4D Trajectory Planning of Aircraft Taxiing considering Time and Fuel

Most of the traditional taxi path planning studies assume that the aircraft is in uniform speed, and the model is optimized based on the shortest taxi time. Although it is easy to solve, it does not consider the change of the speed profile when the aircraft turns, and the optimal taxiing time of the aircraft does not necessarily bring the optimal taxiing fuel consumption. In this paper, the aircraft’s taxi distance and the number of turns in the taxi are considered. *e aircraft path planning model with the shortest total distance of the airport surface is established. *e improved A∗ algorithm is used to obtain the shortest path P. Based on this, the shortest path P is established. Considering the multitarget velocity profile model of time and fuel consumption, a heuristic search is used to generate an accurate velocity profile for each path to obtain a 4D trajectory of the aircraft and then quantitative analysis of the impact of aircraft pollutant emissions on the airport environment based on 4D trajectory taxi time.*e experimental results show that, compared with the traditional optimization method without considering the turning times, the total taxiing distance and turning times of the aircraft are greatly reduced. By balancing the taxiing time and fuel consumption, a set of Pareto-optimal velocity profiles is generated for the aircraft taxiing path; at the same time, it will help the airport save energy and reduce emissions and improve the quality of the airport environment. It has a high practical application value and is expected to be applied in the real-time air traffic control decision of aircraft surface in the future.


Introduction
With the rapid development of the air transport industry, the flight volume of major airports in China is increasing, which makes the airport surface congested, especially causing the aircraft at the airport surface to take too long to taxi, and the runway entrances are queuing up to wait for the number of departing flights, resulting in the work of controllers being overloaded, which seriously threatens the taxiing safety of the aircraft. Due to the conflict or crowded waiting of aircraft at the airport surface, each additional 1 min of taxi time will increase the fuel consumption by 10-20 kg [1,2], resulting in an increase in aircraft exhaust emissions and affecting the quality of air around the airport. For the sustainable development of air transportation, scientific and efficient taxi path planning methods are adopted, which can not only reduce the taxi time and fuel consumption of aircraft at the airport surface but also ensure the reliability and safety of actual airport operations and improve the safety and security of scene operations.
Many scholars at home and abroad have studied the taxiing path and 4D trajectory prediction of aircraft at the airport surface and have obtained a series of research results. In 2014, Ravizza et al. [3] and other researchers studied the path planning of aircraft at the airport surface considering time and fuel consumption and introduced a sequence diagram-based algorithm to solve the problem. In 2015, Weiszer et al. [4] proposed an aircraft at the airport surface motion database for the high calculation time requirements of existing speed configuration optimization methods and effectively separated path planning (routing and scheduling) and speed profile generation modules through precalculation to avoid the same repeated optimization of taxiway sections. In 2015, Weiszer et al. [5] used a multiobjective optimization method to solve the comprehensive optimization problem combining runway scheduling and ground motion problems. e proposed evolutionary algorithm is based on an improved congestion distance, taking into account delay costs and fuel prices. In 2016, Li and Lu [6] used support vector machines to perform position classification and trajectory determination of scene taxiing aircraft and applied data mining technology to predict scene aircraft taxiing time, determine scene taxiing hotspots, and determine conflict areas of the study. In 2016, Chen et al. [7] and others proposed the concept of active routing, combining 4D trajectory and routing scheduling into a multiobjective optimization problem and finally generating a more environment-friendly and cost-effective 4D trajectory. In 2017, Stewart et al. [8] considered that the routes and timetables generated by taxi time prediction may not be flexible, based on multiobjective fuzzy rules, and quantified the routes and time generated by taxi time prediction based on historical aircraft taxi data table uncertainty. In 2017, Wang et al. [9], based on the aircraft's taxiing motion model, discretized the taxiing speed and adopted a multitarget immune optimization method to study the specific relationship between taxiing speed and fuel consumption when an aircraft is launched using a fixed path relationship. In 2018, Zhang et al. [10] proposed an online velocity profile generation method, which simplified the nonlinear optimization model into three easy-to-handle composition problems and further optimized the feasible velocity curve to produce an improved high fuel efficiency velocity profile. In 2019, Zhu et al. [11] and others considered the aircraft taxi time and the number of large turns during taxiing to establish an aircraft at the airport surface taxi path optimization model with the shortest total taxi time as the goal. e genetic algorithm was used to solve the model.
It can be seen from the research situation at home and abroad that the taxi planning problem has achieved fruitful results in both theoretical research and practical application. However, most of the current studies assume that the aircraft is modeled based on the shortest taxi time under uniform taxi conditions, without considering the actual situation. Due to the turning section of the airport surface, the aircraft's speed profile changed, resulting in additional taxi time. Although precise algorithms such as multiobjective optimization take full consideration of various scene constraints, such algorithm models are complex and computationally intensive, and it is generally difficult to obtain the optimal solution in an acceptable time. erefore, this article comprehensively considers the aircraft's taxiing distance and the number of turns during taxiing and plans the shortest path for the aircraft taxiing on the scene. Based on this, a multitarget speed profile model is established to weigh the time and fuel consumption during taxiing. Each path generates a more accurate speed profile that takes into account time and fuel efficiency, obtaining a scene aircraft taxiing 4D trajectory. e concept of maximum theoretical speed is added to the heuristic search process, which further simplifies the calculation amount. Compared with other complicated algorithms that consider multiple factors, the calculation speed is faster, from an environmental perspective, and considering the taxi time and thrust changes of the 4D trajectory and the comparison and calculation of the pollutant emissions when the ground aircraft adopts a multitarget speed profile, the accurate multitarget taxi 4D trajectory is more conducive to energy saving and emission reduction has a higher practical application value.

