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C. Badea
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10 records found
1
Journal article
(2025)
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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.
...
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.
Urban air mobility (UAM) is presented as a potential solution to urban congestion. By utilising aerial vehicles for tasks like parcel delivery, public transport, and surveillance, pressure on traditional ground-based transportation infrastructure can be alleviated. This is particularly important with the rise of e-commerce and the increasing demand for fast and efficient delivery methods. UAM has the potential to revolutionise urban travel, offering faster commutes and enhancing surveillance capabilities for improved traffic management and emergency response.
The U-space concept, developed within the European Union, provides a framework for the safe integration of drones and small unmanned aircraft systems (sUAS) into urban airspace. It focuses on establishing services, regulations, and procedures to manage UAM operations effectively. An important component of this concept is Type Zu airspace, designated for high-density urban operations. This airspace requires strict regulations and safety-critical services like dynamic capacity management, conflict resolution, and continuous monitoring to ensure safe and efficient U-space operations.
Conflict detection and resolution (CD&R) of air traffic is required to ensure the safety of such operations, and VLL urban airspace presents unique challenges compared to conventional air traffic management. Buildings and other obstacles restrict aircraft movement, making manoeuvring and conflict avoidance more difficult. Unpredictable urban wind patterns further complicate flight planning and trajectory prediction. These factors, combined with the inherent complexity of urban environments, necessitate the development of robust CD&R algorithms and rules specifically tailored to the challenges of VLL urban airspace.
The core research objective of this dissertation is to identify and develop effective CD&R algorithms and rules for safe and efficient UAM operations in VLL urban airspace. This involves evaluating the limitations of existing CD&R methods, designing new algorithms that address the specific challenges of urban environments, and defining clear rules and procedures for aircraft navigation and conflict resolution…
...
The U-space concept, developed within the European Union, provides a framework for the safe integration of drones and small unmanned aircraft systems (sUAS) into urban airspace. It focuses on establishing services, regulations, and procedures to manage UAM operations effectively. An important component of this concept is Type Zu airspace, designated for high-density urban operations. This airspace requires strict regulations and safety-critical services like dynamic capacity management, conflict resolution, and continuous monitoring to ensure safe and efficient U-space operations.
Conflict detection and resolution (CD&R) of air traffic is required to ensure the safety of such operations, and VLL urban airspace presents unique challenges compared to conventional air traffic management. Buildings and other obstacles restrict aircraft movement, making manoeuvring and conflict avoidance more difficult. Unpredictable urban wind patterns further complicate flight planning and trajectory prediction. These factors, combined with the inherent complexity of urban environments, necessitate the development of robust CD&R algorithms and rules specifically tailored to the challenges of VLL urban airspace.
The core research objective of this dissertation is to identify and develop effective CD&R algorithms and rules for safe and efficient UAM operations in VLL urban airspace. This involves evaluating the limitations of existing CD&R methods, designing new algorithms that address the specific challenges of urban environments, and defining clear rules and procedures for aircraft navigation and conflict resolution…
...
Urban air mobility (UAM) is presented as a potential solution to urban congestion. By utilising aerial vehicles for tasks like parcel delivery, public transport, and surveillance, pressure on traditional ground-based transportation infrastructure can be alleviated. This is particularly important with the rise of e-commerce and the increasing demand for fast and efficient delivery methods. UAM has the potential to revolutionise urban travel, offering faster commutes and enhancing surveillance capabilities for improved traffic management and emergency response.
The U-space concept, developed within the European Union, provides a framework for the safe integration of drones and small unmanned aircraft systems (sUAS) into urban airspace. It focuses on establishing services, regulations, and procedures to manage UAM operations effectively. An important component of this concept is Type Zu airspace, designated for high-density urban operations. This airspace requires strict regulations and safety-critical services like dynamic capacity management, conflict resolution, and continuous monitoring to ensure safe and efficient U-space operations.
