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J.M. Hoekstra

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Journal article (2026) - Jean Claude Lebègue, Andréas Guitart, Daniel Delahaye, Jacco Hoekstra
Weather avoidance algorithms play a crucial role in significantly enhancing aircraft safety during flight operations, particularly in the presence of severe weather conditions. This paper presents a novel obstacle avoidance strategy based on the use of alternative paths to circumvent obstacles during the cruise phase. The objective of this study is to assess the benefits of using strategic information to address tactical avoidance issues. Firstly, the new strategy is simulated in a dynamic space populated with weather obstacles. Subsequently, the proposed strategy is compared to a classical avoidance maneuver in several dynamic simulations, varying the size of the obstacles. The results show that including strategic information on dynamic rerouting can be of significant benefit to both the pilot and air traffic controller, providing a supportive decision-making tool for bad weather avoidance. ...
This study investigates how navigation uncertainty affects conflict detection and resolution (CD&R) for uncrewed aircraft in U-space. Position and velocity errors are modelled as zero-mean Gaussian noise consistent with ADS-L accuracy, and propagated through conflict metrics using Monte Carlo and analytical approximations. Under uncertainty, state-based detection becomes probabilistic. The probability of detection depends on both the level of uncertainty and the encounter geometry, and falls below 50 % when the nominal intrusion time equals the look-ahead. Operationally, detection is re-evaluated over time as the encounter develops, yielding multiple observations with varying probabilities. Two resolution algorithms are compared: Modified Voltage Potential (MVP) and Velocity Obstacle (VO). MVP proves more robust under uncertainty because it explicitly maximises distance at the closest point of approach (CPA). By maximising CPA distance, MVP maintains an outward push and avoids reversal behaviour during the manoeuvre, whereas VO performance degrades at low relative speeds and shallow angles. BlueSky simulations confirm these effects: MVP achieves higher intrusion-prevention rates and larger post-resolution miss distances across conflict scenarios, with its advantage most pronounced at low relative velocity. The findings highlight the importance of maximising CPA distance as a conflict resolution strategy. Moreover, the look-ahead horizon and protected zone can be tuned to achieve a desired target level of safety. ...
Journal article (2026) - A. Vlaskin, D.J. Groot, Emmanuel Sunil, Joost Ellerbroek, J.M. Hoekstra, Dennis Nieuwenhuisen
Drones are expected to support applications such as emergency response, parcel delivery, and infrastructure monitoring in dense urban airspaces, creating traffic levels that are unmanageable for human operators. Autonomous separation management is therefore essential, combining strategic and tactical control to prevent conflicts. This paper addresses the tactical landing phase by introducing a centralized landing flow manager—a reinforcement learning (RL) agent that adjusts drone speed and heading to merge landing flows safely and efficiently prior to a final approach fix. The objective of the work was to demonstrate the potential of reinforcement learning in this novel context, by implementing and evaluating it in simulation and testing its capabilities with 10 concurrent landing drones. The RL agent learns to successfully separate traffic, thereby lowering intrusion counts compared to the baseline autopilot, but is outperformed in safety by the decentralized Modified Voltage Potential (MVP) method due to outlier scenarios. Nevertheless, the RL-based system achieves faster scenario completion and thus a higher overall throughput, by speeding up the vehicles towards the final approach fix. Future work will explore improved network architectures, transfer learning across varied scenarios, and algorithmic fine-tuning to further enhance safety performance. ...
Journal article (2025) - Calin Andrei Badea, Andrija Vidosavljevic, Joost Ellerbroek, Jacco Hoekstra
Very-low-level (VLL) urban air operations have been extensively investigated as a solution for mitigating congestion in cities. However, the manner in which the management of such traffic should be performed is still actively investigated. One important component of such a system is the conflict detection and resolution (CD&R), mainly composed of the strategic and tactical CD&R module. While many approaches towards these have been studied, insufficient analysis has been conducted on their compatibility when functioning within a unified, hybrid system. Additionally, their robustness to operational uncertainties such as wind and departure delays is often overlooked. In this work, we investigate the performance of strategic planing methods when combined with tactical CD&R and subjected to a wide range of traffic demand levels and uncertainty conditions. Simulations indicate that the performance of the strategic deconfliction module is highly sensitive to the presence of wind and delay. This decline in performance is partially mitigated by the tactical deconfliction module. Thus, the results suggest that increased use of tactical CD&R could lessen the required level of detail of strategic deconfliction methods, leading to improved compatibility between the two modules. ...

