REAL-TIME AUTONOMOUS TRAJECTORY CONFLICT DETECTION AND RESOLUTION IN RESTRICTED AIRSPACE

Yutong Chen, Lei Yang, Haoran Zhang, Zheng Zhao, Minghua Hu, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China

AbstractAiming at achieving the autonomous Air

Traffic Management (ATM) in the Trajectory-Based Operation (TBO) context, a two-stage real-time autonomous four-dimensional trajectory conflict detection and resolution method in restricted Free Route Airspace (FRA) supporting the synchronized air-ground situational awareness was proposed. Cellular concept was used for airspace discretization to balance the accuracy and computation cost. At stage one, the desired trajectory for each upcoming flight is generated by searching a path in a network constructed based on the entry and exit point, as well as boundary points of each restricted area inside the airspace. At stage two, in order to avoid conflict during travelling, the Space-Time Prism model, which is capable of visualizing the conflict situation for both controllers and pilots, is introduced to generate the feasible conflict-free trajectories while keeping the Controlled Time of Arrival (CTA) in mind. A case study based on a typical en route sector in Western China was carried out to test the effectiveness of the proposed method. In the end, sensitivity of cell size was investigated in terms of computational cost and operational efficiency. Results showed that the proposed autonomous trajectory planning would be a promising solution for future autonomous ATM system.

1. IntroductionIn order to satisfy the increasing demand of air

traffic and to meet the diverse expectations of stakeholders for safety, efficiency, economy and pro-environment, the concepts of Trajectory-Based Operation (TBO) and Free Route Airspace (FRA)

have been put forward and preliminarily applied [1, 2]. Meanwhile, the improved performance of satellite-based navigation and surveillance, as well as 4D-Flight Management System (4D-FMS) capabilities, enhance the flexibility of flight trajectory and the situation awareness for both controllers and pilots [3]. To keep controllers from becoming a bottleneck of high-density operation [4] ， especially in unstructured and partially-restricted airspace in TBO context, where the spatiotemporal randomness of conflicts will likely lead to unexpected high workload for controllers and operational risk [5], it is essential to establish a novel autonomous trajectory Conflict Detection and Resolution (CD&R) technology [6].

Studies on autonomous 4D trajectory (4DT) planning at tactical level in TBO context were initially started [7], the significant research effort has been put on autonomous Air traffic Management (ATM) technology, named “Free Flight”, which can effectively reduce fuel consumption and travel time, and can reduce airspace congestions [8]. Although the Free Flight concept [9, 10] of operations was developed regardless of the TBO, its research achievements would still provide basic referable technical outlines for Trajectory-Based Autonomous ATM (TBA-ATM) and have great adaptable potentials to develop TBA-ATM operational technologies. One of the critical issues that widely discussed in Free Flight was the Control Mode: Centralized and Distributed.

The advantage of centralized control is that it can make full use of global information to obtain the optimal solution [11], while its disadvantage is the high computational cost. Therefore, centralized

control is often used in the pre-tactical phase. A direct method composed of multiple shooting discretization and a Sequential Quadratic Programming (SQP) method was used to solve the problem of conflict resolution based on nonlinear optimization [12]. A space-discretized mixed-integer linear model for air-conflict resolution with speed and heading maneuver was proved to solve complex situations without incurring more than a few kilograms of extra fuel consumption per aircraft [13]. A two-step approach using pre-tactical conflict resolution in FRA is applied to minimize the airborne delay. The mathematical model of the first step presents alternative entry points on both sides of existing sector entry points to minimize delays by directing aircraft to the most convenient entry points. The second step suggests a vector deflection maneuver to minimize extra fuel consumption caused by conflict resolution [14].

Contrary to the centralized control, the advantage of distributed control is that the calculation cost is low, but the disadvantage is that it cannot guarantee an optimal solution. Therefore, distributed control is often used in the tactical phase. The so-called Distributed ATM means that much of the current ATC functionality will be moved onboard of each aircraft. Hybrid systems were used to generate conflict resolution strategies between aircraft, and in-flight mode switching logic [15]. The widespread application of artificial intelligence technology has greatly promoted the development of distributed ATM [16]. The degree of congestion of airspace suitable for distributed control has gradually become a concern of scholars [17]. A mixed-integer linear optimization approach for collision avoidance in ATM is considered useful for real-time scenarios due to its fast calculation speed [18]. A strategic de-confliction algorithm based on a causal model was designed to enable the processing of thousands of trajectories within a few seconds or minutes and encompass a global network scope with a planning horizon of approximately 2–3 h [19]. An adaptive and automated decision-engine is designed for

improving autonomous systems' inherent resilience in uncertain worlds and the D* Lite algorithm was used in it [20].