Conflict detection and resolution (CD&R) of air traffic is required to ensure the safety of such operations, and VLL urban airspace presents unique challenges compared to conventional air traffic management. Buildings and other obstacles restrict aircraft movement, making manoeuvring and conflict avoidance more difficult. Unpredictable urban wind patterns further complicate flight planning and trajectory prediction. These factors, combined with the inherent complexity of urban environments, necessitate the development of robust CD&R algorithms and rules specifically tailored to the challenges of VLL urban airspace.
The core research objective of this dissertation is to identify and develop effective CD&R algorithms and rules for safe and efficient UAM operations in VLL urban airspace. This involves evaluating the limitations of existing CD&R methods, designing new algorithms that address the specific challenges of urban environments, and defining clear rules and procedures for aircraft navigation and conflict resolution…
The U-space concept, developed within the European Union, provides a framework for the safe integration of drones and small unmanned aircraft systems (sUAS) into urban airspace. It focuses on establishing services, regulations, and procedures to manage UAM operations effectively. An important component of this concept is Type Zu airspace, designated for high-density urban operations. This airspace requires strict regulations and safety-critical services like dynamic capacity management, conflict resolution, and continuous monitoring to ensure safe and efficient U-space operations.
Conflict detection and resolution (CD&R) of air traffic is required to ensure the safety of such operations, and VLL urban airspace presents unique challenges compared to conventional air traffic management. Buildings and other obstacles restrict aircraft movement, making manoeuvring and conflict avoidance more difficult. Unpredictable urban wind patterns further complicate flight planning and trajectory prediction. These factors, combined with the inherent complexity of urban environments, necessitate the development of robust CD&R algorithms and rules specifically tailored to the challenges of VLL urban airspace.
The core research objective of this dissertation is to identify and develop effective CD&R algorithms and rules for safe and efficient UAM operations in VLL urban airspace. This involves evaluating the limitations of existing CD&R methods, designing new algorithms that address the specific challenges of urban environments, and defining clear rules and procedures for aircraft navigation and conflict resolution…
Journal article
(2023)
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C. Badea, A. Morfin Veytia, Niki Patrinopoulou, Ioannis Daramouskas, Joost Ellerbroek, Vaios Lappas, Vassilios Kostopoulos, J.M. Hoekstra
The use of small aircraft for a wide range of missions in urban airspace is expected to increase in the future. In Europe, efforts have been invested into developing a unified system, called U-space, to manage aircraft in dense very-low-level urban airspace. The Metropolis II project aimed to research what degree of centralisation an air traffic management system should use in such airspace. The paper at hand is a follow-up, and investigates improvements that can be brought to the tactical conflict prevention, detection, and resolution module of such a system in order to harmonise these components with an organic high-density U-space environment. The proposed improvements are: the prioritisation of vertical conflict prevention in intersections, the use of intent in detecting and resolving conflicts, and the use of heading-based manoeuvres in open airspace. Results show that the use of intent information in the conflict detection process, as well as the implementation of suitable tactical prevention procedures, can greatly increase airspace safety. Furthermore, the experiments revealed that the effectiveness of conflict resolution algorithms is highly dependent on the airspace rules and structure. This reiterates the potential for increasing the safety and efficiency of operations within constrained airspace if the tactical separation modules are unified with the other components of air traffic management systems for U-space.
...
The use of small aircraft for a wide range of missions in urban airspace is expected to increase in the future. In Europe, efforts have been invested into developing a unified system, called U-space, to manage aircraft in dense very-low-level urban airspace. The Metropolis II project aimed to research what degree of centralisation an air traffic management system should use in such airspace. The paper at hand is a follow-up, and investigates improvements that can be brought to the tactical conflict prevention, detection, and resolution module of such a system in order to harmonise these components with an organic high-density U-space environment. The proposed improvements are: the prioritisation of vertical conflict prevention in intersections, the use of intent in detecting and resolving conflicts, and the use of heading-based manoeuvres in open airspace. Results show that the use of intent information in the conflict detection process, as well as the implementation of suitable tactical prevention procedures, can greatly increase airspace safety. Furthermore, the experiments revealed that the effectiveness of conflict resolution algorithms is highly dependent on the airspace rules and structure. This reiterates the potential for increasing the safety and efficiency of operations within constrained airspace if the tactical separation modules are unified with the other components of air traffic management systems for U-space.