An Optimal Trajectory Approach

Conference paper (2025) - Aidana Tassanbi, Junzi Sun, Jacco Hoekstra
The mass of an aircraft is crucial for performance-related studies, such as predicting flight trajectories and analyzing flight emissions. In these studies, the flight trajectories are often reconstructed using a point-mass aircraft performance model combined with flight profiles from surveillance data and take-off mass information. However, airlines do not usually disclose take-off mass information, considering its sensitive nature. Thus, aircraft masses often need to be assumed or estimated. This paper presents a simple and computationally effective approach for estimating take-off mass using only open data and models. We explore the strong correlation between take-off mass, flight distance, cruise altitude, and partially, the airspeed during the cruise. The main idea is to generate fuel-optimal trajectories with known masses and distances, and then compare them with actual flight data. The optimal trajectories are generated using the open aircraft performance and optimization library. By assuming that actual flights follow quasi-fuel-optimal trajectories, the take-off mass of a flight can be estimated based on simple regression models trained on the optimal trajectory dataset. This open-loop take-off mass estimation approach requires no proprietary information from aircraft manufacturers or airlines. We verified the model with an anonymized dataset containing actual A320 flights with known take-off mass. Our two- and three-feature multi-linear models yield mean absolute percentage errors of 5.95 % and 4.89 %, respectively. This study is another step forward in open science and a contribution to the aircraft trajectory studies. ...
Journal article (2025) - D. J. Groot, J. Ellerbroek, J. M. Hoekstra
Reinforcement learning (RL) is a method that has been studied extensively for the task of conflict-resolution and separation management within air traffic control, offering advantages over analytical methods. One key challenge associated with RL for this task is the construction of the input vector. Because the number of agents in the airspace varies, methods that can handle dynamic number of agents are required. Various methods exist, for example, selecting a fixed number of aircraft, or using methods such as recurrent neural networks or attention to encode the information. Multiple studies have shown promising results using these encoder methods, however, studies comparing these methods are limited and the results remain inconclusive on which method works better. To address this issue, this paper compares different input encoding methods: three different attention methods – scaled dot-product, additive and context aware attention – and long short-term memory (LSTM) with three different sorting strategies. These methods are used as input encoders for different models trained with the Soft Actor–Critic algorithm for separation management in high traffic density scenarios. It is found that additive attention is the most effective at increasing the total safety and maximizing path efficiency, outperforming the commonly used scaled dot-product attention and LSTM. Additionally, it is shown that the order of the input sequence significantly impacts the performance of the LSTM based input encoder. This is in contrast with the attention methods, which are sequence-independent and therefore do not suffer from biases introduced by the order of the input sequence. ...
Journal article (2025) - Cǎlin Andrei Badea, Joost Ellerbroek, Andrija Vidosavljević, Jacco Hoekstra
The concept of urban air mobility is rapidly advancing, with much research being dedicated towards the development of the air traffic management services required for such operations. An important component of unmanned air traffic management (U-space/UTM) is conflict detection and resolution (CD&R), tasked with ensuring the operational safety of such systems. Strategic flight plan optimisation and tactical CD&R methods have generally been studied independently, leading to suboptimal performance when deployed simultaneously in simulated high-density very-low-level constrained urban airspace environments. Furthermore, the limited flexibility of pre-departure 4D trajectory planning methods towards dynamic and uncertain environmental and operational conditions (i.e., wind and delay) produces a degradation in safety that is difficult to mitigate using tactical manoeuvring. In this work, we design a traffic-flow capacity strategic optimisation method that aims to achieve robustness against flight plan deviations and to better complement tactical CD&R manoeuvring. The performance of the proposed strategic and tactical deconfliction module is tested within constrained urban airspace traffic scenarios simulated using the BlueSky Open Air Traffic Simulator. The results are compared with other methods, such as 4D trajectory planning and state-based CD&R. ...
Journal article (2024) - D. J. Groot, J. Ellerbroek, J. M. Hoekstra