Airport Surface Structure Modeling.
e optimization object studied in this paper is the flight area where the aircraft runs on the ground, which mainly includes the runway, taxiway, and apron system in scene resources. On the roads of the airport surface, there are various types of intersections, and various types of intersections are composed of straight and curved roads interwoven to varying degrees. erefore, the network structure of the airport surface is redefined to simplify the representation of the connection relationship in the scene network structure. Taking Xi'an Xianyang International Airport as an example, the simplified diagram of the simplified airport surface structure is as shown in Figure 1.
After simplifying the structure of the airport surface, the network connection relationship of the airport surface system can be clearly and intuitively understood. But it is not applicable to the design and solution processing of path planning algorithms. To this end, the scene structure is represented abstractly as G � (V, E) in the form of an undirected graph, where V represents the set of nodes in the taxiway system, which is composed of the intersections between taxiways, the intersections between taxiways and runways, parking spots, two ends of the runway, and so forth; E represents the set of edges connecting various nodes in the taxiway system and is composed of taxiway sections between adjacent nodes in the taxiway system.
In this paper, the adjacency matrix is used to represent the connection relationship between nodes and the directed graph model is transformed into a matrix representation. Suppose that there are m nodes in the airport surface structure diagram, which are represented by a matrix C of m * m, and define the element C ij of the matrix: 1, there is an edge from node i to node j, 0, there is an edge from node i to node j.
In the path planning, the nodes of the scene road network and the taxiway sections must consider their attributes, and the attributes of the scene road network are defined according to the following requirements of E-R relationship model: (1) Road network (node number and path number) (2) Path node (node number, x-coordinate, and y-coordinate); directional segment of the path (path number, start point, end point, distance, taxiway to which it belongs, wingspan restriction, running direction, and disable or fault) When planning a route, the aircraft must consider its attributes. e attributes of the aircraft identification are as follows: (1) Aircraft call sign (2) Aircraft type . . , f n , the system generates P preselected paths for it, and its z-th preselected taxi pathL kz (1 ≤ k ≤ n, 1 ≤ z ≤ p) is composed of a set of ordered nodes N 1 , N 2 , . . . , N q . ere are M nodes in the airport network model. ere are q ≤ M, N i , N j , N r ∈ V, (N i , N j )∈∈E, i � 1, 2, . . . , q, j � 1, 2, . . . , q. e variables used are as follows.
x ij � 1, indicating that aircraft k passes through node N i of the taxiway and then taxies straight to node N j ; otherwise x ij � 0; d ij is the length of the straight taxiway road section (N i , N j ) in the taxiway system; t ij is the taxi time of the aircraft on the straight taxiway (N i , N j ); R r � 1, indicating that the aircraft k turns when passing through the taxiway node N r ; otherwise R r � 0; d r is the turning length of the aircraft k at the node N r during taxiing of the scene; t r is the turning and taxiing time of the aircraft at the node N r . en the total taxi distance D of the aircraft can be obtained by the following formula: (2) m i�1 m j�1 x ij d ij is the taxi distance of the aircraft on each straight taxi section, where x ij is based on whether the edge (N i , N j ) is the taxiing path of aircraft k, and x ij takes the value of 1 or 0. m i�1 R r d r is the turning distance of the aircraft at each node that needs to turn, where R i is 1 or 0 according to whether the node N r is the turning point of aircraft k. d r can be expressed as According to [11], the cosine theorem is used to solve the aircraft steering angle. e taxiing process of the aircraft during the turn is as follows.
As shown in Figure 2, because the scene topology diagram is simplified, the scene aircraft k initially taxies at node N u and then continuously taxies through the two nodes N g and N w . In reality, the aircraft has a turn length at point N g , and the aircraft started to taxi at point N u and started to turn from point N r . After the turn at point N f , it continued to taxi to N w . en the taxi distance of this road section is actually the sum of the straight line length d ur , the turning length d r , and the straight line length d fw .