Journal article
(2023)
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A. Morfin Veytia, C. Badea, Niki Patrinopoulou, Ioannis Daramouskas, Joost Ellerbroek, Vaios Lappas, Vassilios Kostopoulos, J.M. Hoekstra
The interest in urban air mobility as a potential solution for urban congestion is steadily growing. Air operations in urban areas can present added complexity as compared with traditional air traffic management. As a result, it is necessary to test and develop novel airspace designs and rules. As airspace in urban areas is a scarce resource, creating structures and rules that effectively utilise the airspace is an important challenge. This work specifically focuses on layered airspace design in urban operations constrained to fly between the existing buildings. Two design parameters of airspace design are investigated with two sub-experiments. Sub-experiment 1 investigates layer function assignment by comparing concepts from previous research with different layer assignment distributions. Sub-experiment 2 investigates the flight rules of vertical distribution of traffic within the airspace, to determine whether this is best achieved in a static (pre-allocated) or dynamic manner. Both sub-experiments analyse the overall system safety, route duration, and route distance under increasing traffic demand. Results reveal that the importance of cruising airspace is apparent at high densities. Results also shows that the safest layer allocation flight rule depends on the traffic density. At lower densities dynamic rules help to spread traffic locally. However, when the airspace is saturated it is safer to pre-allocate flight heights if achieved uniformly.
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The interest in urban air mobility as a potential solution for urban congestion is steadily growing. Air operations in urban areas can present added complexity as compared with traditional air traffic management. As a result, it is necessary to test and develop novel airspace designs and rules. As airspace in urban areas is a scarce resource, creating structures and rules that effectively utilise the airspace is an important challenge. This work specifically focuses on layered airspace design in urban operations constrained to fly between the existing buildings. Two design parameters of airspace design are investigated with two sub-experiments. Sub-experiment 1 investigates layer function assignment by comparing concepts from previous research with different layer assignment distributions. Sub-experiment 2 investigates the flight rules of vertical distribution of traffic within the airspace, to determine whether this is best achieved in a static (pre-allocated) or dynamic manner. Both sub-experiments analyse the overall system safety, route duration, and route distance under increasing traffic demand. Results reveal that the importance of cruising airspace is apparent at high densities. Results also shows that the safest layer allocation flight rule depends on the traffic density. At lower densities dynamic rules help to spread traffic locally. However, when the airspace is saturated it is safer to pre-allocate flight heights if achieved uniformly.
Metropolis II
Investigating the Future Shape of Air Traffic Control in Highly Dense Urban Airspace
Conference paper
(2022)
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N. Patrinopoulou, I. Daramouskas, V. Lappas, A. Morfin Veytia, C. A. Badea, J. Ellerbroek, J. Hoekstra, V. De Vries, J. Van Ham, More authors...
Metropolis II aims to provide insights in what is needed to enable high-density urban air operations. It does this by investigating the foundation for U-space U3/U4 services. The final goal is to provide a unified approach for strategic deconfliction, tactical deconfliction, and dynamic capacity management. Highly-dense operations in constrained urban airspace will likely require a degree of complexity that does not exist in modern-day air traffic management. The expected high traffic demand will require a shared use of the airspace instead of assigning exclusive use of blocks of the airspace to some flights. A unified approach for traffic management is needed because at high-densities, airspace design, flight planning, and separation management become increasingly interdependent. Metropolis II builds upon the results of the first Metropolis project. Three concepts with a varying degree of centralisation will be compared using simulations. (1) The centralised concept will take a global approach for separation management. (2) The decentralised concept aims to give the individual agents separation responsibility. (3) The hybrid concept tries to combine a centralised strategic planning agent with a robust tactical separation strategy.