Conventional Air Traffic Control is still predominantly being done by human Air Traffic Controllers, however, as the traffic density increases, the workload of the controllers increases as well. Especially for the area of unmanned aviation, driven by the rise in drones, having human controllers might become unfeasible. One of the methods that is currently being investigated for replacing the conflict resolution task of Air Traffic Control is Reinforcement Learning. As violation of the required separation margins, also called an intrusion, is an event of relatively low frequency, using Reinforcement Learning for this task comes with difficulties that can potentially be attributed to data imbalance. This paper artificially increased the traffic density during the training phase of the Reinforcement Learning method to investigate what the importance is of a balanced data set on the performance of the Reinforcement Learning method. It was found that as the traffic density increased, the Reinforcement Learning methods started to outperform the analytical methods. Beyond this it was found that methods trained at higher traffic densities, but tested at lower traffic densities, outperformed the methods trained at that specific density. This indicates that it might be better to always ensure that the training scenarios are more complex than anticipated during the execution phase, even if that results in unrealistic scenarios. ...
Conference paper (2024) - Jean Claude Lebegue, Andréas Guitart, Céline Demouge, Daniel Delahaye, Jacco Hoekstra, Eric Feron
Weather obstacles in the airspace can interfere with an aircraft’s flight plan. Pilots, assisted by air traffic controllers (ATCs), perform avoidance maneuvers that can be optimized. This paper addresses the generation of alternative aircraft trajectories to resolve unexpected events. The authors propose a solution based on the RRG algorithm, K-means clustering, and Dynamic Time Warping (DTW) similarity metric to address the problem. The mixed algorithm succeeds in generating a set of paths with diversity in an obstacle constrained airspace between Paris-Toulouse and London-Toulouse airports. This tool could help to reduce the workload of pilots and ATCs when such a situation arises. ...
Conference paper (2024) - Jean Claude Lebègue, Daniel Delahaye, Jacco Hoekstra
Many transportation networks have complex infrastructures (road, rail, airspace, etc.). The quality of service in air transportation depends on weather conditions. Technical failures of the aircraft, bad weather conditions, strike of the company’s staff cause delays and disrupt traffic. How can the robustness of such networks be improved? Improving the robustness of air transportation would reduce the cascading delays between airports and improve the passenger journey. Many studies have been done to find critical links and nodes, but not so many analyze the paths. In this paper, we propose a new method to measure network robustness based on alternative paths. Besides improving the robustness of the French (respectively Turkish Airlines and European) low-cost flight network by 19% (respectively 16% and 6.6%), the method attempts to show the relevance of analyzing the network vulnerability from a path-based approach. ...
Conference paper (2024) - A. Vlaskin, Emmanuel Sunil, Joost Ellerbroek, J.M. Hoekstra, Dennis Nieuwenhuisen
Abstract—In the coming decades, drones are expected to operate within urban areas at high volumes, and if implemented suc- cessfully, applications such as infrastructure inspection, medical supply and parcel delivery can be improved by the technology. This poses a challenge: how are these drones to be guided in this highly-constrained airspace? Many existing projects have approached the problem from different angles: some place more importance on the Tactical Layer and thus resolving conflicts in flight, while other research focuses on the Strategic Layer with scheduling or airspace design. While analysis is done on a complete system, with all separation management layers implemented, work remains to be done regarding quantifying how these layers interact, and what positive characteristics of these interactions can be utilised to make the system more efficient, safe, and robust to uncertainties. This paper proposes a framework on which this analysis can be performed. Firstly, lay- ers are investigated independently. A feedback system is proposed, where layer outputs are measured, as is the resulting system performance. For instance, an initial hypothesis is that reducing airspace complexity in the Strategic layer, while accounting for uncertainty, will lead to better overall system performance. This can help with minimising flight times and improving overall safety. Also, manoeuvres performed by the Tactical (in-flight) layer should take this complexity metric into account. The feedback loop approach also proposes that the complexity be fed back to the central planner, and that the Strategic (Pre-Flight) layer should be able to take system status into account when performing planning. ...
