Exploring mission planning method for a team of carrier aircraft launching

Yu WU ,Yanyang WANG ,Xiangju QU ,Liguo SUN

a College of Aerospace Engineering,Chongqing University,Chongqing 400044,China

b School of Aeronautic Science and Engineering,Beihang University,Beijing 100083,China

KEYWORDS Aircraft carrier;Carrier aircraft;Distributed planning architecture;Mission planning;Path planning

Abstract High-level efficiency and safety are of great significance for improving the fighting capability of an aircraft carrier.One way to enhance efficiency and safety level is to organize the carrier aircraft into combat effectively.This paper studies the mission planning problem for a team of carrier aircraft launching,and a novel distributed mission planning architecture is proposed.The architecture is hierarchical and is comprised of four levels,namely,the input level,the coordination level,the path planning level and the execution level.Realistic constraints in each level of the distributed architecture,such as the vortex flow effect,the crowd effect and the motion of aircraft,are considered in the model.To solve this problem,a distributed path planning algorithm based on the asynchronous planning strategy is developed.The proposed Mission Planning Approach for Carrier Aircraft Launching(MPACAL)is validated using the setups of the Nimitz-class aircraft carrier.Compared to the isolated planning architecture and the centralized planning architecture,the proposed distributed planning architecture has advantages in coordinating the launch tasks not only belonging to the same catapult but also when all different catapults are considered.The proposed MPACAL provides a modeling method for the flight deck operation on aircraft carrier.

1.Introduction

Carrier aircraft is the main weapon equipped on the carrier,which plays an important role in enhancing the combat effectiveness of the whole carrier-aircraft system.As the platform for aircraft launching and landing,the organization of flight deck operation is crucial for the efficiency and safety of aircraft devoting to combat.1,2To improve the launch efficiency,motion planning for a single aircraft is studied,and the strategy of saving more preparation time is proposed.3However,when a team of aircraft are required to launch within a short period of time to form the fighting capacity in the air,the solution which can guarantee the launch efficiency and safety is not explored.As the taxiing of aircraft is guided by staffs on flight deck at present, this problem raises a higher demand to coordinate the aircraft and ensure the safety of flight deck operation because it is hard for the staffs to deal with the complicated situations when a team of aircraft are required to launch within a short period of time.4,5To reduce the workload and improve the efficiency and safety level of a launch mission,an automatic mission planner for a team of aircraft launching is desirable and imperative.

Mission planning has become a highly active research area,and has been extensively studied for different objects,such as distributed spacecraft systems,6multi-UAV coordination7,8and heterogeneous robots coordination.9For example, in order to estimate the neighbor spacecraft's relative states,an unscented Kalman filtering approach with measuring principles of both the pseudorange and the carrier phase is proposed to address the coordinated motion problem of distributed spacecraft.6An online rectangle based scheduling algorithm is developed to improve the autonomy of multiple UAVs to search a field of forest together.7The purposes of the algorithm are to decide the number of the UAVs to be assigned online and to schedule the path for the assigned UAVs to search the missed areas resulted from the previous search.Besides,the algorithm is robust against the unknown shapes and sizes of the missed areas.Heterogeneous robots coordination is one of the branches of multi-robot system research.Coordination between UAVs and Unmanned Ground Vehicles(UGVs)is studied in Ref.9.The great heterogeneity and complementary between UAVs and UGVs make the Unmanned Aerial and Ground Vehicles Systems(UAGVSs)powerful to complete a variety of complicated tasks.The paper identified the kernel elements for the coordination and possible realizations by building taxonomy for differentiating diverse configurations of UAGVS.

Coordinated system can be classified into centralized systems and decentralized systems according to the overall hierarchical architecture.10,11In centralized systems,a specific entity(called leader)is in charge of organizing the work of the entire team,while the other members act according to the leader's directions.12The main characteristic lies in the ability of optimizing the overall objective function.When the number of members is small,the centralized system is efficient.In most cases,centralized systems are not well suited for coordination of large-scale systems,especially when the total number of the members is relatively large. The centralized system will demand high computation load from the leader and make the communication overhead among the team members.13Besides,a reasonable cost function that can properly consider all factors influencing the system performance is hard to be proposed.

In recent research efforts on large-scale systems,decentralized system is often preferred to address the coordination problem in order to develop the capabilities of team members and reduce the cost of the overall system.14Compared to the centralized systems,distributed systems are generally more flexible.They are efficient in terms of both computation and communication.The information of the team members and tasks can be compressed into numerical bids and computed in parallel by each member.15A variety of bidding strategies have been developed for distributed systems,such as consensus based approaches,16reachability based approaches17and priority based approaches.18

As far as we know,in current practice,isolated systems are established when dealing with the mission planning problem for carrier aircraft launching according to the existing literatures.Each sub-planner receives launch task and plans the taxiing path for a single aircraft.19-21However,lacking communication among these independent sub-planners will make the launch tasks unsafe and inefficient especially when multiple aircraft are taxiing simultaneously.Therefore,coordination among aircraft is needed to guarantee the efficiency and safety.In this mission planning problem,more realistic constraints need to be considered.For example,the maximum number of aircraft that taxi on the flight deck simultaneously must be limited,so the traffic condition can be controlled;the launch time interval between two aircraft which are launched at two adjacent catapults must be restricted because the flow vortex will have an influence on the safety of launch mission.22When the centralized architecture is applied,all sub-planners are integrated into a large centralized planner.The centralized planner is responsible for all the aircraft and generates taxiing paths for them.However,when multiple aircraft are taxiing simultaneously,it is difficult to propose a reasonable overall cost function with low computational load that can satisfy the requirements of each path.In view of the difficulties in formulating reasonable cost function and decreasing the computational load, it is better to develop an autonomous coordination system with higher efficiency using decentralized techniques as mentioned above.

