Flight conflict resolution during low-altitude rescue operation based on ensemble conflict models

Abstract

In a low-altitude rescue operation, the safety and efficiency of the rescue can be guaranteed by adopting the conflict-avoidance mode of the collaboration type of flight rescue. In this article, we first introduce a protection zone model based on the visual flight separation standard, adopt resolution early warning time as a criterion, and divide the conflict into two modes, namely, two-aircraft (including fleet) and multiple-aircraft modes. Second, during each conflict mode, we distinguish different conflict scenarios based on the flight course of the conflict aircrafts and the tasks they carry out. Finally, we introduce a multi-agent system. We regard each aircraft as an independent agent that includes four modules. Each agent decides its own conflict resolution sequence based on the priority rules. By combining the relative movement trend, we select resolution strategies, such as adjusting the aircraft to fly higher, veering it off-course, or adjusting its speed. Finally, we draw the conflict-free flight track. We create a collaboration type of flight conflict resolution under different rescue priorities. Simulation examples show that this method can realize correction of the flight track and guarantee the safety and high efficiency of aircrafts according to the initial rescue flight track and under rescue priority.

Introduction

In our work on earthquake relief, countering with emergency rescue and sudden events, air rescue presents the characteristics of strong flexibility, quick response, no limitation by ground transportation, and so on. This rescue method is currently one of the most effective rescue means adopted by many developed countries worldwide. ¹ During the implementation of low-altitude (below 1000 m) ² rescue, the flight safety and efficiency of transportation should be considered. The free-flying operation mode is an efficient and safe operation mode. The Federal Aviation Administration implemented the Free Flight Program ¹ in 1998 and has been planning the Next-Generation Air Transportation System (NGATS) ³ since 2005. These actions indicate a further development step toward free flight. In the NGATS system, a more flexible and intelligent air traffic control (ATC) system will be set up. Through several advanced technologies, the aviator can select a better flight route. However, in low-altitude rescue flight, many problems have to be addressed to achieve improved conflict resolution. These problems include the flight rules in initializing navigation, flight planning information, rescue flight environment, timeliness, and reliability. These areas entail relatively complex work. In low-altitude airspace, the topography is complex, and less equipment monitoring work is conducted in this space. Dead zones in terms of functionality exist. Effective monitoring via a ground radar is difficult to achieve. Hence, the method of guaranteeing the safe separation of aircrafts from the centralized control on the ground needs be changed to manage aviator and airborne equipment. We need aviators to make autonomous evasion of flight conflict and adopt a more distributed type of control. Many resolution methods to address free-flight conflict have been proposed in the academe. The earliest research result that has been recognized worldwide is the air traffic system separation standard proposed by Reich.^4–6 The earliest aircraft collision risk model was established in the conflict analysis research area. In this model, collision between two aircrafts is considered equal to the collision between a particle and a cuboid. Since then, a large number of researchers have comprehensively discussed the uncertain factors that influence flight safety based on the model provided by Reich. They have conducted further study on the estimation of collision risk and have obtained safety protection areas with different shapes. For example, a cylinder-shaped protection area was proposed by Kuenz and Peinecke, ⁷ and an axiolitic-shaped protection area was presented by Menon et al. ⁸ With the above-mentioned aircraft collision risk model, three methods of research for flight conflict resolution technology have been established. The first method involves predetermining the means of resolution. ⁹ During the system design phase in this method, the conflict resolution scheme is set to correspond to several presupposed flight conflict scenarios. For example, the ground proximity warning system sends out a standard pull-up warning when flight conflict exists between an aircraft and the ground. However, it does not provide an optimized resolution operation strategy. The predetermined resolution method is simple, direct, and easy to operate. When an aviator is trained, he can reflexively carry out the conflict resolution operation when a flight conflict warning is received. However, this method is inapplicable to complex free-flight scenarios. The second one is the conflict resolution method based on a force field.^10–12 In this method, each aircraft is assumed to be a charged particle. With the revised static electricity equation, the operation strategy for flight conflict resolution can be obtained. This method of solving the equation is simple, but sometimes, the result obtained is impractical. For example, it requires significant changes in aircraft speed and discontinuity exists. Hence, this method is not widely used at present. However, when this method is combined with the participation of humans and implemented in an interactive manner, the problems mentioned above can be solved. Matsuno ¹⁰ and Emami^11,12 presented certain achievements on this aspect. The third method is based on the programming type of optimization method, such as mixed-integer linear programming,^13–18 mixed-integer nonlinear programming,^18,19 and dynamic optimization. ²⁰ Other optimization methods include game theory, ²¹ genetic algorithm, ²² ant colony algorithm, ²³ and branch-and-bound algorithm. ¹⁹

Compared with flight-route conflict detection and resolution under radar monitoring, real-time flight conflict detection and resolution under low-altitude rescue flight is more difficult to realize. Therefore, the motivation on the study has the following reasons. The first reason is the variety in conflict mode, such as conflict between two aircrafts and conflict among multiple aircrafts. In addition, rescue aircrafts usually fly in a formation. The scenario of conflict occurring during formation flying should also be considered. The multi-conflict type of situation makes conflict resolution highly complicated. The second reason is that low-altitude flight is a point-to-point visual flight. Hence, no air route for guidance exists, significant flight deviation could appear, and an adverse influence on real-time conflict detection could occur. The third reason is that a helicopter is generally utilized as the main rescue aircraft to carry out the rescue task. A helicopter has strong mobility, especially in the vertical direction. Frequent maneuvering occurs during the flight, and this increases the difficulty of conflict detection. At the same time, maneuverability could provide more options for conflict resolution. Under this type of distribution environment, the possibility of flight conflict increases as the utilization ratio of airspace increases. Multiple modes of integration and collaboration for rescue flight conflict resolution should be developed to solve these problems.

The main contributions of this article can be summarized as follows.

• We set up a timing conflict protection area based on safe separation and early conflict warning timing along three dimensions of aircrafts.

• By combining the prediction flight track of other aircrafts in this airspace, real-time flight conflict detection can be achieved.

• Under qualified flight conflict conditions, we determine the conflict situation faced by an aircraft and implement the conflict resolution process. This procedure allows the aircraft to avoid conflict autonomously.

The rest of this article is organized as follows. Section “Division of conflict mode” introduces division of conflict and includes identifying the conflict mode based on early warning timing, two-aircraft conflict mode, and multi-aircraft conflict mode; section “Detection of flight conflict” proposes detection of flight conflict; section “Real-time flight conflict resolution based on the multi-agent system” establishes real-time flight conflict resolution based on the multi-agent system; section “Computational instances and analysis” presents the simulation and data analysis results; Finally, section “Conclusion” concludes and suggests areas for further work.

Division of conflict mode

Traffic Collision Avoidance System (TCAS) ²⁴ provides that some pilots have been unsure how to act when their aircraft was requested to climb while flying at their maximum altitude. The accepted procedure is to follow the climb resolution advisory (RA) as best as possible, temporarily trading speed for height. The climb RA should quickly finish. In the event of a stall warning, the stall warning would take priority. We used the TCAS for reference and adopted the conflict mode based on early warning time; ²⁴ we then determined the mode of conflict resolution. As shown in Figure 1, basically, two-aircraft conflict resolution, three-aircraft conflict resolution, four-aircraft conflict resolution, conflict resolution in a single-aircraft fleet, and conflict resolution between two fleets were involved. As for the single-aircraft and fleet forms, we established a rescue priority strategy individually and implemented conflict resolution. Double-aircraft conflict resolution was further divided into off-course resolution strategy under head-to-head flight, increasing height resolution strategy under cross flight, and off-course surpass resolution under catch-up flight. For the resolution strategy of three and four aircrafts, we can realize multi-aircraft resolution under the strategy of two-aircraft resolution based on the priority strategy.