Urban air mobility can be a potential solution for urban congestion, and high-level concepts of operations (e.g., UTM, U-space) have been developed with the help of large-scale simulations of multi-agent systems. However, one aspect that should be researched more is the effect of wind on the safety and efficiency of missions in an urban environment. While studies that analyse the potential effect of wind on U-space operations exist, they mostly use constant wind fields, or highly simplified wind models. The study at hand investigates whether medium-fidelity CFD models can be used to predict and match recorded wind data in the city centre of The Hague. Six locations with distinct urban features were chosen, and wind measurements were recorded on two separate days. Using the rooftop wind properties obtained during the measurement sessions, computational fluid dynamics (CFD) simulations were performed within a large urban model of the city. Results indicate that there are large discrepancies between the simulated and measured values. Some wind phenomena observed within the measured wind data were also replicated by the CFD model. Thus, based on the results presented in this work, future research should focus on improving computer city models and wind measurement methods to ensure the development of concepts of operations that maximise the safety and efficiency of future U-space operations. ...
Conference paper (2024) - Sasha Vlaskin, Emmanuel Sunil, Dennis Nieuwenhuisen, Joost Ellerbroek, Jacco Hoekstra
U-Space drone operations are expected to be a driver for further urban development, especially through use cases such as medical and commercial parcel delivery. In particular, package delivery using small drones shows great promise, with e-commerce giants such as Amazon deploying limited-scale drone delivery trials in rural areas. As the technology matures, large-scale operations will take place in constrained urban areas, leading to high airborne traffic densities. It is necessary to develop a robust automated separation management system that actively ensures safe separation of drones both in the air and on the ground. This paper focuses on the Strategic element, more specifically on pre-departure planning. The aim of this is to reduce the chance of conflicts around vertiports, where spatial and environmental constraints make tactical resolutions difficult. This work focuses on two scenarios: a single pad for both takeoffs and landings (in a spatially constrained urban area) and 4 takeoff-landing pad pairs (for a distribution center). Several methods are compared for this takeoff sequencing task, coupled with a conflict detection algorithm: A First-Come First-Served method that applied delay to conflicting flights, a Mixed-Integer Programming approach, a Genetic Algorithm, Particle Swarm Algorithm and Simulated Annealing were used. For a single-pad approach, first-come first-served works best in terms of computation time and total deployment time (or makespan). For the multi-pad approach however, changing the flight sequence through metaheurisitic methods and mixed-integer linear programming show a reduction in total deployment time. ...
Conference paper (2024) - Esther Roosenbrand, Junzi Sun, Jacco Hoekstra
Contrail optimization offers an efficient and cost-effective way for aviation to immediately reduce its climate impact. Open-source optimization, wherein the contrail and emission effects are balanced based on meteorological open data, has been presented in previous work. However, prior research overlooks the importance of using forecasting data, as opposed to post-processed reanalysis data. For contrail optimization to be implementable, forecasting data needs to be available at a sufficient quality in the flight planning stage in order to perform the optimization. In this paper, a fully open non-linear optimal control flight optimization is implemented and applied using both forecasting and reanalysis data. A total of 120 days (175.440 flights) of flight data from OpenSky are used in the analysis. We show that forecasts with larger lookahead times (up to 12 hours) are equally effective when compared to more recent forecasts (1 hour lookahead time) for contrail optimization, with equally high accuracy. However, when compared to more accurate post-processed reanalysis data, there are considerable differences in predicted contrails formed. This research shows there is still a long way to go before we can actually implement contrail optimal flight planning. ...
U-space/UTM operations are considered an integral part of the future development of cities, with applications ranging from package delivery to urban air mobility. However, this new complex environment also poses challenges for the conflict detection and resolution (CD&R) process, especially if aircraft will have to navigate above the existing street network due to privacy and obstacle constraints. The research at hand aims to investigate how information about the environment and other aircraft can be used to improve the performance of CD&R methods in constrained urban airspace. For this, three algorithms are developed and tested, each with different levels of information availability: the first solely uses current state information for conflict solving, the second includes additional information about the urban environment within the CD&R process, and the last also incorporates trajectory intent data to solve conflicts. These methods are tested within simulations of urban air traffic scenarios at various demand and wind levels to determine their safety and efficiency performance. Results show the use of street geometry information benefits the resolution process greatly, increasing the safety level while minimally affecting efficiency. Intent information is shown to not be critical for achieving this. ...