Solving Path Planning Models.
e aircraft path taxiing path planning model established in this paper has many variables, some equations are nonlinear, and traditional algorithms are difficult to solve, such as integer programming. In order to solve this problem, the Bellman-Ford algorithm and the A * algorithm are combined to solve the model. e model solving algorithm designed in the paper is as follows.
In this paper, the goal is to find the path with the shortest taxiing distance of P aircrafts; let g (n) be the taxiing distance from the start of the path to the current node n, and h (n) represents the shortest slip distance from the current node to the target node. en f (n) represents the total slip distance of the aircraft from the start node of the path to the target node. Among them, h (n) is executed before the algorithm is executed and preprocessed: all road sections of the airport T5   T10   T20   B7  B6   B6   B5   T5   B5  B4  B7   A5  A4   B3   B3   A3   B2   A2   T1   T1   T3   T4  T4   T2   T3 Figure 1: Xi'an Xianyang Airport structure simplified diagram.

Mathematical Problems in Engineering 3
are reversed, and the Bellman-Ford algorithm is executed from the punctuation point as the starting point to find the shortest taxi distance from the target point to all points. e value is H (n) value at this point.

Modeling Taxi Time Profile considering Time and Fuel
Based on the P taxi paths obtained from the shortest path planning, the purpose of multiobjective speed profile modeling is to generate a set of unobstructed speed curves that satisfy the optimal time and fuel for each path, called the Pareto solution set Y i . erefore, the 4D trajectory of the aircraft at the airport surface taxiing is obtained, as shown in Figure 3.

Discretization of Aircraft Taxi Trajectory.
During the taxiing of an aircraft, its taxiing speed is continuously changing. In order to reduce the computational complexity and calculation time of the algorithm, it is necessary to discretize the taxi speed and taxi trajectory. During the aircraft's taxiing process, the speed curve on each link (N i , N j ) can be subdivided into 4 parts, as shown in Figure 4. e length of each part represents the taxiing distance of the aircraft in different operating phases, and the taxiing speed of the aircraft also changes according to the operating status.
In the first stage, the aircraft performs uniform acceleration motion, the acceleration a 1 is a constant value, and the taxi speed is accelerated from v 0 to v 1 . e value of v 1 depends on the length d 1 of the first stage.
e aircraft maintains a speed v 1 , the duration of which depends on the length d 2 of the second phase.
In the third and fourth stages, the aircraft performs deceleration. e difference between these two stages is that the fourth stage needs to be decelerated from v 3 (the final speed of the third stage of the aircraft) to v 4 in the shortest time at the maximum deceleration rate a 4 � a max . e length of the third stage is In the formula, we have the following: TT ij is the taxi time used by the aircraft on the link t s is the time consumption of each stage of the speed curve, and s � 1, 2, 3, 4 For the complete taxi path L kz of aircraft k, which is composed of multiple links, the objective function g 1 of taxi time can be further expressed as