Academic researches on the free-flight problem in recent 20 years provided a promising direction evolving towards autonomous ATM. Nevertheless, the ATM system, especially the ATC activities are still in the so-called “Human-Centric” mode. The real-world practice of free-flight has not been carried out even in low-density airspace sector. In order to facilitate the progress of autonomous ATM development, some key issues about Human-Machine Collaboration (HMC) shall be concerned in system design [21]: (1) operations must be safely taken over by human in any circumstances; (2) the mechanism of the machine shall be transparent and understandable; (3) the cognition of human and machine needs to be strongly synchronized; (4) the level of automation can be dynamically customized; (5) the most important one is to adapt the management philosophy on both human and technology side. In view of this, in this paper, we proposed a two-stage real-time autonomous 4DT CD&R in restricted FRA with the help of geometry model to increase the decision transparency between controllers, pilots and automations.

The remainder of the paper is organized as follows: Section 2 introduces the airspace discretization concept based on cellular to improve the efficiency of the computation. In section 3, a method of autonomous planning of desired trajectory [22] for avoiding multiple restricted areas is proposed, using a Visibility Graph (V-Graphic) theory and Dijkstra algorithm. In section 4, we establish a real-time autonomous 4DT CD&R model based on a “Later-Entry-First-Adjust” (LEFA) principle, through geometric visualization based on Space-Time Prism (STP) to enhance cross-level situation awareness sharing in tactical ATC operation. In section 5, an en-route sector in western China is adopted to validate the feasibility and effectiveness of the proposed method through

fast-time simulation. The conclusions and future work are stated in Section 6.

2. Airspace discretization based on cellular

The FRA is a novel type of airspace within which users shall freely plan their routes between an entry point and an exit point without reference to the ATS route network. This operational concept was proposed by EUROCONTROL and is being gradually applied in practice to improve air traffic operation efficiency, cost-effectiveness, etc. This research adapts the current FRA concept as the basic operating environment.

In the TBO context, aircraft need to fly adhere to the Controlled Time of Arrival (CTA) at critical waypoints. Therefore, when a flight encounters conflict, the automated system needs to search for a reroute point and corresponding speed to minimize the deviation of the CTA constraints at the exit/entry point of a sector. However, it is time-consuming to achieve precise optimal reroute point in continuous space, while searching for discrete points in space seems to be a matter of course. The way we discrete airspace is to divide the airspace into a set of neatly arranged cells. Considering the time limitation for real-time decision-making, we have to make a trade-off between accuracy and calculation time. The key parameter is the cell size determined by objective factors, such as navigation and positioning accuracy, aircraft performance, and airspace size, etc. Obviously, the cell size is directly proportional to the problem-solving speed and inversely proportional to the calculation accuracy. In addition, another advantage of cellular-based airspace discretization is that the cell can easily represent the status of different areas in the airspace. The horizontal plane of the airspace is mapped to neatly arranged square cells, as shown in Figure 1.

Figure 1. Cellular-based Airspace Discretization

Cells are divided based on the X(longitude)-Y(latitude) axis. We name the cell with coordinates

as , and other cells are denoted similarly. Two types of cells are defined according to the availability state of the area in the airspace, namely, Available Cells (AC) and Restricted Cells (RC) due to hazardous weather, military activities, etc. Please noted that, for safety concern, if and only if the airspace in a cell is all available, like the

, it is labelled as an available cell. On the contrary, it would be identified as a restricted cell,

see and .

For each cell, it has 5 main positional points, they are centre point, northwest point, northeast point, southwest point and southeast point, respectively (see Figure 2).

Figure 2. Main Positional Points of a Cell

Assuming that the length of the side of each

cell is and the origin of coordinates is ,

then the actual coordinates of the five main position

points of the cell whose cell coordinate is can be expressed as:

(1)

where , , , and represent the actual coordinates of the center point, northwest point, northeast point, southwest point and southeast point, respectively.