Figure 1.

Conflict resolution process of mode integration.

Identifying the conflict mode based on early warning timing

When conflict based on the prediction of the flight track is detected, the prediction track of three or more aircrafts could possibly be interlaced, as shown in Figure 2. In Figure 2(a), many two-aircraft conflicts exist in the track of three aircrafts. In Figure 2(b) and (c), aircraft A₁ is in conflict with A₂ and A₃; however, no conflict exists between A₂ and A_3.

Figure 2.

Conflicts among many aircrafts: (a) conflicts in the track of three aircrafts, (b) conflicts in parallel trajectory of opposite direction, and (c) conflicts in parallel trajectory of same direction.

Evidently, as the prediction track distance increases, the possibility of multi-aircraft conflict increases. Hence, the definition of two- or multi-aircraft conflict should be clarified. For example, we predict that an aircraft will be in conflict with two aircrafts in 20 or 300 s; this is only a judgment based on the prediction track, and it is a multi-aircraft conflict, as shown in Figure 2(c). However, in terms of timing, the time interval between the two conflicts is long. Aircraft A₁ has sufficient time to implement resolution maneuvering with A₂ and A₃ successively. Hence, this scenario can be regarded as two-aircraft conflict, and the number of conflicts occurring among multiple aircrafts in the rescue airspace is reduced.

In this article, we referred to TCAS, ²⁴ which is widely used in passenger aircrafts. We retained the early warning and decision-making time. ²⁴ We defined conflicts with a time interval between two conflicts of less than 40 s as interlink conflicts, that is, aircraft A₁ is in conflict with A₂ at time t₀ and is in conflict with A₃ within the time range of (t₀, t₀ + 40 s). We judged A₁, A₂, and A₃ as multiple aircrafts in conflict.

Two-aircraft conflict mode

Based on the number of times that aircrafts encounter conflict within a specific period, we can define conflict individually as two-aircraft and multi-aircraft conflict modes. Based on whether the conflict is concerned with aircraft formation, we can define the mode of two-aircraft conflict as two aircrafts in conflict and conflict with a fleet.

In this study, the two-aircraft conflict mode includes two types of conflict, namely, conflict between two aircrafts and conflict among fleets. A fleet can be regarded as a whole because their shape and size remain the same during flying; hence, we can regard two fleets in conflict as two-aircraft conflict.

Two tasks, namely, go around flying (GAF) and turn around flying (TAF), are usually carried out by aircrafts during low-altitude rescue. Based on their type, these tasks can be divided into transportation of wounded personnel (TWP), transportation of goods (TG), and information acquisition (IA). TG can be divided into fast-moving consumer goods (FMCG) and durable goods (DG).

Conflict between two aircrafts

According to the geometric relation in flight path and the relative movement relation among aircrafts, the conflict situation of aircrafts includes head-to-head, catch-up, cross, and pass-through-the-height conflicts.

Head-to-head conflict means that when two aircrafts make a reverse parallel flight based on a level flight path, the horizontal distance between the two aircrafts is less than the safety clearance, and the vertical distance is less than the safety clearance.

Catch-up conflict means that when two aircrafts make a same-direction parallel flight along a level flight path, the horizontal distance between the two aircrafts is less than the safety clearance, and the vertical distance is less than the safety clearance.

Cross conflict means that when two aircrafts make a flight along a cross flight path, the horizontal distance between the two aircrafts is less than the safety clearance, and the vertical distance is less than the safety clearance.

Passing-through-the-height conflict means that one level flight aircraft is in conflict with an aircraft that is at climbing/descending state or with two aircrafts that are at a climbing/descending state. It includes three types, namely, same flight path catch-up, same flight path head-to-head, and cross through the height, as shown in Figure 3.

Figure 3.

Cross-through-the-height conflict.

Fleet flight conflict

The carrying capacity of a single aircraft is limited. During rescue operation, many aircrafts are usually dispatched and fly in a formation. By having tasks carried out by the fleet, rescue efficiency is guaranteed, airspace utilization is enhanced, and flight conflicts among many individual flying aircrafts are avoided.

Detection of fleet conflict is based on detecting two aircrafts’ conflict. We set the formation logo G (group) for aircrafts that fly in a formation in airspace. When the aircrafts in formation detect flying conflicts along the aircraft-planned flying track and the target aircraft prediction flying track, the formation type of the other party’s aircraft can be determined. By checking whether the conflict aircraft is in a formation, we can divide fleet conflict into two types. The first is formation flight aircraft in conflict with a single aircraft, as shown in Figure 4(a). The second one is conflict between two-aircraft formations, as shown in Figure 4(b). The scenario is defined as

$$S_G=\{n=2|G,A\}$$

(1)

Figure 4.

Two types of fleet conflict: (a) conflict between aircraft formation and a single aircraft and (b) conflict between two aircraft formations.

Aircraft formation has five properties, as shown in Table 1.

Table 1.

Properties of rescue aircraft formation.

	Transport of wounded personnel	Durable goods	Fast-moving consumer goods
Going around	(GAF, TWP)	(GAF, DG)	(GAF, FMCG)
Turning around	(TAF, TWP)	(TAF, TG)

GAF: go around flying; TAF: turn around flying; TWP: transportation of wounded personnel; TG: transportation of goods; FMCG: fast-moving consumer goods; DG: durable goods.

Analysis of Table 1 shows that eight types of conflict scenarios exist for two-aircraft formation.

SG1 = {n = 2|GGAF,DG, GGAF,FMCG}	SG5 = {n = 2|GGAF,FMCG, GGAF,TWP}
SG2 = {n = 2|GGAF,DG, GGAF,TWP}	SG6 = {n = 2|GGAF,FMCG, GTAF,TG}
SG3 = {n = 2|GGAF,DG, GTAF,TG}	SG7 = {n = 2|GGAF,FMCG, GTAF,TWP}
SG4 = {n = 2|GGAF,DG, GTAF,TWP}	SG8 = {n = 2|GTAF,TG, GTAF,TWP}

Multi-aircraft conflict mode

When defining an aircraft property, the flight process and task type are considered. Six types of aircrafts can carry out rescue operations, as shown in Table 2. Given that the aircraft that transports fast-moving consumer and DG unloads the goods at the rescue area and carries no load in its return, (GAF, DG) and (GAF, FMCG) can be combined as (TAF, TG). The aircraft that captures aerial photos only consumes fuel during the entire process, so the state of its back-and-forth travel can combine (GAF, IA) and (TAF, IA) as IA.

Table 2.

Properties of the rescue aircraft.

	Transport of wounded personnel	Durable goods	Fast-moving consumer goods	Information acquisition
Going around	(GAF, TWP)	(GAF, DG)	(GAF, FMCG)	IA
Turning around	(TAF, TWP)	(TAF, TG)

GAF: go around flying; TAF: turn around flying; TWP: transportation of wounded personnel; TG: transportation of goods; FMCG: fast-moving consumer goods; DG: durable goods.

Scenario of three-aircraft conflict

When flight conflict occurs among three aircrafts, in consideration of the six different properties of an aircraft, eight types of conflict combinations exist, as shown in Figure 5.

Figure 5.

Scenario of three-aircraft conflict.