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Metropolis II aims to provide insights in what is needed to enable high-density urban air operations. It does this by investigating the foundation for U-space U3/U4 services. The final goal is to provide a unified approach for strategic deconfliction, tactical deconfliction, and dynamic capacity management. Highly-dense operations in constrained urban airspace will likely require a degree of complexity that does not exist in modern-day air traffic management. The expected high traffic demand will require a shared use of the airspace instead of assigning exclusive use of blocks of the airspace to some flights. A unified approach for traffic management is needed because at high-densities, airspace design, flight planning, and separation management become increasingly interdependent. Metropolis II builds upon the results of the first Metropolis project. Three concepts with a varying degree of centralisation will be compared using simulations. (1) The centralised concept will take a global approach for separation management. (2) The decentralised concept aims to give the individual agents separation responsibility. (3) The hybrid concept tries to combine a centralised strategic planning agent with a robust tactical separation strategy.
In order to enable the safe and efficient integration of Unmanned Aerial Vehicles into very low level airspace, current day research focuses on the development of new traffic services and procedures. One of these is the geovectoring protocol, which aims to reduce traffic complexity by setting limits on the allowed ground speed, course, and vertical speed. A geovector can be used to increase the capacity of an airspace by lowering the conflict rate. However, problems emerge when performing avoidance maneuvers in geovectored airspace, as the limits are ignored in this process. A powerful conflict resolution algorithm is the Modified Voltage Potential (MVP). This paper proposes an extension to the MVP algorithm, based on Velocity Obstacle theory. Making use of an alternative horizontal conflict resolution maneuver which respects the geovector, five resolution strategies are defined with different priority settings for the separate limits. The performance of these strategies is compared to pure MVP on geovector, safety, and stability measures, making use of fast-time simulations in a corridor airspace. All geovector resolution strategies show improvements on the ability to perform conflict resolution maneuvers within the geovector limits, while having marginal effects on the overall airspace safety level. It is recommended to further investigate the performance of the geovector resolution strategies for other types of airspace, to verify whether the observed reduction in conflict rate from the geovectors can be reinforced by the resolution strategies.
...
In order to enable the safe and efficient integration of Unmanned Aerial Vehicles into very low level airspace, current day research focuses on the development of new traffic services and procedures. One of these is the geovectoring protocol, which aims to reduce traffic complexity by setting limits on the allowed ground speed, course, and vertical speed. A geovector can be used to increase the capacity of an airspace by lowering the conflict rate. However, problems emerge when performing avoidance maneuvers in geovectored airspace, as the limits are ignored in this process. A powerful conflict resolution algorithm is the Modified Voltage Potential (MVP). This paper proposes an extension to the MVP algorithm, based on Velocity Obstacle theory. Making use of an alternative horizontal conflict resolution maneuver which respects the geovector, five resolution strategies are defined with different priority settings for the separate limits. The performance of these strategies is compared to pure MVP on geovector, safety, and stability measures, making use of fast-time simulations in a corridor airspace. All geovector resolution strategies show improvements on the ability to perform conflict resolution maneuvers within the geovector limits, while having marginal effects on the overall airspace safety level. It is recommended to further investigate the performance of the geovector resolution strategies for other types of airspace, to verify whether the observed reduction in conflict rate from the geovectors can be reinforced by the resolution strategies.
