safety must be guaranteed all over the trajectory: encounters below the regulatory separation minima, termed as conflicts, must never occur. In this paper, we consider the problem of optimally planning conflict free aircraft trajectories, based on a minimal time criterion and taking into account an ambient wind field. Aircraft motions are restricted to the horizontal plane only to reduce the dimension of the problem and to avoid costly changes of flight level. Since global optimality for the whole set of aircraft is sought after, the admissible space is modeled after a Cartesian product of the individual, 2‐dimensional state spaces with forbidden configurations removed. A Hamilton‐Jacobi‐Bellman approach in the so‐called configuration space obtained that way is then applied to get a coordinated, conflict‐free optimal planning. One of the main advantages of this method is the insurance of getting a global optimum without having to rely on a complex initialization procedure. In this work, the Ultra‐Bee scheme is adapted to configuration spaces and solved in a 4‐dimensional plus time setting.

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“…In addition, Baxter et al 23 implemented a new approach based on the APF method and described the application of a multi-robot system in rescue and search. Moreover, Guys 24 focused on the potential fields method to plan conflict-free trajectories for a large number of aircrafts. It is also important to note the study of Matoui et al, 25 who addressed the problem of the local minimum in the multi-robot system.…”

Section: Introductionmentioning

confidence: 99%

Distributed path planning of a multi-robot system based on the neighborhood artificial potential field approach

2018

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The current study is set up to investigate the problem of planning the trajectories of a multi-robot system. It puts emphasis on the idea of using distributed architecture to plan the trajectories of a group of wheeled mobile robots. Each robot must be able to detect and avoid collision with both static and dynamic obstacles present in its environment/neighborhood. This study seeks to improve the artificial potential field (APF) method in order to have good trajectory planning of a multi-robot system. In order to address the purpose of this work, we employed the hybrid approach, which is a combination of three techniques: the APF method; the neighborhood system; and the notion of priority between the robots. Moreover, the minimum local problem is handled in this paper using the non-minimum speed algorithm. The implemented approach is adapted to solve the trajectory planning problem for a multi-robot system. So, the problem of intersection of robots at the same passage point is solved through using the method of assignment of priority between robots. We also used the neighborhood detection technique to reduce the influence area of each robot and to optimize the time of calculation. The overall system equations associated to the robots are updated at each time of simulation to react at any condition that might suddenly emerge. The approach is implemented with MATLAB/Simulink and Solidworks/Simmechanics.

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Automatic Conflict Solving using Biharmonic Navigation Functions

Cited by 5 publications

References 4 publications

Dynamic collision avoidance using local cooperative airplanes decisions

Dynamic collision avoidance using local cooperative airplanes decisions

On a Hamilton‐Jacobi‐Bellman approach for coordinated optimal aircraft trajectories planning

Distributed path planning of a multi-robot system based on the neighborhood artificial potential field approach

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