Analysis of Figure 5 shows that the different combinations of three-aircraft conflict are as follows:

S1 = {n = 3|AGAF,TWP, AGAF,DG, AGAF,FMCG}	S5 = {n = 3|ATAF,TWP, AGAF,DG, AGAF,FMCG}
S2 = {n = 3|AGAF,TWP, AGAF,DG, AIA}	S6 = {n = 3|ATAF,TWP, AGAF,DG, AIA}
S3 = {n = 3|AGAF,TWP, AGAF,FMCG, AIA}	S7 = {n = 3|ATAF,TWP, AGAF,FMCG, AIA}
S4 = {n = 3|AGAF,TWP, ATAF,TG, AIA}	S8 = {n = 3|ATAF,TWP, ATAF,TG, AIA}

Scenario of four-aircraft conflict

When flight conflict occurs among four aircrafts, in consideration of the six different properties of an aircraft, six types of conflict combinations exist, as shown in Figure 6.

Figure 6.

Scenario of four-aircraft conflict.

Analysis of Figure 6 shows that the different combinations of four-aircraft conflict are as follows:

S9 = {n = 4|AGAF,TWP, AGAF,DG, AGAF,FMCG, AIA}	S12 = {n = 4|ATAF,TWP, ATAF,TG, AGAF,FMCG, AIA}
S10 = {n = 4|AGAF,TWP, AGAF,DG, ATAF,TG, AIA}	S13 = {n = 4|ATAF,TWP, AGAF,DG, AGAF,FMCG, AIA}
S11 = {n = 4|AGAF,TWP, AGAF,FMCG, ATAF,TG, AIA}	S14 = {n = 4|ATAF,TWP, ATAF,TG, AGAF,DG, AIA}

For a conflict scenario involving five aircrafts and more, the rules above are adopted, and the same analogy applies.

Detection of flight conflict

Assuming that all the aircrafts that participate in rescue are equipped with automatic dependent surveillance–broadcast (ADS-B) and each aircraft can broadcast its location, flight course, ground speed, rate of climb, and flight plan information to other aircrafts in airspace through the air-to-air data chain, each aircraft can predict the flight track of the other aircrafts based on the signal it receives. We should check the conflict in the spatial dimension by comparing the planned flight track of an aircraft with the prediction track of the target aircraft. If conflict exists, we check it in the time dimension targeted to the conflicting point. If the time windows when the two aircrafts arrive at the conflict point overlap each other, then the two aircrafts will have flight conflict at this point.

No standard and complete flight rules on rescue work exist under low altitudes. Hence, in this article, we established a flight conflict detection model based on the visual flight separation standard. ²⁵ In this separation standard, the longitudinal separation between aircrafts with the same flight track and height and at visual flight is as follows: 5 km between aircrafts with indicated airspeed above 250 km/h and 2 km between aircrafts with indicated airspeed below 250 km/h. The vertical separation between aircrafts that fly at different heights should be over or equal to 300 m. In addition, when surpassing the aircraft in front or avoiding a head-on aircraft, the lateral separation should not be less than 500 m.

Assuming that aircrafts A_i and A_j are in the airspace and A_i is in a state of climbing up while A_j is in a state of level flight, the predicted individual flying tracks are L_i and L_j. $L{\prime }_i$ and $L{\prime }_j$ are the tracks of aircrafts A_i and A_j, that is, the projection of L_i and L_j on the Earth’s surface. An intersection point P exists, as shown in Figure 7. When four-dimensional (4D) predicted flight track information is known, we can obtain flight height H_i and H_j and time T_i and T_j when A_i and A_j reach point P. Then, the vertical separation of two aircrafts is ΔH = |H_i − H_j|. If ΔH is less than the minimum safety separation of H_min in the vertical direction, we can further determine the time window when two aircrafts go through point P.

Figure 7.

Diagram of the conflict situation.

Solving the coordination of P is equal to solving the intersection point of segments $L{\prime }_i$ and $L{\prime }_j$ .

The current location points p_i1 and p_j1 of aircrafts A_i and A_j and flight planning time p_i2 and p_j2 should be transferred to the rectangular plane coordinate system from the latitude and longitude of the geodetic coordinate system. The direct formula for Gaussian projection is

$$\{\begin{array}{c}x=X+\frac{N}{2{\rho ″}^2}\sin B\cos B{l″}^2\hfill \\ \multicolumn{1}{c}{+\frac{N}{24{\rho ″}^4}\sin B{\cos }^{3}B(5-t^2-9{\eta }^2){l″}^4}\\ \multicolumn{1}{c}{y=\frac{N}{\rho ″}\cos \mathrm{Bl}″+\frac{N}{6{\rho ″}^3}{\cos }^{3}B(1-t^2+{\eta }^2){l″}^3}\\ \multicolumn{1}{c}{+\frac{N}{120{\rho ″}^5}{\cos }^{5}B(5-18t^2+4t^4){l″}^5}\end{array}$$

(2)

where X represents the arc length of the meridian; B represents latitude; t = tan B; ρ″ is a constant 206,265, that is, the seconds corresponding to 1 radian; ${\eta }^2=e{\prime }^2{\cos }^{2}B$ ; $e\prime =\sqrt{a^2-b^2}/b$ represents second eccentricity; and N represents the radius of curvature in prime vertical. After the conversion, from the coordination of four points, the analytic expression of segments $L{\prime }_i$ and $L{\prime }_j$ can be obtained, and the common solution is the coordination of conflict point P.

The confirmation method for aircraft A_i and A_j passing through potential conflict point P time window is as follows.

Assuming that the minimum value of the longitudinal safety separation of an aircraft is L_min, then the time window for A_i passing through point P is t_i = [T_i − L_min/v_i, T_i]. The time window for A_j passing through point P is t_j = [T_j − L_min/v_j, T_j]. v_i and v_j are the cruising speed of aircrafts A_i and A_j, respectively. According to the cruising speed of an aircraft, we set L_min to 3 or 5 km.

According to the potential location of conflict and the time window when passing through the point, the conditions that cause the conflict between aircrafts A_i and A_j can be defined

$$\{\begin{array}{c}{L}_i\prime \cap L_j\prime \ne \varnothing \hfill \\ \multicolumn{1}{c}{|H_i-H_j|<H_{\min }}\\ \multicolumn{1}{c}{[T_i-L_{min}/v_i,T_i]\cap [T_j-L_{min}/v_j,T_j]\ne \varnothing }\end{array}$$

(3)

Real-time flight conflict resolution based on the multi-agent system

Considering the inadequate ground ATC guidance during flying in rescue areas, negotiation, cooperation, and collaboration among all aircrafts are effective in solving flight conflict. The multi-agent system is a distribution-type collaboration method of conflict resolution. It regards a single aircraft as an intelligent agent; in a specific airspace, multiple aircrafts are combined as a multi-agent system.^26,27 When an individual aircraft agent detects flight conflict, based on its own flight target timing, the resolution strategy and resolution priority of each aircraft jointly define the resolution track for each aircraft.

Aircraft agent module

The aircraft agent has four modules: aircraft information, flight conflict detection, negotiation and strategy, and resolution strategy generation. The four modules in the aircraft agent collaborate and autonomously avoid the dangers encountered in flight conflict, as shown in Figure 8. The function of each module is shown in the following.

Figure 8.

Agent structure and interaction diagram.

Aircraft information module

The information for this module is inputted into the module before each flight. It includes information on whether the aircraft is in a formation, the task it carries out, flight information on going and turning around, and number of real-time conflicts encountered by the aircraft.

Flight conflict detection module

With ADS-B loaded on the aircraft, the aircraft agent can obtain the flight state and flight plan of other aircrafts in the rescue airspace, and the flight track can be predicted. By analyzing the predicted flight track, the agent can determine whether flight conflict objects exist. The number of potential conflicts can then be further determined depending on the existence of conflict between two aircrafts or conflict among many aircrafts.