Cellular-based airspace discretization has three main functions. Firstly, the classification of cells is used to restrict the aircraft to flying only in the available cells, thus ensuring that the aircraft does not accidentally enter the restricted area and cause danger. Secondly, when the aircraft is planning the desired trajectory, the boundary cells of the restricted area are used to determine alternative trajectory points, i.e., waypoints. Last but not least, all trajectory points are located at the center of the cells, which is the core rule of the autonomous operation paradigm described in this article.

3. Autonomous planning of the desired trajectory for avoiding multiple restricted areas

During operation, hazardous weather and military activities are often inevitable, which could lead to significant capacity drop and flight delay. To make matters more difficult, the status of these restricted areas is often temporary and dynamic. Therefore, it is essential to update the desired trajectory for each aircraft before entering the sector. It is noted that it is time-consuming and less effective to achieve global optimization of conflict-free trajectories for all upcoming aircraft while avoiding the restricted area in some abnormal situation. In view of this, we propose a network-

based shortest trajectory re-planning algorithm respecting to the individual economic speed, regardless of uncertain potential conflict when travelling inside. This is the first stage of the proposed two-stage method, named the modification stage, when agreed trajectories [22]are going to be translated to desired trajectories.

The autonomous trajectory planning functional relies on the air-ground integration of airspace situation, especially the location and geometric model of restricted areas. Based on the airspace information, aircraft performance and pilot’s individual preference, a shortest path together with desired speed will be efficiently planned subject to the restrictions of the restricted area. For simplification, here we assume that all pilots have the strongest intent to fly at the economic speed.

Therefore, we introduced a path planning method called "Visibility Graphs", which was first proposed by Lozano-Perez and Wesley [23]. Using visibility graphs for determining the shortest path was proved to be highly practical and intuitive. The visibility graph of a set of nonintersecting polygonal obstacles in the plane is an undirected graph whose vertices are the vertices of the obstacles and whose edges are pairs of vertices such that the open line segment between every two vertices does not intersect any of the obstacles [24].

Figure 3. Visibility Graphs

When we are planning for a desired trajectory before entering airspace, we need to generate a VG based on the restricted areas (see Figure 3). We use

to represent this graph where is the set of vertexes, is the set of edges and is the corresponding relations between vertexes and edges. According to VG theory and the characteristics of cell discretization, we let

(2)

(3)

(4)

where is the vertex, is the coordination of

centre of vertex , is the set of cells of

the restricted area , and are the coordinates of the aircraft’s entry point and exit point respectively.

(5)

(6)

where is edge and is the connection between

vertex and . The edges of the graph are non-directional and the weights of the edges in the graph depend on the optimization parameter(s). Here we take the shortest distance as the optimization goal, so we use the length of the edge as the weight. At this point, a non-directional and weighted graph is generated.

Then, based on the graph, we use Dijkstra algorithm [25](Dijkstra, 1959) to search the shortest

path. The agreed trajectory of the aircraft is straight and the rerouting will definitely generate extra flight distance, which will cause delay. However, we assume that the pilots prefer to fly at the economic speed rather than accelerating to absorb delay due to not only the priority of economic effects but also trajectory flexibility reservation for future real-time conflict resolution.

Through the VG theory and Dijkstra algorithm, the updated desired trajectory for each aircraft is then achieved. This will help aircraft to focus more on CD&R between aircraft when flying in airspace, thereby improving real-time operation efficiency.

4.Real-time autonomous 4DT CD&R model based on STP

After entering the airspace, the aircraft would fly along the desired trajectories. Although the initial agreed trajectories of the aircraft are conflict-free [26], it is inevitable that the aircraft with the updated desired trajectories modified due to restricted area, will encounter conflict during operation. This is the second stage of the proposed two-stage method, named the real-time operation stage, where desired trajectories are going to be translated to the executed trajectories [22]

4.1 Position update

For effective CD&R, we discretize time as the time interval, that is, the aircraft movement information is updated every time (see Figure 4).