Comparing Historical and Real-time Aggregate Flow Data

Conference paper (2024) - A. Morfin Veytia, J. Ellerbroek, J. Hoekstra
As urban ground transportation congestion increases, there is growing interest in urban air transportation, such as delivery drones and air taxis. However, managing air traffic in densely populated urban areas poses significant challenges, which require effective flight planning, separation management, and airspace design. This paper investigates dynamic capacity balancing methods to manage air traffic in constrained urban airspace, where drones must fly above the existing road network. Specifically, it compares the effectiveness of labelling high-complexity zones using historical data versus real-time aggregate flow data. The results indicate that while both approaches reduce airspace intrusions and improve safety, the best approach depends on traffic demand levels. At lower demand levels, using historical data yields better safety outcomes, whereas using real-time data is more effective at higher demand levels due to its flexibility. At their best, both methods increase the travel distance by less than 6% while reducing airspace intrusions by 30% compared to a case without dynamic capacity balancing. ...

A Large-Scale Trade-off Analysis Using Open Data and Models

Conference paper (2024) - E.J. Roosenbrand, Junzi Sun, J.M. Hoekstra
Emissions and contrails are key factors in aviationinduced climate change, often presenting conflicting objectives in flight trajectory optimization. Previous research typically lacks in optimizer efficiency or in addressing these trade-offs, with limited use of extensive meteorological and flight data. In this paper, a fully open non-linear optimal control flight optimization approach is designed for contrail avoidance and emission reduction, with high computational efficiency. This is achieved by leveraging the most recent trajectory optimizer, OpenAP.TOP, and atmospheric data handling tool, fastmeteo. We present a new compound grid-based objective function that considers both contrails and emissions and introduce four different metrics for evaluating the performance. A total of four months’ worth of data, containing around half a million flights, are gathered from OpenSky for analyses. We show that high levels of contrail mitigation can be achieved, without significantly increasing flight time, distance, or emissions. ...

Dynamically Generating and Acting Upon Aggregate Flow Data

<p>There are several efforts to explore employing drones to replace ground transportation in cities. However, this would mean that the expected traffic densities would be significantly higher than existing air traffic management. A decentralised system for traffic management may be necessary in this future because (1) not all airspace actors will want to freely share data, (2) the uncertainty of missions due to wind or other factors could make a previous plan inoperable, and (3) the ad hoc nature of urban missions makes them difficult to plan in advance. This work focuses on the challenges of drone operations within constrained urban airspace. We define constrained airspace as a virtual network overlaid on the physical environment, where tall buildings and urban infrastructure dictate the allowed routes. Drones are restricted to flying within this virtual network, either above the existing street network or along other predetermined segments. A dynamic and decentralised traffic management method is presented. The method uses current aggregate flow data to identify and alter the cost of travelling through high-density clusters. The goal is to reduce local traffic density and complexity by encouraging alternate routes. Three different clustering strategies are presented that look at the current position of aircraft and recent safety events. The dynamic traffic management method is first illustrated with two simple example scenarios. Then an experiment is conducted with different traffic demand levels within the city of Rotterdam. It was observed that when using traffic complexity indicators, the method is able to reduce safety events by 30 percent while only increasing the distance travelled by 6 percent.</p><p> </p> ...
Conference paper (2024) - M.F. Rahman, Joost Ellerbroek, J.M. Hoekstra
Abstract—The integration of unmanned aerial systems (UASs) into existing airspace is imminent as the concept is maturing. U- Space is a concept in which UASs are allowed to fly alongside general aviation aircraft, requiring all aircraft in the airspace to transmit navigation data using radio and network identification. Nevertheless, a consensus is required for the separation in case of conflict amidst the limitations of communication, navigation, and surveillance (CNS) systems. Update rate and probability depict the uncertainty in the communication systems, while spread around the ground truth in position describes the navigation accuracy. Then, BlueSky, an open-source simulator, produces thousands of conflict detection and resolutions to evaluate the CNS limitation on the intrusion prevention rate and loss of separation severity. This paper concludes that higher update rate, probability, and position accuracy lead to safer conflict resolution, and selecting 50 meters as the radius of the protected zone results in a 25-meter intrusion in the worst case. ...
Conference paper (2024) - R.W. Vos, Junzi Sun, J.M. Hoekstra
Air traffic sector demand and capacity balancing are necessary for safe and efficient flight execution. Demand and capacity are determined in current operations based on schedules and flight plans. This research aims to improve air traffic demand forecasting by exploring machine learning-based trajectory prediction, specifically the newly emerged transformer-based neural network models. The predicted trajectories are considered to improve demand forecasts for Air Traffic Control in the Netherlands. We successfully built a transformer neural network using available traffic messages from the EuroControl B2B connection and actual trajectories obtained from the OpenSky ADS-B repository. A new lost function is specifically designed to improve this prediction model’s performance. This trajectory predictor could accurately generate trajectories, outperforming the flight plan and other neural network approaches by a good margin. For demand prediction, introducing improved trajectories provided small gains that could lead to more stable predictions. ...