Negotiation and strategy module

A temporary dialog among all aircrafts is set up by the agent concerned with conflict according to the information of all agent aircrafts, such as formation and task. The resolution priority among all aircrafts is negotiated and confirmed.

Resolution track generation module

Once the resolution priority of all aircrafts is confirmed, a resolution track is generated based on the priority sequence from high to low. Assuming that every two aircrafts are in conflict among Agent (1), Agent (2), and Agent (3) and that the resolution priority order is Agent (1) > Agent (2) > Agent (3), then Agent (1) retains its original track R₁ as constant, Agent (2) maneuvering on track R₂ performs avoidance in reference to Agent (1), and the resolution track R₃ of Agent (3) is in conflict with R₁ and R₂. This scenario applies to the situation in which many conflicts exist among aircrafts.

Rule of resolution priority

The priority of each aircraft is decided by the task it carries out and the phases it stays in (whether it is going around or turning around). The priority of a single aircraft is lower than that of an aircraft formation. The priority of fleets is based on the scale of a fleet. If the scale is the similar, the priority is based on the tasks it carries out and the situation of going around and turning around.

Resolution priority for single-aircraft conflict

The general rules to determine the priority are as follows: the more urgent the rescue task is, the higher the priority is; the priority of a going-around aircraft is higher than that of a turning-around aircraft; and the priority of an aircraft with a low maneuvering function is higher than that of an aircraft with a high maneuvering function. Based on these rules, we provide the following discussion.

For an aircraft that is going around, because A_GAF,TWP is at an empty loaded state, its maneuvering function is far better than that of a fully loaded aircraft. The aircraft can conveniently carry out resolution maneuvering, so we set the priority to lower than A_GAF,DG and A_GAF,FMCG.

Among aircrafts that undertake the transportation of relief goods, DG are transported by A_GAF,DG and FMCG are transported by A_GAF,FMCG. Given that the time sensitivity of DG is lower than that of FMCG, we set ${\pi }_{\mathrm{GAF},\mathrm{DG}}$ with a relatively high priority.

In turning-around flight, aircraft A_TAF,TWP is at a state of transporting wounded personnel. In consideration of the necessity of comfort for passengers and the urgency for curing the wounded, we set the priority of this task ${\pi }_{\mathrm{TAF},\mathrm{TWP}}$ as the highest. A_TAF,TG is at a state of empty load with strong maneuvering, so we set the priority ${\pi }_{\mathrm{TAF},\mathrm{TG}}$ relatively low.

Among A_GAF,TWP, A_TAF,TG, and A_IA, the priority of A_GAF,TWP is the highest because it undertakes the relief work for wounded personnel. A_IA has a strong maneuvering function and is idle for a long time; it carries out detection work, so we set ${\pi }_{\mathrm{IA}}$ with a low priority.

Hence, the priority for each aircraft is as follows

$${\pi }_{\mathrm{TAF},\mathrm{TWP}}>{\pi }_{\mathrm{GAF},\mathrm{FMCG}}>{\pi }_{\mathrm{GAF},\mathrm{DG}}>{\pi }_{\mathrm{GAF},\mathrm{TWP}}>{\pi }_{\mathrm{TAF},\mathrm{TG}}>{\pi }_{\mathrm{IA}}$$

Priority of fleet conflict resolution

For conflict scenario S_G = {n = 2|G, A}, avoidance measures are implemented by a single aircraft while the fleet formation keeps flying following its original track. In terms of economy, the fuel consumed by a single aircraft during its resolution maneuvering operation is less than that of a formation aircraft. In terms of safety, the difficulty level when formation aircrafts perform integration resolution maneuvering is higher than that of a single aircraft.

When flight conflict occurs among aircraft fleets, the small-scale fleet usually makes way for the large-scale fleet. If the number of aircrafts in each of the two fleets is the same, the priority should be determined based on the relief task each fleet carries out and the flying state it stays in. By analyzing the different conflict scenarios mentioned above, we determined the priority $\pi$ for each scenario as follows:

SG1: ${\pi }_{\mathrm{GAF},\mathrm{DG}}>{\pi }_{\mathrm{GAF},\mathrm{FMCG}}$	SG5: ${\pi }_{\mathrm{GAF},\mathrm{FMCG}}>{\pi }_{\mathrm{GAF},\mathrm{TWP}}$
SG2: ${\pi }_{\mathrm{GAF},\mathrm{DG}}>{\pi }_{\mathrm{GAF},\mathrm{TWP}}$	SG6: ${\pi }_{\mathrm{GAF},\mathrm{FMCG}}>{\pi }_{\mathrm{TAF},\mathrm{TG}}$
SG3: ${\pi }_{\mathrm{GAF},\mathrm{DG}}>{\pi }_{\mathrm{TAF},\mathrm{TG}}$	SG7: ${\pi }_{\mathrm{TAF},\mathrm{TWP}}>{\pi }_{\mathrm{GAF},\mathrm{FMCG}}$
SG4: ${\pi }_{\mathrm{TAF},\mathrm{TWP}}>{\pi }_{\mathrm{GAF},\mathrm{DG}}$	SG8: ${\pi }_{\mathrm{TAF},\mathrm{TWP}}>{\pi }_{\mathrm{TAF},\mathrm{TG}}$

When carrying out conflict resolution, the formation with low priority should make way for the high-priority fleet.

Generation of conflict-free flying track

Three types of maneuvering are available for conflict avoidance. These three are adjusting height, off-course, and adjusting speed (Figure 9(a)–(c)).

1. Maneuvering of adjusting height. It pertains to the climbing or descending maneuvering flight of an aircraft within the same vertical plane while keeping the track angle unchanged. The equation of motion for an aircraft adjusting its height of maneuvering is

   $$p(t+\mathrm{\Delta }t)=p(t)+\left(\begin{array}{c}{v}_{\mathrm{GS}}·\sin \psi ·\mathrm{\Delta }t\hfill \\ \multicolumn{1}{c}{v_{\mathrm{GS}}·\cos \psi ·\mathrm{\Delta }t}\\ \multicolumn{1}{c}{v_H·\mathrm{\Delta }t}\end{array}\right)$$

   (4)

2. Maneuvering off-course. It involves changing the course of maneuvering flight of an aircraft within the same horizontal plane while keeping the flying height unchanged. With ΔΨ as the yaw angle, the equation of motion for an aircraft under off-course maneuvering is

   $$p(t+\mathrm{\Delta }t)=p(t)+\left(\begin{array}{c}{v}_{\mathrm{GS}}·\sin (\psi +\mathrm{\Delta }\psi )·\mathrm{\Delta }t\hfill \\ \multicolumn{1}{c}{v_{\mathrm{GS}}·\cos (\psi +\mathrm{\Delta }\psi )·\mathrm{\Delta }t}\\ \multicolumn{1}{c}{0}\end{array}\right)$$

   (5)

3. Maneuvering of adjusting speed. It means that an aircraft accelerates or decelerates with a fixed acceleration speed while keeping the flying track on a straight line. The equation of motion for an aircraft adjusting its speed is

   $$p(t+\mathrm{\Delta }t)=p(t)+(v_{\mathrm{TAS}}+a·\mathrm{\Delta }t/2)\left(\begin{array}{c}\cos \varphi \sin \psi \hfill \\ \multicolumn{1}{c}{\cos \varphi \cos \psi }\\ \multicolumn{1}{c}{\sin \varphi }\end{array}\right)\mathrm{\Delta }t$$

   (6)

Figure 9.