Figure 4. Update of Aircraft’s Real-time Position

For example, An aircraft flies along the desired trajectory. There are three waypoints on the

trajectory, , , .Their actual

coordinates are , , and

their CTA are , , . The three aircraft positions in the figure represent the actual positions

of the aircraft at three moments, , and ,

respectively. Among them, represents the time when the collision detection is performed for the -th time. Because the time interval is ,we can get:

(7)We assume that the actual position coordinates

of the aircraft at the three moments , and

are , and .This is intended to represent two cases. The first case is that the aircraft is still in the same flight segment

after a position update, such as from to .In this case, we can get:

(8)

That is, the actual coordinates of can be expressed as:

(9)If we use continuous flight dynamics model to

calculate the real-time positions of the aircraft in this situation, supposing the aircraft is moving in a straight line at a constant speed, we can get:

(10)

and are the x-coordinate and y-coordinate of the actual position of the aircraft at

time , respectively. Therefore, the real-time position of the aircraft can be expressed as:

where is the coordinate of the actual position

of the aircraft at time .

The second case is that the aircraft is in the different flight segment after a position update, such

as from to .In this case, we can get:

(12)

That is, the actual coordinates of can be expressed as:

(13)Similarly, if we use continuous flight dynamics

model to calculate the real-time positions of the aircraft in this situation, supposing the aircraft is moving in a straight line at a constant speed, we can get:

(14)

where and are the x-coordinate and y-coordinate of the actual position of the aircraft at

time , respectively. Therefore, the real-time position of the aircraft can be expressed as:

(15)

where is the coordinate of the actual position

of the aircraft at the time .

4.2 Conflict detectionBased on the position updating, a local conflict

detection method is proposed. This means that we will not conduct a global conflict detection, but instead of focusing on detecting potential conflicts

within a certain distance. Here we define to represent the circular conflict detection zone of aircraft (see Figure 5).

Figure 5. Local Conflict Detection

Detecting aircraft means the one who is proactively performing conflict detection. As demonstrated in the Figure 5, the aircraft inside the detection range are called detected aircraft, while

the outside ones are undetected aircraft. Only potential conflict between detecting and detected aircraft are considered. The advantage of using the Local Detection is that it can effectively save computing resources to increase the calculation speed, which is critical for safety and efficiency concern in autonomous trajectory operation.

Here, we define the horizontal separation minimum . Apparently, if and only if the minimum lateral distance between any two aircraft during flight would be less than at some time, potential conflicts are detected.

As stated in section 4.1, it is clear that there would be two possible situations for aircraft position updating, that is, whether it is still in the same flight segment or not. Therefore, for the relative positions of any two aircraft, there are different situations, as shown in Figure 6.

Figure 6. 4 Relative Positional Relationship

Without loss of generality, we only describe the pairwise conflict detection in most complex case (see Figure 6, No.4) for simplification. In this

case, aircraft and are detecting and detected

aircraft, respectively. , , are the 3 waypoints along the updated desired trajectory of

aircraft . Their actual coordinates are ,

and , respectively, and their

CTA are , , . The parameters of aircraft n are denoted similarly. The position coordinates of

aircraft and n at time and are ,

, and , respectively. Therefore, the real-time coordinates of aircraft and can be expressed as:

(16)

(17)

and are the coordinate of the actual position of the aircraft and at time

, respectively. From this, we can see that because the aircraft moves in a straight line at a constant speed in each flight segment, the position of the aircraft changes linearly with time.

Then, the distance between aircraft and at time can be expressed as:

(18)Because the positions of both aircraft change

linearly with time, the square of the distance between them is a piecewise function and each part is a quadratic function. We can represent the -th part as

(19)

where, , and are constant and .Also

because , the minimum values of and

are with the same . So, the minimum value

of can be expressed as:

(20)Then, it is easy to get the minimum of the

distance, that is,

When a conflict is detected, the aircraft's trajectory needs to be adjusted. To simplify the problem, trajectory adjustment sequence follows the principle of “Later-Entry-First-Adjust” (LEFA). LEFA means that the aircraft who enters into the airspace later needs to modify its trajectory to avoid conflict. This rule would be acceptable because it is equivalent to the First-Come-First-Served (FCFS) principle, which means the aircraft entering airspace first has higher priority to retain its current trajectory.