Aircraft Taxiing Fuel Consumption
Modeling. e discrete aircraft speed profile includes four phases: acceleration, constant speed, braking, and emergency braking. e thrust level of the aircraft in the acceleration and constant speed segments is obtained according to [8], assuming that the thrust level in the braking and emergency braking phases ε � 5%, and the turning phase ε � 7%. According to the fuel flow rate in the ICAO emission database and linear interpolation, the fuel flow rate f s corresponding to the thrust level at each stage in the speed profile is obtained by linear  Mathematical Problems in Engineering interpolation. en, for each link (N i , N j ), the fuel consumption of taxiing at this speed curve can be determined as follows: In the formula, we have the following: f s is the fuel flow rate at each stage of the speed curve, and s � 1, 2, 3, 4 t s is the time consumption of each stage of the speed curve, ands � 1, 2, 3, 4 For the complete taxiing path L kz of aircraft k, which is composed of multiple links, the objective function of taxiing fuel consumption g 2 can be further expressed as 3.3. Restrictions. For each link (N i , N j ), the taxi speed profile of aircraft k is mainly determined by four decision variables a 1 , d 1 , d 2 , d 4 . Decision variables are calculated sequentially, and, once determined, they will be used to further calculate the next decision variable. Due to the need to integrate the best speed curve generation method into the routing and scheduling module to provide online decision making, many decision variables may result in failure to meet time requirements. In view of this, the following assumptions are made on the problem of multitarget velocity profile generation: (1) e aircraft accelerates with the maximum acceleration a max to minimize the acceleration time.
(2) Based on the ICAO emission database method, the fuel consumption during braking is equivalent to the fuel combustion during constant speed. Because braking does not save fuel, the aircraft's constant speed travel distance d 2 is maximized. Using the maximum deceleration, the driving distance d 4 during the rapid braking phase when decelerating from v 1 to v 4 can be expressed by the following formula: Based on this assumption, the only undecided decision variable is the acceleration distance d 1 , and heuristic search method is used to search for the best value of v 1 within the allowable range to determine d 1 .
Before searching forv 1 , the maximum theoretical speed v theory is added, and its value is determined by the length d ij of the link (N i , N j ); the formula is as follows: In the formula, we have the following: ere are two situations: Speed (m/s)

Mathematical Problems in Engineering
At this time, it is shown that the link is long enough, and the aircraft satisfies the acceleration of a 1 to v max and then decelerates to the final speed v t of the link (N i , N j ). Search for the best value of v 1 within v max .
At this point, it is shown that the link length is not enough to accelerate to v max . e aircraft will accelerate to v theory by a 1 and then decelerate by a max to meet the situation where the link end reaches v t . Search for the best value of v 1 within v theory .

Multiobjective Velocity Profile Model Solution.
is paper uses a heuristic search method to search the decision variable v 1 , weighs the taxi time and fuel consumption, and finally generates a multitarget speed profile for the selected path. e specific search steps are as follows: (1) Input the segmented path L kz (2) Traverse weights u 1 and u 2 : u 1 from 0 to 1 in steps of 1/12 (3) Corresponding to the determined weight, take the chain (N i , N j ) on the path L kz :

a total of 12 schemes
Introduce v theory to traverse the speed value during the acceleration phase Corresponding to the determined speed v 1 , find the taxi time TT ij and fuel consumption FF ij of the link (N i , N j ) Solve u 1 * TT ij + u 2 * FF ij Select the corresponding v 1 when the benefit is the smallest, and use this value to determine the speed profile of the link (N i , N j ) (2) Turn link Calculate the cornering speed of 5.14 m/s, and find the cornering benefit value  Table 1.
It can be seen from Table 1 that the amount of pollutant emissions during the taxi phase is much larger than that in other phases, which deserves special attention. Because the LTO cycle defined by ICAO calculates taxi emissions according to a fixed taxi thrust and, in reality, due to the different taxi actions of the aircraft, the engine thrust is not always maintained at 7%, so the pollutants in the aircraft ground taxi phase are calculated by this calculation model. e amount of emissions is quite different from the actual situation, so this paper considers the actual taxiing speed and corresponding thrust of the aircraft during the ground taxi phase and obtains the actual taxi speed based on the fuel flow rate and pollutant emission coefficient values corresponding to different taxi thrust values. e amount of pollutant emissions has further improved the accuracy of emissions calculations.
e total amount of taxiing emissions from surface aircraft E can be expressed as where t s indicates the taxi time of the aircraft in the speed profile phase s, f s indicates the aircraft's fuel consumption coefficient in the speed profile phase s, EI s,w indicates the aircraft's emission coefficient of the pollutant w discharged in the speed profile phase s, E ij,w and indicates the aircraft is in the link. e amount of pollutant w discharged during taxiing E f n represents the total amount of pollutant discharged when the aircraft f n taxis.