Three types of conflict resolution maneuvering: (a) adjusting height, (b) off-course, and (c) adjusting speed.

In equations (4)–(6), p(t) represents an aircraft’s current location, $v_{\mathrm{GS}}$ represents ground speed, $v_H$ is the climbing rate, $v_{\mathrm{TAS}}$ represents the true airspeed, Ψ represents the intersection angle between the track and Y axle, $\varphi$ represents the intersection angle between $v_{\mathrm{TAS}}$ and the horizontal plane, and Δt represents the time increment.

The conflict detection module of the aircraft agent can detect conflict between two aircrafts and among many aircrafts or fleets based on the conflict information.

After negotiation among aircraft agents, the resolution sequence is fixed. The resolution track generation module of the low-priority party integrates the conflict state, predicted conflict location, its own task, and the three types of information to determine the resolution maneuvering method.

When flying over the predicted conflict point and when conflict resolution condition equation (7) or (8) is satisfied, the aircraft completes conflict resolution and goes back to the original track to fly

$$d_{\mathrm{ij}}=\sqrt{{(x_i-x_j)}^2+{(y_i-y_j)}^2}>d_{min}$$

(7)

$$h_{ij}=\left|h_i-h_j\right|>h_{\min }$$

(8)

Resolution strategy for two-aircraft conflict

π_i and π_j represent the priority of Agent (i) and Agent (j), respectively.

By integrating the relative movement situation and task property of two aircrafts, the resolution module selects the optimal resolution maneuvering.

1. Head-to-head conflict between two aircrafts.

According to the rules of avoidance during visual flying, Agent (j) needs to veer off-course rightward, as shown in Figure 10. P is the predicted conflict point. When the distance between this point and Agent (j) is D_long, that is, the longitudinal safety clearance, Agent (j) begins to veer off-course. TCP₁, TCP₂, TCP₃, and TCP₄ are track change points during the resolution course.

Figure 10.

Diagram of off-course resolution track.

Longitudinal safety clearance is represented by D_long, lateral safety clearance is represented by D_lat, v_i and v_j are the ground speeds of Agent (i) and Agent (j), and D_ij represents the distance between the two aircrafts at the beginning of the resolution.

Off-course leg TCP₁ → TCP₂: TCP₁ corresponds to the beginning time t₁ of the resolution. We set the optimal off-course angle to ΔΨ, and the time needed for minimum D_lat from off-course to being parallel to the two aircrafts is

$$t=\frac{D_{\mathrm{ij}}}{v_i+v_j\cos \mathrm{\Delta }\psi }$$

(9)

From the geometrical relation among the optimal resolution track, D_long, and D_lat, we obtain

$$D_{\mathrm{long}}^2=D_{\mathrm{lat}}^2+{\left(\frac{D_{\mathrm{ij}}·v_j}{v_i+v_j\cos \mathrm{\Delta }\psi }\right)}^2$$

(10)

Then, the optimal resolution off-course angle is

$$\mathrm{\Delta }\psi ={\cos }^{-1}(\frac{D_{\mathrm{ij}}}{\sqrt{D_{\mathrm{long}}^2-D_{\mathrm{lat}}^2}}-\frac{v_i}{v_j})$$

(11)

By incorporating the value of ΔΨ into the off-course maneuvering equation (5), we obtained the resolution track of leg TCP₁ → TCP₂.

Cornering leg TCP₂ → TCP₃: TCP₂ corresponds to cornering beginning time t₂. We set the coordination of P, TCP₂, and TCP₃ to (x₀, y₀), (x₂, y₂), and (x₃, y₃), respectively, according to the law of uniform circular motion. We have

$$\{\begin{array}{c}{x}_3=D_{\mathrm{lat}}\cos (\psi +\mathrm{\Delta }\psi )\hfill \\ \multicolumn{1}{c}{=x_0+|x_2-x_0|\cos \mathrm{\Delta }\psi -|y_2-y_0|\sin \mathrm{\Delta }\psi }\\ \multicolumn{1}{c}{y_3=D_{\mathrm{lat}}\sin (\psi +\mathrm{\Delta }\psi )}\\ \multicolumn{1}{c}{=y_0+|y_2-y_0|\cos \mathrm{\Delta }\psi +|x_2-x_0|\sin \mathrm{\Delta }\psi }\end{array}$$

(12)

(x_t, y_t, z_t) is the coordination of Agent (j) at time t, and the turning rate is ω (°/s). Then, the TCP₂ → TCP₃ flying track is

$$\begin{array}{l}p(t_2+\mathrm{\Delta }t)=p(t_2)\\ +\left(\begin{array}{c}\left|x_{t_2}-x_0\right|\cos (\omega ·\mathrm{\Delta }t)-\left|y_t-y_0\right|\sin (\omega ·\mathrm{\Delta }t)\\ \left|y_{t_2}-y_0\right|\cos (\omega ·\mathrm{\Delta }t)+\left|x_t-x_0\right|\sin (\omega ·\mathrm{\Delta }t)\\ 0\end{array}\right)\end{array}$$

(13)

When the course change value of Agent (j) is 2ΔΨ, it is entered into the next course of flight.

Turning-around leg TCP₃ → TCP₄: TCP₃ corresponds to the end time of cornering t₃. The track is similar to TCP₁ → TCP₂, and the flying track of aircraft Agent (j) in this leg is

$$p(t_3+\mathrm{\Delta }t)=p(t_3)+\left(\begin{array}{c}{v}_j·\sin (\psi -\mathrm{\Delta }\psi )·\mathrm{\Delta }t\hfill \\ \multicolumn{1}{c}{v_j·\cos (\psi -\mathrm{\Delta }\psi )·\mathrm{\Delta }t}\\ \multicolumn{1}{c}{0}\end{array}\right)$$

(14)

After flying for about t times (similar to equation (9)), the aircrafts veer off-course rightward for an angle of about ΔΨ, resume their original track, and complete the conflict engagement.

• 2. Cross conflict occurring between two aircrafts.

According to the rules of avoidance in visual flying, the aircraft on the left side of the conflict point should climb and the aircraft on the right side of the conflict point should descend to avoid flight conflict. In a situation in which cross conflict exists between aircraft Agent (i) and Agent (j) and Agent (j) is at the left side of the conflict point, then Agent (j) should adopt the conflict resolution strategy of climbing. As shown in Figure 11, P is the predicted conflict point. When the distance between Agent (j) and point P is D_long, the aircraft begins to climb. TCP₁, TCP₂, and TCP₃ represent track-changing points during the resolution process. H represents the vertical safety clearance.

Figure 11.

Diagram of adjusting the height resolution track.

Climbing leg TCP₁ → TCP₂: p₁(x₁, y₁, z₁) is the coordination of aircraft Agent (j) at TCP₁. Its speed is v, and the time needed for resolution is

$$t=\frac{\sqrt{D_{\mathrm{long}}^2+H^2}}{v}$$

(15)

The resolution maneuvering climbing rate is

$$v_0=\frac{H}{t}=\frac{\mathrm{Hv}}{\sqrt{D_{\mathrm{long}}^2+H^2}}$$

(16)

The flying track of TCP₁ → TCP₂ refers to equation (4).

Returning around leg TCP₂ → TCP₃: When Agent (j) climbs to above P at a ground speed of v_j, Agent (i) has already flown over the predicted conflict point P. Agent (j) can be transferred to a descending mode and back to its original track. The flying track of TCP₂ → TCP₃ is

$$p(t+\mathrm{\Delta }t)=p(t)+\left(\begin{array}{c}{v}_j·\sin \psi ·\mathrm{\Delta }t\hfill \\ \multicolumn{1}{c}{v_j·\cos \psi ·\mathrm{\Delta }t}\\ \multicolumn{1}{c}{-v_0·\mathrm{\Delta }t}\end{array}\right)$$

(17)

After a period of $t$ (equation (15)) flying, Agent (j) changes to level flight and resumes its original track.