4.3 Conflict resolution based on STPIn order to achieve human-machine situational

awareness synchronization, we introduced the STP [27]. Through the STP model, based on CTA, we can deduce that the potential rerouting area of the aircraft within a specific ellipse which is the projected shape of the prism [28].

Figure 7. Space-Time Prism

In the TBO, the aircraft needs to meet the CTA of each waypoint (see Figure 8).

Figure 8. STP-based Rerouting Optimization

We assume that, at time , the coordinates of

the aircraft’s current position are , the

coordinates of the aircraft’s -th waypoint and

its CTA are and , the coordinates of a

potential rerouting waypoint are where and are the waypoint’s cell coordinates, and

the maximum speed of the aircraft is . According to the requirements of CTA, we can get the following constraint,

(21)

where , that is,

(22)When the left side is equal to the right side, all

eligible make up an ellipse, that is,

(23)where

(24)Therefore, any point in the ellipse is a potential

rerouting waypoint for the aircraft unless it is in a restricted area simultaneously. Due to the idea of discretization of our cells, we only consider whether the center point of each cell is within this ellipse and if it is within this ellipse, we list it as a potential rerouting waypoint for further screening, that is,

(25)

(26)Due to the limitations of aircraft flight

performance, these potential rerouting waypoints also need to meet the turning angle restriction, assuming it is , that is,

(27)Then, the potential rerouting trajectory should

be conflict-free with restricted areas, that is,

(28)Moreover, local detection methods will be

applied again, to judge the feasibility of the potential rerouting trajectory, that is,

(29)

where is the minimum distance of this aircraft and other aircraft which is in the range of

detection, if this aircraft execute the potential

rerouting waypoint of .

Among all potential rerouting waypoints that meet the restrictions, according to user preferences, the optimal point is selected as the actual rerouting waypoints. For example, we take the minimum flight distance as the optimization goal and the optimization model is as follows:

(30)

where is the minimum flight distance when

the is the rerouting waypoint.

When all potential rerouting waypoints do not meet the restrictions, the aircraft will decelerate to expand the solution space for searching conflict-free rerouting points (see Figure 9) due to that lower speed results in larger and b.

The overall logic of conflict detection and resolution is shown in Figure 10. Conflict-free trajectories are autonomously generated with the help of the STP visualization, which can be displayed on the ground and cockpit human-machine interface to enhance the situation awareness and decision transparency between controllers and pilots seamlessly, especially in emergency situations.

Figure 9. Expanding Solution Space by Adjusting the CTA at the Next Waypoint

Figure 10. CD&R Flow Chart

5.Numerical study

5.1 Scenario setupIn this case study, we select the Lanzhou No.7

en route sector (ZLLL07) as an instance, which is representative in size and route structure among en route airspace in western China. To validate our proposed autonomous trajectory planning techniques, the highest-density flight level (FL310) operation is investigated. We first transform the latitude and longitude coordinates of boundary points into plane coordinates using the Miller cylindrical projection method [29], as shown in Figure 11. This sector has one entry point and one exit point in each direction.

Based on the concept of TBO, we randomly generate 100 Boeing 737 aircraft with conflict-free agreed trajectories. Due to restricted areas (1 military activity area and 2 hazardous weather areas) that are unexpected in the sector, which block 54% of the agreed trajectories, desired trajectories shall be generated before entry. According to the real-world operation rules, we set the minimum horizontal safety separation as 10 kilometres, which equals to the side length of discrete cells, see Figure 11.

Figure 11. Agreed Trajectories

According to the performance parameters of the Boeing 737 provided by BADA, the economic and maximum speed of simulated aircraft is set as 828 km/h and 876 km/h, respectively. To avoid aggressive maneuvering, the turning angle shall not

larger than 90 degrees. The CD&R of each aircraft is triggered autonomously every 10 seconds after entering into the sector.

5.2 Validation resultsBased on the simulation scenario and

fundamental parameters, desired trajectories together with new CTAs were generated to avoid restricted areas remaining at the economic speed, as shown in Figure 12. During the autonomous flight in the sector, 42 aircraft were involved in potential conflict while conflicts resolution actions were taken for 33 times (40% of the 42 aircraft experienced more than 1 potential conflict). The planar and temporal-spatial conflict-free executed trajectories are demonstrated in Figure 13 and 14, respectively. According to the constrains in trajectory-based CD&R, aircraft accelerated to meet the CTA requirements as much as possible when extending flight distance. However, if the flight was not able to catch the CTA at its maximum speed, the arrival time at the waypoint will be delayed.