Experimental Settings.
is article takes the ground taxi system of Xi'an Xianyang Airport as an example and uses the A * algorithm to optimize the model. Xi'an Xianyang Airport has 3 terminals and two parallel runways. e flight data of Xi'an Xianyang Airport on May 2nd, 2019, from 15 :16 : 00 to 15 : 28 : 20 was used for simulation calculation. e taxi schedule of the flight is shown in Table 2. Plan 3 preselected taxi paths for each aircraft according to their respective flight plans; that is, the number of preselected pathsp � 3.

Simulation Results.
e system gives the feasible taxi path of each aircraft and the taxi path length and number of turns of taxiing from the starting node to the target node     Table 3.
As can be seen from Table 3, the taxi path planning system considers the number of turns and provides three different preselected paths for each aircraft, which are sorted in increasing order according to the total taxi distance. For a nonsteering node on the aircraft's taxi path, the aircraft is considered to taxi directly into the node and only takes up the node at a certain moment; for a turning node on the aircraft's taxi path, it is considered that the aircraft takes a certain amount of time to perform a turning operation after taxiing into the node, and then the aircraft taxies out of the node. Figure 5 shows the taxi path without considering the turn and the turning distance of the aircraft path. e red section indicates the section that cannot be driven due to direction restrictions. It can be seen from the figure that the route considering the turning distance reduces the aircraft's taxi nodes and the number of turns. e taxi data of the six aircraft paths listed in Table 3 before and after considering the taxi turn distance are calculated. e comparison results are shown in Table 4.
Comparing the statistical data in Table 4, it can be seen that the total taxi distance and turning distance of the aircraft are reduced after the path optimization, and the taxi turn distance is the main factor for the reduction of the total taxi distance.

Experimental Settings.
According to ICAO standards, the aircraft's linear speed does not exceed 30 knots, and the turn taxi speed does not exceed 10 knots. It is assumed that the minimum taxi speed v min of the aircraft is 5.14 m/s and the maximum speed v max is 15.43 m/s. e speed of the aircraft is constant when turning. e turning speed is set to 5.14 m/s. In order to ensure passenger comfort, the maximum acceleration and deceleration rate a max is set to 0.98 m · s − 2 .
Based on the obtained shortest taxi path for taxiing, the taxi path is divided into straight sections and turning sections, and the initial speed, final speed, and section length information of each section are obtained, as shown in Table 5.
Take flight number NS8264 as an example. e flight is an approaching aircraft. e initial speed is 5.14 m/s and the taxiing speed is 5.14 m/s on the path segment "6-12" to the turning node "12." At a speed of 5.14 m/s, the taxi is at a constant speed at the turning point "12," and then taxies on the path segment "12-16" at a speed of 5.14 m/s to reach the next turning point "16" at a speed of 5.14 m/s. e speed of 5.14 m/s taxies on the turning taxiway at a constant speed, and so on, until all the paths are completed, and the speed is finally reduced to 0 when it reaches the apron. e system generated the speed profile of each aircraft on the shortest preselected path, as shown in Figure 6 (the abscissa of the speed profile is the taxi time and the ordinate is the taxi speed; the abscissa of the thrust curve is the taxi time, and the ordinate is the thrust value).
It can be seen from Figure 6 that when searching with different weights, the aircraft generates completely different speed profiles, which depends on the decision of the controller in practical applications. Taking the shortest path of flight NS8264 as an example, the taxi data of the speed profile at different weights are counted. e comparison results are shown in Table 6.
Comparing the statistical data in Table 5, it can be seen that when the time weight is the largest, the total taxi time of the speed profile generated is the least, but the fuel consumption is the largest; otherwise, when the fuel weight is the largest, the total taxi time in the speed profile is the longest, but the fuel consumption is the smallest. When the aircraft is taxiing at different speeds and accelerations on a specified path, the effect on taxi time cost and taxi fuel consumption cost is different. e pursuit of the optimal time cost will inevitably cause excessive fuel consumption, and the taxi time when the fuel consumption is optimal is not really optimal from the perspective of the total taxi cost. Taking the shortest path of flight NS8264 as an example, the Pareto front of the best speed profile is shown in Figure 7.
It can be clearly seen from the experimental results that the optimal taxiing time for the aircraft to complete the designated path does not correspond to the optimal taxiing fuel consumption, and the two are not in direct relationship. Decreasing the taxi time of the aircraft does not mean that the fuel consumption is reduced. On the contrary, reducing the taxi time of the aircraft will change the taxi speed, and frequent acceleration and deceleration will bring more fuel consumption.
is paper compares the time of the system running algorithm before and after the improvement, as shown in Table 7.
Under the premise of ensuring the generation of accurate 4D taxiing trajectories, the algorithm in this paper significantly shortens the running time of the algorithm and satisfies the application in the actual dynamic environment (ICAO, 2004). e path planning algorithm in this paper is more effective than before.