Conference paper
(2022)
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C. Badea, D.J. Groot, A. Morfin Veytia, M.J. Ribeiro, Ramon Dalmau, J. Ellerbroek, J.M. Hoekstra
Air traffic demand has increased at an unprecedented rate in the last decade (albeit interrupted by the COVID pandemic), but capacity has not increased at the same rate. Higher levels of automation and the implementation of decision-support tools for air traffic controllers could help increase capacity and catch up with demand. The air traffic control problem can be effectively modelled as a Markov game, where a team of aircraft (the agents) interact in the airspace (the environment) and cooperatively take resolution actions to achieve a common goal: safe separation in the most efficient way. As in any Markov game, the optimal policy for the team could be learnt through trial and error in a simulated environment using reinforcement learning algorithms. In this paper, we use the soft actor-critic algorithm to unravel the optimal air traffic control policy. Unlike some previous works, we propose a global (i.e., shared) reward that encourages cooperative behaviour. Furthermore, we propose a versatile policy model capable of performing heading, speed, and/or altitude resolution actions. We also demonstrate that the policy is robust and can maintain safe separation even in the presence of uncertainty regarding aircraft position, delays in implementing resolution actions, and wind. The findings of this paper also suggest that there is still significant room for improvement when controlling three degrees of freedom at the same time.
...
Air traffic demand has increased at an unprecedented rate in the last decade (albeit interrupted by the COVID pandemic), but capacity has not increased at the same rate. Higher levels of automation and the implementation of decision-support tools for air traffic controllers could help increase capacity and catch up with demand. The air traffic control problem can be effectively modelled as a Markov game, where a team of aircraft (the agents) interact in the airspace (the environment) and cooperatively take resolution actions to achieve a common goal: safe separation in the most efficient way. As in any Markov game, the optimal policy for the team could be learnt through trial and error in a simulated environment using reinforcement learning algorithms. In this paper, we use the soft actor-critic algorithm to unravel the optimal air traffic control policy. Unlike some previous works, we propose a global (i.e., shared) reward that encourages cooperative behaviour. Furthermore, we propose a versatile policy model capable of performing heading, speed, and/or altitude resolution actions. We also demonstrate that the policy is robust and can maintain safe separation even in the presence of uncertainty regarding aircraft position, delays in implementing resolution actions, and wind. The findings of this paper also suggest that there is still significant room for improvement when controlling three degrees of freedom at the same time.
Conference paper
(2022)
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C. Badea, Joost Ellerbroek, J.M. Hoekstra
The interest for using small aircraft for missions in urban airspace is growing for applications like parcel deliveries. Research shows that conventional airspace structure and conflict detection and resolution techniques are not suitable for main- taining a high level of safety in constrained urban environments, especially when aircraft are restricted to flying within the limits of the road network. The problem at hand becomes even more complex when factoring in cities with topologically organic street networks, thus increasing the probability of crossing and merging traffic flows. Preliminary results show that such networks induce the detection of false-positive conflicts when using classical state- based conflict detection, decreasing the effectiveness of conflict resolution. Velocity-obstacle based conflict resolution methods were able to improve airspace safety, but require further de- velopment in order to handle conflicts in such an unpredictable and constrained environment. Thus, the doctoral project at hand seeks to develop and research improved methods for conflict prevention, detection and resolution in constrained, urban, very low-level urban airspace.
...
The interest for using small aircraft for missions in urban airspace is growing for applications like parcel deliveries. Research shows that conventional airspace structure and conflict detection and resolution techniques are not suitable for main- taining a high level of safety in constrained urban environments, especially when aircraft are restricted to flying within the limits of the road network. The problem at hand becomes even more complex when factoring in cities with topologically organic street networks, thus increasing the probability of crossing and merging traffic flows. Preliminary results show that such networks induce the detection of false-positive conflicts when using classical state- based conflict detection, decreasing the effectiveness of conflict resolution. Velocity-obstacle based conflict resolution methods were able to improve airspace safety, but require further de- velopment in order to handle conflicts in such an unpredictable and constrained environment. Thus, the doctoral project at hand seeks to develop and research improved methods for conflict prevention, detection and resolution in constrained, urban, very low-level urban airspace.
Metropolis II
Benefits of Centralised Separation Management in High-Density Urban Airspace
Conference paper
(2022)
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A. Morfin Veytia, C. Badea, Joost Ellerbroek, J.M. Hoekstra, N. Patrinopoulou, I. Daramouskas, V. Lappas, Vassilis Kostopoulos, Vincent de Vries, More authors...