• 3. Catch-up conflict between two aircrafts.

According to the rules of avoidance in visual flying, Agent (j) should veer off-course rightward, surpassing the aircraft in the front, as shown in Figure 12. TCP₁, TCP₂, TCP₃, and TCP₄ are the track change points during the engagement process.

Figure 12.

Diagram of off-course surpassing track.

Off-course leg TCP₁ → TCP₂: The time of this leg is

$$t=\frac{D_{\mathrm{lat}}}{v_j\sin \mathrm{\Delta }\psi }$$

(18)

because

$$\tan \mathrm{\Delta }\psi =\frac{D_{\mathrm{lat}}}{D_{\mathrm{long}}+(v_j\cos \mathrm{\Delta }\psi -v_i)t}$$

(19)

Introducing equation (18) into the above formula yields

$$\mathrm{\Delta }\psi ={\sin }^{-1}\frac{D_{\mathrm{lat}}{v}_i}{D_{\mathrm{long}}{v}_j}$$

(20)

By introducing ΔΨ into the off-course maneuvering equation (5), the track of aircraft Agent (j) in leg of TCP₁ → TCP₂ is obtained.

Parallel leg TCP₂ → TCP₃: The function of this leg lies in surpassing Agent (i) under the condition of guaranteeing safety clearance. When longitudinal safety clearance is satisfied, the aircraft returns to its original track. By setting the corresponding time of TCP₂ to t₂, the equation of motion of this leg is

$$p(t_2+\mathrm{\Delta }t)=p(t_2)+\left(\begin{array}{c}{v}_j·\sin \psi ·\mathrm{\Delta }t\hfill \\ \multicolumn{1}{c}{v_j·\cos \psi ·\mathrm{\Delta }t}\\ \multicolumn{1}{c}{0}\end{array}\right)$$

(21)

Returning leg TCP₃ → TCP₄: When the distance between aircraft Agent (i) and Agent (j) is satisfactory, the corresponding time of TCP₃ is set to t₃. Then, the equation of motion of this leg is

$$p(t_3+\mathrm{\Delta }t)=p(t_3)+\left(\begin{array}{c}{v}_j·\sin (\psi -\mathrm{\Delta }\psi )·\mathrm{\Delta }t\hfill \\ \multicolumn{1}{c}{v_j·\cos (\psi -\mathrm{\Delta }\psi )·\mathrm{\Delta }t}\\ \multicolumn{1}{c}{0}\end{array}\right)$$

(22)

The value of ΔΨ can be calculated with equation (20).

• 4. When conflict between two aircrafts occurs during high flying, Agent (j) is at a state of level flight. We can select the resolution strategy according to the geometry relation of the track of the two aircrafts. When head-to-head conflict exists among same-track aircrafts, Agent (j) conducts off-course maneuvering. When catch-up conflict exists among same-track aircrafts, Agent (j) conducts off-course surpassing maneuvering. When cross conflict exists, such as when Agent (i) is higher than the predicted conflict point, Agent (j) conducts descending and adjusting height maneuvering; otherwise, Agent (j) conducts climbing and adjusting height maneuvering.

When Agent (j) is at a state of climbing/descending, the speed is adjusted to disengage the conflict. By setting the time window for Agent (i) passing through the conflict point as $[t_i^{(1)},t_i^{(2)}]$ and the distance between Agent (j) and the conflict point as D, then the time t_j that Agent (j) arrives at the predicted conflict point should meet $t_j<t_i^{(1)}$ or $t_j>t_i^{(2)}$ . a₁ as the minimum acceleration speed required for $t_i^{(1)}$ to pass through prior, and a₂ is the maximum acceleration speed required for $t_i^{(2)}$ to pass through later. $v_j$ is the initial speed of Agent (j). From the law of uniformly variable motion, we have

$$a_1=\frac{2[D-v_j(t_i^{(1)}-t)]}{{(t_i^{(1)}-t)}^2}$$

(23)

$$a_2=\frac{2[D-v_j(t_i^{(2)}-t)]}{{(t_i^{(2)}-t)}^2}$$

(24)

that is, the acceleration speed a of Agent (j) should meet a > a₁ or a < a₂. By inputting a₁ and a₂ into the speed adjustment maneuvering formula, we can determine that Agent (j) passes through the conflict point earlier than Agent (i) and later than the track of Agent (i) passing through the conflict point.

Resolution strategy for fleet conflict

Fleet conflict involves eight scenarios. In S_G1, S_G4, and S_G7, ${\pi }_{\mathrm{GAF},\mathrm{DG}}>{\pi }_{\mathrm{GAF},\mathrm{FMCG}}$ , ${\pi }_{\mathrm{TAF},\mathrm{TWP}}>{\pi }_{\mathrm{GAF},\mathrm{DG}}$ , and ${\pi }_{\mathrm{TAF},\mathrm{TWP}}>{\pi }_{\mathrm{GAF},\mathrm{FMCG}}$ , respectively. The low-priority agent that requires resolution maneuvering is going around the fleet carrying out good transportation. In scenarios S_G2, S_G3, S_G5, S_G6, and S_G8, ${\pi }_{\mathrm{GAF},\mathrm{DG}}>{\pi }_{\mathrm{GAF},\mathrm{TWP}}$ , ${\pi }_{\mathrm{GAF},\mathrm{DG}}>{\pi }_{\mathrm{TAF},\mathrm{TG}}$ , ${\pi }_{\mathrm{GAF},\mathrm{FMCG}}>{\pi }_{\mathrm{GAF},\mathrm{TWP}}$ , ${\pi }_{\mathrm{GAF},\mathrm{FMCG}}>{\pi }_{\mathrm{TAF},\mathrm{TG}}$ , and ${\pi }_{\mathrm{TAF},\mathrm{TWP}}>{\pi }_{\mathrm{TAF},\mathrm{TG}}$ , respectively. The low-priority agent that requires adopting avoidance measures is going around the fleet carrying the wounded and turning around the fleet carrying out good transportation. When conflicts exist between two fleets, many conflict points may emerge. The earliest one is regarded as the predicted conflict point. Based on the conflict situation of the two fleets, we select the resolution strategy by referring to the conflict situation of the two fleets.

Resolution strategy for multi-fleet conflict

Under the situation of conflict among multi-aircrafts, all the aircraft agents concerned should negotiate and confirm the respective resolution sequence based on their own resolution priority. If conflicts exist among Agent (h), Agent (i), Agent (j), and Agent (k) in the airspace and the priority is lower one by one, then the conflict resolution sequence is as follows: Agent (i) that has the highest priority should keep flying in its original track, Agent (j) with the second highest priority only needs to calculate the conflict-free track with Agent (i), Agent (j) should consider the conflict-free track with Agent (h) and Agent (i), and for the lowest priority Agent (k), we need to calculate the conflict-free flying track with Agent (h), Agent (i), and Agent (j) one by one.