Calculation of Taxiing Pollutant
Emission. 6Check the fuel consumption rate and pollutant emission coefficient of the aircraft through the ICAO engine emission database (as shown in Table 8). Use the above multitarget speed profile model to obtain the thrust values of each stage of the aircraft surface taxi, according to the engine installed in each aircraft Type and linear interpolation to obtain the fuel consumption rate and pollutant emission coefficients corresponding to different thrust values and to obtain the pollutant emissions when each aircraft adopts a multitarget speed profile. e three glide speed profiles of NS8264 and their pollutant emissions are shown in Table 9.
In order to verify the rationality and effectiveness of the method in this paper, the flight volume data of Xi'an Xianyang Airport in the first half of 2019 is counted, and the pollutant emissions are solved based on the accurate multitarget taxi speed profile, and the average total pollutant emissions for flights in the first half of the year are obtained. e calculated results are compared with the actual total emissions, as shown in Table 10.

Conclusion
is article first considered the aircraft's taxi distance and the number of turns during taxiing and established an aircraft path optimization model with the shortest total taxi distance of the scene as the target. e improved A * algorithm was used to solve the model to obtain the P shortest path from the starting node to the target node. Based on this, a multitarget speed profile model considering taxi time and fuel consumption was established.      Heuristic search was used for each path producing an accurate velocity profile. Simulations were performed using real flight data. e results show that after the aircraft's taxiing path is optimized, the total taxiing distance and number of turns of the aircraft are reduced. Compared with the traditional optimization method that does not take into account the number of turns, the airport operation efficiency is improved. By considering different weights, the multitarget speed profile model generates a set of Paretooptimal speed profiles for the aircraft's taxi path to achieve high-precision planning of the aircraft's taxi path. e concept of maximum theoretical speed is added to the heuristic search process, which further simplifies the calculation. It is faster than other complicated algorithms that consider multiple factors, which is helpful for real-time air traffic control decisions. From the perspective of the environment, considering the taxi time of the 4D trajectory and the comparison and calculation of the pollutant emissions when the ground aircraft adopts different speed profiles, the accurate multitarget taxiing 4D trajectory is more helpful for energy saving and emission reduction and practical application value. Future research will increase the actual interference factors of the airport, comprehensively analyze the actual situation of airport inbound and outbound flights, dynamically adjust the taxi path of the aircraft and maintain the real-time nature of the system, and further optimize the algorithm to improve the performance of the algorithm.

Data Availability
e data used to support the findings of this study are included within the supplementary information file. e supplementary information file contains the raw data for the calculation (the three XLS data files) and the program in the Python environment.

Conflicts of Interest
e authors declare that they have no conflicts of interest.