The Metropolis II project aimed to study the impact of centralised separation management for urban aerial mobility. Three concepts were developed in this study: a fully centralised, strategically separated concept, a hybrid concept featuring cen- tralised strategic separation and distributed tactical separation, and a fully distributed tactical concept. A comparative simu- lation study was performed, using traffic scenarios based on predicted demand in an urban airspace in the city of Vienna. Simulations were performed with varying traffic densities and situations. Results show that the purely strategic and purely tactical strategies perform comparably in terms of safety, and that further improvements can be achieved with a combination of those strategies.
...
The Metropolis II project aimed to study the impact of centralised separation management for urban aerial mobility. Three concepts were developed in this study: a fully centralised, strategically separated concept, a hybrid concept featuring cen- tralised strategic separation and distributed tactical separation, and a fully distributed tactical concept. A comparative simu- lation study was performed, using traffic scenarios based on predicted demand in an urban airspace in the city of Vienna. Simulations were performed with varying traffic densities and situations. Results show that the purely strategic and purely tactical strategies perform comparably in terms of safety, and that further improvements can be achieved with a combination of those strategies.
Conference paper
(2021)
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C. Badea, A. Morfin Veytia, M.J. Ribeiro, M.M. Doole, J. Ellerbroek, J.M. Hoekstra
Road traffic delay and urban overcrowding are increasing rapidly all over the world. As a result, several companies have proposed the use of small unmanned aerial vehicles (sUAVs) as an alternative to road-based transportation. These small autonomous drones are expected to operate within a thin airspace band (Very Low Level) in high traffic densities in constrained urban environments. This presents a challenge for ensuring the safe separation and efficient routing of drone flights. Current research has made modest progress towards finding solutions for conflict detection and prevention in highly dense and constrained environments (e.g., in-between buildings). In this paper, the state of the art of urban airspace design and conflict prevention and resolution research are discussed, and their applications to constrained environments. Additionally, fasttime high-fidelity simulations of high-density traffic scenarios are used along a non-orthogonal city layout to identify bottlenecks in the performance of speed-based conflict resolution in a multilayered airspace structure. Results show that the current airspace structure and conflict detection and resolution concepts need to be refined to further reduce conflicts and intrusions that occur in constrained environments. First, additional measures must be adapted to further prevent conflicts during turning and merging. Second, conflict resolution manoeuvres must account for speed limits resulting in turn radii which do not cross physical boundaries. Finally, conflict detection needs to consider the topology of the streets to prevent false-positive conflicts and to prepare in advance for conflicts resulting from heading changes in non-linear streets.
...
Road traffic delay and urban overcrowding are increasing rapidly all over the world. As a result, several companies have proposed the use of small unmanned aerial vehicles (sUAVs) as an alternative to road-based transportation. These small autonomous drones are expected to operate within a thin airspace band (Very Low Level) in high traffic densities in constrained urban environments. This presents a challenge for ensuring the safe separation and efficient routing of drone flights. Current research has made modest progress towards finding solutions for conflict detection and prevention in highly dense and constrained environments (e.g., in-between buildings). In this paper, the state of the art of urban airspace design and conflict prevention and resolution research are discussed, and their applications to constrained environments. Additionally, fasttime high-fidelity simulations of high-density traffic scenarios are used along a non-orthogonal city layout to identify bottlenecks in the performance of speed-based conflict resolution in a multilayered airspace structure. Results show that the current airspace structure and conflict detection and resolution concepts need to be refined to further reduce conflicts and intrusions that occur in constrained environments. First, additional measures must be adapted to further prevent conflicts during turning and merging. Second, conflict resolution manoeuvres must account for speed limits resulting in turn radii which do not cross physical boundaries. Finally, conflict detection needs to consider the topology of the streets to prevent false-positive conflicts and to prepare in advance for conflicts resulting from heading changes in non-linear streets.