Figure 12. Desired Trajectories

Figure 13. Executed Trajectories (planar)

Figure 14. Executed Trajectories (temporal-spatial)

Figure 15. Frequency of Conflicts and Instantaneous Traffic Volume

Specifically, Figure 15 shows the frequency of conflicts and instantaneous traffic volume in the sector evolving with time during simulation every 10 seconds, where the desired and executed traffic is slightly higher than agreed due to time delay for avoiding restricted areas and flight conflicts. In execution, the stably busy state of traffic volume was around 20 with the maximum number of 23. Most of the conflicts occurred when there were more than 15 aircraft. Obviously, the increasing number of aircraft would still be one of the significant factors leading to potential conflicts in autonomous operation.

Figure 16. Extra Flight Time Distribution (value)

Figure 17. Extra Flight Time Distribution (accumulation)

Figure 18. Extra Flight Distance Distribution (value)

Figure 19. Extra Flight Distance Distribution (accumulation)

Table 1. Data Analysis

TypeAverage Value

(all)

Number of

Affected

Aircraft

Standard

Deviation (all)

Standard

Deviation

(affected)

L1T 10.84 s 54 12.93 s 11.14 sL2T 9.8 s 16 28.32 s 43.14 sTT 20.64 s 60 31.79 s 34.8 s

L1D 2.49 km 54 2.97 km 2.56 kmL2D 2.09 km 27 5.35 km 7.88 kmTD 4.58 km 60 6.75 km 7.26 km

As we stated above, constrained by speed performance, the extra flight time and distance were inevitable in a complex operation. Figure 16 and Figure 17 show the extra flight time distribution, Figure 18 and Figure 19 show the extra flight distance distribution, and Table 1 shows its statistical data during the simulation. In order to facilitate the discussion, we define the following parameters:

(31)where the related description of the parameters is shown in Table 2.

Table 2. Parameter Description

Parameter DefinitionLevel 1 extra flight timeLevel 2 extra flight timeTotal extra flight timeFlight time of agreed trajectory

Flight time of desired trajectoryFlight time of executed trajectoryLevel 1 extra flight distanceLevel 2 extra flight distanceTotal extra flight distanceFlight distance of agreed trajectory

Flight distance of desired trajectoryFlight distance of executed trajectory

It should be noted that affected aircraft means the aircraft with corresponding non-zero parameters. For example, since there are 54 aircraft with L1T, number of affected aircraft are 54 for L1T.

For the affected aircraft, more than 60% of aircraft with L2T experienced L1T. Obviously, conflicts between aircraft are induced by restricted areas. On the other hand, that means less than 20% of aircraft with L1T experienced L2T. There are probably 2 reasons for this. One is, in operation, aircraft will accelerate to meet the CTA requirements as much as possible when extending flight distance. More than 40% of aircraft with L2D avoid L2T through accelerating. The other may prove the effectiveness of the method in the modification stage in the opposite direction, that is

modification stage could not only avoid restricted areas in advance, but also not causing too many unavoidable delays. In addition, it is a coincidence that the number of affected aircraft with TT is same as that with TD. The number of affected aircraft with L1T and L1D is the same, simply because the speeds of agreed and desired trajectories are the same.

In terms of standard deviations, the impact of the aircraft during the modifying stage is much more average than the real-time operational stage. This is because the path of agreed trajectory is specific (12 kinds), and the path of desired trajectory corresponds to that of agreed trajectory. However, the higher value and more significant fluctuation of CTA delay are resulted in conflict resolution due to complex airspace situation and relatively narrow speed space between the economic and maximum speed of aircraft. That means the intermedium reroute points were hardly achieved inside the solution space area. It implies that it might be promising to appropriately assign CTA delay to aircraft by reducing speed in the presence of airspace restrictions, based on the trajectory robustness assessment using the feasible cell space.