Computational instances and analysis

We assume that in rescue airspace, we have going-around fleet G_GAF,DG carrying out the transportation of DG, turning-around fleet G_TAF,TG carrying materials, turning-around fleet A_TAF,TWP transporting the wounded, and disaster detection aircraft A_IA, as shown in Figure 13. According to the description above, the resolution priority from high to low are G_GAF,DG, G_TAF,TG, A_TAF,TWP, and A_IA. Assuming that the ground speeds of G_GAF,DG, G_TAF,TG, A_TAF,TWP, and A_IA are 77.75 knots (40 m/s), 97.19 knots (50 m/s), 106.91 knots (55 m/s), and 136.10 knots (70 m/s), respectively, the track angles are 270°,150°, 80°, and 210°, respectively. G_GAF,DG, G_TAF,TG, and A_TAF,TWP conduct flying at the height of 2952.76 ft (900 m). A_IA descends starting from the height of 5249.34 ft (1600 m), and the descending speed rate is 19.44 knots (10 m/s). Their initial parameters and coordination are shown in Tables 3 and 4.

Figure 13.

Diagram of planned flight track.

Table 3.

Initial parameters of aircrafts.

Aircraft	Ground speed (m/s)	Track angles	Height (m)	Descending speed rate (m/s)
G GAF,DG	40	270°	900	0
G TAF,TG	50	150°	900	0
A TAF,TWP	55	80°	900	0
A IA	70	210°	1600	10

Table 4.

Initial coordination value.

Aircraft	Latitude	Longitude	X coordinates	Y coordinates
G GAF,DG	31°43′57.14″N	118°51′59.86″E	3,512,259.252	505,973.017
G TAF,TG	31°46′2.76″N	118°48′18″E	3,516,126.774	500,132.625
A TAF,TWP	31°43′19.82″N	118°44′3.96″E	3,511,110.107	493,444.483
A IA	31°46′19.43″N	118°48′59.76″E	3,516,640.304	501,231.461

A total of six intersection points exist in the track of aircrafts A_TAF,TWP and A_IA and fleets G_GAF,DG and G_TAF,TG. These points result in six potential conflicts, as shown in Figure 14. The coordination of each point is listed in Table 5.

Figure 14.

Diagram of the intersection points of the track.

Table 5.

Coordination of the intersection points of the track.

Intersection points	Latitude/longitude coordinates	Cartesian coordinates
1	31°43′58.95″N/118°49′41.31″E	(3,512,313.536, 502,325.752)
2	31°43′58.91″N/118°48′3.57″E	(3,512,312.045, 499,752.815)
3	31°43′58.98″N/118°47′24.36″E	(3,512,314.277, 498,720.639)
4	31°44′13.46″N/118°49′31.71″E	(3,512,760.407, 502,072.949)
5	31°45′39.26″N/118°48′33.79″E	(3,515,402.957, 500,548.171)
6	31°43′51.69″N/118°47′19.36″E	(3,512,089.754, 498,588.987)

Once each aircraft agent has detected multi-aircraft conflicts, it will judge the priority as G_GAF,DG > G_TAF,TG > A_TAF,TWP > A_IA based on the relief tasks that each aircraft or fleet carries out. After the negotiation, the resolution sequence is G_GAF,DG, G_TAF,TG, A_TAF,TWP, and A_IA. The detailed resolution scheme is (1) G_GAF,DG keeps flying in its original planned track and (2) G_TAF,TG disengages from its track.

Intersection 1 exists for the tracks of G_GAF,DG and G_TAF,TG. Moreover, they have the same flying height of 2952.76 ft (900 m). From the spatial view, we can see that conflict exists.

Furthermore, the arrival time window of G_GAF,DG is [41.19, 91.19], the arrival time window of G_TAF,TG is [47.98, 87.98], and the intersection of the two is not empty. Hence, intersection point 1 is the predicted conflict point of G_GAF,DG and G_TAF,TG, and avoidance measures should be adopted by G_TAF,TG. According to the rules of lowering the aircraft flying height for the aircraft located at the right side (viewed by the direction of forward motion) of the conflict point, G_TAF,TG should conduct descending maneuvering.

Given that the minimum value of longitudinal safety clearance is 1.08 nautical mile (2 km), the coordination of the starting point of the descending leg of TCP₁ → TCP₂ is (3,514,472.492, 501,066.701). The corresponding longitude and latitude are (3,514,472.492, 501,066.701), the flying time is 39.55 s, and the descending rate is 14.73 knots (7.58 m/s). The renewed location formula for this phase is

$$\begin{array}{l}p(t)=p(t_1)+\left(\begin{array}{c}v·\sin \psi ·\mathrm{\Delta }t\\ v·\cos \psi ·\mathrm{\Delta }t\\ v_0·\mathrm{\Delta }t\end{array}\right)=\left(\begin{array}{c}3,514,472.492\\ 501,066.701\\ 900\end{array}\right)\\ +\left(\begin{array}{c}50·\sin 150°·\mathrm{\Delta }t\\ 50·\cos 150°·\mathrm{\Delta }t\\ -7.58·\mathrm{\Delta }t\end{array}\right)(\mathrm{\Delta }t\le 39.55)\end{array}$$

(25)

The flight duration of turning-around leg TCP₂ → TCP₃ is the same, that is, 39.55 s, with a climbing rate of 14.73 knots (7.58 m/s). The flying track of this leg is

$$\begin{array}{l}p(t)=p(t_2)+\left(\begin{array}{c}v·\sin \psi ·\mathrm{\Delta }t\\ v·\cos \psi ·\mathrm{\Delta }t\\ -v_0·\mathrm{\Delta }t\end{array}\right)=\left(\begin{array}{c}3,512,313.536\\ 502,325.752\\ 600\end{array}\right)\\ +\left(\begin{array}{c}50·\sin 150°·\mathrm{\Delta }t\\ 50·\cos 150°·\mathrm{\Delta }t\\ 7.58·\mathrm{\Delta }t\end{array}\right)(\mathrm{\Delta }t\le 39.55)\end{array}$$

(26)

• 3. Resolution track of A_TAF,TWP.

A_TAF,TWP, which is in the third place in the resolution sequence, has an intersection point with the tracks of G_GAF,DG, G_TAF,TG, and A_IA. However, its priority is higher than that of A_IA. Hence, we only need to check whether it has conflicts with G_GAF,DG and G_TAF,TG. From the spatial view, points 2 and 4 are the potential conflict points for A_TAF,TWP and G_GAF,DG, G_TAF,TG, respectively. The time window for A_TAF,TWP arrival at point 2 is [80.40, 116.76]; for G_GAF,DG, it is [45.84, 95.84]. Hence, conflict exists. Given that it is a cross conflict and A_TAF,TWP is at the left side of conflict point 2, A_TAF,TWP needs to perform climbing maneuvering.

Considering that the minimum value of longitudinal safety clearance is 6561.68 ft (2 km), the coordination of the starting point of the climbing leg of TCP₁ → TCP₂ is (3,511,937.736, 497,792.890). The corresponding longitude and latitude are (31°43′46.75″N, 118°46′49.12″E), the climbing duration is 36.77 s, and the climbing rate is 15.84 knots (8.15 m/s). We set the time corresponding to TCP₁ as t₁. The equation of motion of this climbing leg is

$$\begin{array}{l}p(t)=p(t_1)+\left(\begin{array}{c}v·\sin \psi ·\mathrm{\Delta }t\\ v·\cos \psi ·\mathrm{\Delta }t\\ v_0·\mathrm{\Delta }t\end{array}\right)=\left(\begin{array}{c}3,511,937.736\\ 497,792.890\\ 900\end{array}\right)\\ +\left(\begin{array}{c}55·\sin 80°·\mathrm{\Delta }t\\ 55·\cos 80°·\mathrm{\Delta }t\\ 8.15·\mathrm{\Delta }t\end{array}\right)(\mathrm{\Delta }t\le 36.77)\end{array}$$