A novel distributed planning architecture with realistic constraints and an asynchronous planning strategy is developed for the mission planning problem in this paper.The proposed architecture is consistent with the flight operation of launch mission.Compared to the centralized planning architecture,the distributed planning architecture can keep stable when the tasks are changed.The flow vortex,the traffic condition and the motion of aircraft are all taken into account,which make the established model more realistic.Considering the disadvantage of the synchronous strategy in dealing with the predictive information of path planning,23an asynchronous strategy is developed to avoid the deadlock and Buckets effect.The major contributions are summarized as follows:

(1)The mission planning problem for a team of carrier aircraft launching is formulated,and a novel distributed planning architecture which is hierarchical for the problem is proposed.

(2)The mathematic model for the problem is established.The model contains realistic constraints in each level of the planning architecture. The objective function and the optimization model are also included.

(3)An asynchronous planning strategy is developed in the distributed path planning algorithm.The planning order of each local planner is determined by the token passing procedure;the deadlock and the Buckets effect in path planning are avoided.

The remainder of the paper proceeds as follows.Section 2 describes the problem and designs a novel distributed planning architecture.Section 3 establishes the mathematic model.Section 4 presents the distributed path planning algorithm.Experimental results are reported in Section 5 and the concluding remarks are contained in Section 6.

2.A novel distributed planning architecture

In this section,a novel distributed planning architecture for mission planning is proposed.This architecture is hierarchal and consistent with the flight deck operation of launch mission.A general view of flight deck arrangement on Nimitzclass aircraft carrier is shown in Fig.1.

Four catapults are equipped to assist the launch tasks.The aircraft are parked,taxiing or preparing for launch.Coordination is needed among different launch tasks,and a reasonable planning architecture can deal with the coordination effectively.

The proposed distributed planning architecture transforms the centralized planning problem into local optimization problem for each aircraft and reduces the scale of solution.As shown in Fig.2,the architecture is hierarchical and consists of four levels:the input level,the coordination level,the path planning level and the execution level.Each local planner is responsible for the launch tasks belonging to one catapult.The coordination agent has a global view of the system.The coordination works in different stages of launch mission(the details are presented in Section 4).

Fig.1 A general view of flight deck arrangement and state of aircraft.

The proposed architecture has the following characteristics.Firstly,the coordination of launch tasks belonging to different catapults is indirectly realized among local planners,and the coordination of launch tasks belonging to the same catapult is realized directly.Secondly,the coordination agent is responsible for mediating the cooperation among distributed local planners which take charge of their respective planning tasks in a centralized fashion.Moreover,local planner agent can interact with each other directly to strengthen the ability of coordination.

The proposed planning architecture realizes the coordination of different launch tasks.The functions of each level will be introduced.

(1)Input level

Two kinds of information are included in this level,namely,the launch plan information and the state information of aircraft. Launch plan determination is a higher level of decision-making process based on the tactics,24and the launch plan contains the information of launch position and order of each aircraft.The above information is stored in the launch plan information agent.The state information agent saves and updates the state of each aircraft and catapult.Specifically,the latest state of aircraft(parking,taxiing or preparing for launch)will be transmitted to the state information agent immediately.

Fig.2 Distributed planning architecture for launch mission.

(2)Coordination level

This level contains the coordination agent,which is the core of the planning architecture.Firstly,this agent receives the launch plan information and state information from the agents in the input level.Then it calculates the estimated taxiing time of aircraft based on the current state of aircraft and catapults.With a global view of the system,the coordination agent will determine the planning order of local planner based on an asynchronous planning strategy.The details will be introduced in Section 4.

(3)Path planning level

The local planner agents generate non-conflict path according to the planning order determination from the coordination level.The state of aircraft at the next moment is determined by the generated control instructions of aircraft.

(4)Execution level

The control instructions generated by the path planning level are outputted to the execution level.The actuators of aircraft execute the control instructions.The new state of aircraft is recorded and transmitted to the state information agent.Then the state of aircraft and catapults are updated.

Compared with the isolated planning architecture and the centralized planning architectures,the distributed planning architecture realizes the coordination by communicating among local planners.It is feasible and consistent with the fact that aircraft launched at different catapults belong to independent local planners.The coordination agent possesses a global view of the overall system and rationally determines the planning order of different local planner agents.