Figure 20. Calculating Time for Trajectory Modifications

Figure 21. Calculating Time for Real-time Conflict Resolution

Besides the above effectiveness validation, the computational cost is also one of the critical metrics to measure the efficiency and practicability of the proposed algorithm. Figure 20 and Figure 21 show the calculation time of trajectory modifications and real-time conflict resolution, respectively, using python3.8 based on the computer configuration of Intel(R) Core(TM) i7-10510U, CPU @1.80GHz 2.30GHz and the operating system 64x. In trajectory modification, the average calculation time is 0.61s with the standard deviation of 0.00758s. In real-time operation, the average calculation time is 0.90s for CD&R. Although the distribution of real-time CD&R computational cost is more scattered (the standard deviation is 1.06s), statistically, the calculation time of conflict resolution has no significant relationship with the instantaneous traffic volume in the sector. However, from the perspective of the optimization algorithm, calculation time is more sensitive to the size of the solution space area when the aircraft encounters a potential conflict. The larger the solution space area is, the more computational resource will be needed to generate the optimal reroute point.

5.3 Sensitive analysis of cell sizeAirspace discretization into cells is an initial

but critical step to achieve proposed autonomous tactical 4D trajectory operation in a global cognition-sharing paradigm. As aforementioned,

cell size could be reduced by increasing the performance of navigation and positioning system. In this section, a sensitivity analysis experiment was carried out to investigate the relationship between cell size and operational performance in terms of L2T, L2D and computational cost, as shown in Figure 22 and Figure 23. We obtained relevant data when the cell size was 0.625km, 1.25km, 2.5km, 5km and 10km through simulation experiments. It shall be noted that the agreed trajectories, desired reference trajectories, airspace, restricted areas and other parameters were not changed.

The results show that as the cell size changes, the overall trends of the L2T and L2D are generally the same. The operation efficiency starts converging at 2.5km, which means when the cell size is greater than 2.5 km, the L2T and L2D increase significantly as the cell becomes larger. This is because the precision of trajectory optimization is reduced since the rerouting point is allocated in the centre of the cell, which imposes a negative effect on operational performance. In addition, as the cell size becomes smaller, the number of conflicts tends to decrease. Obviously, improving the precision of optimization can promote conflict avoidance.

However, when the cells are too small, the benefits of improved optimization accuracy are partially counteracted by extremely long calculation time (see Figure 23), which ultimately leads to a slight decrease in operational performance. Specifically, when the cell size reduces to 0.625km, the average calculation time is near 2 minutes, which would be unacceptable especially for high-density operation and emergent situations. It implies that an appropriate cell size shall be studied to make tradeoffs between computational cost and operational efficiency.

Figure 22. Cell Size vs Operational Efficiency

Figure 23. Cell Size vs Calculating Time

6.ConclusionsIn this paper, a method of real-time

autonomous trajectory CD&R in restricted airspace was proposed. This method dedicated to solving the problem of air-ground and human-machine situational awareness synchronization in the autonomous ATM operation. To achieve this vision, firstly, the cell-based airspace discretization gives the system the flexibility to choose a balance between control accuracy and computation time. Secondly, through the VG method and the Dijkstra algorithm, the aircraft was able to quickly generate a desired trajectory to avoid restricted areas when it is about to enter the airspace, so that it can focus computing resources on conflicts between aircraft. Finally, the local conflict resolution method is used to reduce the complexity of conflict resolution,

thereby reducing the time for a single conflict detection. Based on the STP theory, the aircraft's feasible rerouting waypoints are calculated within an ellipse, which enables visualization of the trajectory intent.

Case study, which is based on typical airspace in western China, have been carried out to test the effectiveness of the proposed method. The results show that the method can effectively detect and resolve conflicts in airspace with multiple restricted areas. The size of the cells affects not only the calculation time, but also the operating efficiency. With a suitable cell size, the calculation time for both desired trajectory planning and real-time trajectory CD&R is within seconds, which indicates that the method can support the tactical operations.

Possible improvements include considering uncertainty and negotiation mechanisms. Uncertainty must be fully considered in an automated system, which is the only way to improve system reliability and stability. The negotiation mechanism is conducive to building a fairer operating environment and making the operating system more flexible.

AcknowledgementsThis research was supported by the National

Natural Science Foundation of China (Grant No. 61903187), and Natural Science Foundation of Jiangsu Province (Grant No. BK2019041)

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2020 Integrated Communications Navigation and Surveillance (ICNS) Conference

April 21-23, 2020