(27)

The flying duration for turning-around leg TCP₂ → TCP₃ is the same, that is, 36.77 s, and the descending rate is 15.84 knots (8.15 m/s). We set the time corresponding to TCP₂ as t_2. The flying track of this leg is

$$\begin{array}{l}p(t)=p(t_2)+\left(\begin{array}{c}v·\sin \psi ·\mathrm{\Delta }t\\ v·\cos \psi ·\mathrm{\Delta }t\\ -v_0·\mathrm{\Delta }t\end{array}\right)=\left(\begin{array}{c}3,512,312.045\\ 499,752.815\\ 1200\end{array}\right)\\ +\left(\begin{array}{c}55·\sin 80°·\mathrm{\Delta }t\\ 55·\cos 80°·\mathrm{\Delta }t\\ -8.15·\mathrm{\Delta }t\end{array}\right)(\mathrm{\Delta }t\le 36.77)\end{array}$$

(28)

The tracks of A_TAF,TWP and G_TAF,TG share a common point 4. Given that G_TAF,TG has performed descending maneuvering, the resolution track between A_TAF,TWP and G_TAF,TG is needed for conflict detection. G_TAF,TG arrives at intersection point 4 along the resolution track, the height of which is 2227.36 ft (678.9 m). When A_TAF,TWP arrives at the point, it has completed the resolution with G_GAF,DG and resumed to a state of level flight. Hence, the height difference is 725.39 ft (221.1 m), which is less than the vertical safety clearance. Next, we judge the time window by considering the resolution track. The time window for A_TAF,TWP arriving at point 4 is [124.17, 160.54], and the time window for G_TAF,TG arriving at point 4 is [38.17, 78.0]. The intersection of the time window is empty, so no conflict exists within the resolution tracks of A_TAF,TWP and G_TAF,TG.

• 4. Resolution track of A_IA.

A_IA’s priority is the lowest among the others. In the resolution track of A_IA, conflicts with G_GAF,DG, G_TAF,TG, and A_TAF,TWP should be avoided. The track of A_IA has intersection points of 3, 5, and 6 with G_GAF,DG, G_TAF,TG, and A_TAF,TWP, respectively, and the first point being passed is point 5. The coordination of this point is (3,515,402.957, 500,548.171), the corresponding longitude and altitude are (31°45′39.26″N, 118°48′33.79″E), and the height where A_IA stays at an intersection point 5 is 4586.84 ft (1398.07 m). The height difference with G_TAF,TG is 1634.09 ft (498.07 m), which meets with the requirement of vertical clearance. When A_IA arrives at intersection point 3, the height of which is 2905.02 ft (885.45 m), the height difference with G_GAF,DG is 47.74 ft (14.55 m). Conflict exists from the spatial aspect. The arrival time window of A_IA is [42.88, 71.46], and the arrival time window of G_GAF,DG is [106.75, 156.75]. Given that no intersection exists between the two time windows, no conflict occurs. When A_IA arrives at intersection point 6, the height difference with A_TAF,TWP is 169.75 ft (51.74 m), and conflict exists from the spatial aspect. The arrival time window of A_IA arriving is [46.60, 75.17], and the arrival time window of A_TAF,TWP arriving is [58.85, 95.22]. Conflict exists.

Given that A_IA is at a state of descending, we can select the mode of adjusting speed for conflict resolution. With the earliest arrival time of A_TAF,TWP as the boundary, that is, $t_i^{(1)}=58.85\mathrm{s}$ and $t_i^{(2)}=95.22\mathrm{s}$ , the acceleration speed corresponding to A_IA is

$$a_1=\frac{2[D-v_j(t_i^{(1)}-t)]}{{(t_i^{(1)}-t)}^2}=0.67\mathrm{m}/{\mathrm{s}}^2$$

(29)

$$a_2=\frac{2[D-v_j(t_i^{(2)}-t)]}{{(t_i^{(2)}-t)}^2}=-0.31\mathrm{m}/{\mathrm{s}}^2$$

(30)

that is, when A_IA makes an accelerating movement at the acceleration speed of over 0.67 m/s², it goes through conflict point 6 prior to A_TAF,TWP; when A_IA makes a negative acceleration movement at the acceleration speed of over 0.31 m/s², it goes through conflict point 6 later than A_TAF,TWP. The resolution strategy and parameters of resolution strategy for each aircraft are shown in Tables 6 and 7, and the resolution track is shown in Figure 15.

Table 6.

Resolution strategy for each aircraft and effect of flight delay in multi-fleet conflicts.

Aircraft	Priority	Resolution strategy	Flight delay (s)
G GAF,DG	1	Track remains unchanged	0
G TAF,TG	2	Descend	16
A TAF,TWP	3	Climb	22
A IA	4	Speed regulation	11

Table 7.

Parameters of resolution strategy for each aircraft.

Aircraft	Priority	Resolution strategy	Time and speed of resolution	Intersection point
G GAF,DG	1	None	None	None
G TAF,TG	2	Descending	Flying time 39.55 s and the descending rate 7.58 m/s (TCP1–TCP2); flying time 39.55 s and climbing rate 7.58 m/s (TCP2–TCP3).	Intersection point 1, with GGAF,DG
A TAF,TWP	3	Climbing	The climbing duration 36.77 s and the climbing rate 8.15 m/s (TCP1 → TCP2); flying time 36.77 s and the descending rate 8.15 m/s (TCP2 → TCP3).	Intersection point 2, with GGAF,DG
A TAF,TWP	3	The time window is empty and no conflict exists	None	Intersection point 4, with GTAF,TG
A IA	4	The time window is empty and no conflict exists	None	Intersection point 3, with GGAF,DG
A IA	4	The height difference meets with the requirement of vertical clearance, so no conflict exists	None	Intersection point 5, with GTAF,TG
A IA	4	Adjusting speed	Making an accelerating movement at over 0.67 m/s2 or making a negative acceleration at over 0.31 m/s2	Intersection point 6, with ATAF,TWP

Figure 15.

Diagram of the resolution track.

From the above example, we can see that flight conflict resolution plan based on priority can availably avoid the risk of flight conflict. The formation flights have corresponding priority to ensure flight safety. The simulation calculation of this case takes only 0.81 s to start to escape in computer with Intel Pentium dual-core 2.9 GHz, Windows 7. Therefore, in complex relationships of flight conflict resolution, according to TCAS which defined the conflicts with a time interval between two conflicts of less than 40 s as interlink conflict, for the speed of helicopter in low altitude from 250 to 350 km/h, the flight conflict resolution of multi-aircraft was realized in the condition of different conflict scenarios.

Conclusion

In this study, we regarded resolution early warning time as the baseline and divided the conflict into two modes: two-aircraft (including fleets) and multi-aircraft modes. We defined different conflict scenarios based on the flying course of the aircrafts and the tasks being carried out by the aircrafts. From the aspect of disengaging conflicts, we introduced the multi-agent system. In this system, each aircraft is viewed as an independent agent that includes four modules, and each agent determines its own conflict resolution sequence based on the priority rules. By combining the relative movement situation, we selected different strategies, such as adjusting the altitude, veering off-course, and adjusting the speed. Hence, a conflict-free flying track was generated, and a collaboration method of flight conflict resolution was realized.

We only established resolution according to the priority of each task and did not consider the total cost, such as total fuel consumption and off-course distance. This disregard may cause the aircraft with a low priority to perform too much maneuvering. In addition, when many aircrafts are involved in a conflict, adverse factors may be enhanced. Hence, for further study, we can select other means of intelligent resolution to realize three-dimensional (3D) flight conflict resolution.