3.Establishment of mathematical model

In this section,the constraints of the mission planning problem are put into different levels of the distributed planning architecture based on the responsibility of each level,and the optimization goal is emphasized.To begin with,the launch task is divided into four steps:waiting to start,taxiing,preparations on catapult and launching process.The number of aircraft launched at C1,C2,C3and C4are denoted as N1,N2,N3and N4respectively.is defined as the ending moment of waiting to start for the nth aircraft launched at Cm(m=1,2,3,4).Similarly,anddenote the ending moment of taxiing,preparations on catapult and launching process respectively.Note that all the time parameters defined above are initialized as 0,and they will be changed after the aircraft finishes the corresponding step.

3.1.Representation of constraints in coordination level

The goal of the coordination level is to mediate the conflicts among the launch tasks belonging to different catapults.There are two types of conflicts,namely,the vortex flow effect and the collision between aircraft.The mathematical forms of constraints will be represented.

(1)Vortex flow effect

The vortex flow produced by the former aircraft during the launching process will have a bad influence on the launch safety of the following aircraft.25An aircraft can start the launch process after the preparation on catapult is completed and the vortex flow effect has disappeared.This constraint can be formulated as the following equation:

where tvortexis the moment that the vortex flow effect has disappeared,and Tlaunchis the duration of launch process.tvortexcan be further expressed as

where Tvortexis the duration of vortex flow effect.Note that the vortex flow effect can be ignored among the aircraft launching at the same catapult because Tvortexis much shorter than the time of preparation on catapult(defined as Tpre).Besides,the positions of C1and C2are far away from those of C3and C4(see Fig.1),so the vortex flow effect between the two pairs of catapults can also be neglected.The above two rules are expressed as

Eq.(3)denotes that only the two aircraft successively launching at C1and C2(or C3and C4)will be influenced by the vortex flow effect,and the index of catapults meets the equation 1+2=3 or 3+4=7.Eqs.(1)-(3)formulate the constraint of the vortex flow effect between the launch tasks belonging to different catapults,and it is the responsibility of the coordination agent to ensure the safety of launch mission in this regard.

(2)Collision between aircraft

Aircraft taxiing on the flight deck may collide with each other if no action is taken in advance,and it is also the task of the coordination agent to prevent the collision accident.The details of the collision detection method can be consulted in Ref.26.

3.2.Formulation of constraints in path planning level

In the path planning level,each local planner agent generates feasible taxiing path for the corresponding aircraft.Considering the planning area and the launch tasks belonging to the same catapult,the following two constraints must be paid attention to.

(1)Flight deck area

Aircraft must taxi on the flight deck every moment to ensure the safety.V is defined as the area of flight deck,Vi(t)(i=1,2,...,N)denotes the space which aircraft occupies at the moment t,and Ai(i=1,2,...,N)represents the aircraft.As a footnote, parameter N (N=N1+N2+N3+N4)denotes the number of aircraft,and the paths generated by the local planners must satisfy the following constraint:

The constraint in Eq.(4)guarantees that all the aircraft involved in the launch mission taxi within the boundaries of flight deck.The candidate paths exceeding the edges of flight deck will not be selected.

(2)Crowd effect

To avoid the traffic jam,aircraft are not allowed to start to taxi until the former one launching at the same catapult finishes the launch task.The constraint is expressed as

This constraint applies to the launch tasks belonging to the same catapult internally,so the local planner is in charge of the coordination among the aircraft in this regard.

3.3.Motion of aircraft taxiing in execution level

Each aircraft has independent motion model when the control instruction is executed.The motion model of aircraft is presented in Fig.3.26

The coordinate system xdOdydis established at the central axis of end flight deck;(xi,yi)is the location of aircraft on flight deck;viis the taxiing velocity;φiis the yaw angle;L is the distance between the rear wheel and front wheel;θiis the deflection angle of nose wheel.The motion of aircraft can be described by kinematic model of pedicab,which is a group of nonlinear differential equations.

In Eqs.(6)-(8),xi,yiand φiare the state of aircraft.viand θiare control instructions and are changed within a certain range of vi∈[vmin,vmax] and θi∈[θmin,θmax] respectively.Besides,the nose wheel cannot be deflected too rapidly due to its mechanical property,and ˙θi∈[0,˙θmax]must be met.Taxiing is a low-velocity motion,so no more constraint is added to the acceleration.

The time is discretized to denote the state of aircraft in this paper.The state and control instruction of aircraft No.i at the sampling time k can be denoted as

The path point Xi(k+1)can be calculated according to Eq.(11)if the control instruction input Ui(k)is determined.

Fig.3 Motion model of aircraft on flight deck.

3.4.Objective function

The goal is to minimize the overall mission time consumption.The ultimate objective function is established as follows:

(1)The distance between the aircraft and the catapult

The works of predecessors regard the distance as the goal of optimization.At the moment k,the distance between aircraft No.i and the destination can be denoted as

(2)The time consumption of taxiing

At the moment k,assume that aircraft No.i taxies with the current velocity,and the estimated time that the aircraft will spend to reach the destination can be denoted as

(3)The angle between φi(k)and the desired angle required by the launch task

φiis the yaw angle of aircraft No.i.The launch task requires the nose of aircraft to aim at the straight-ahead position of the runway.At the moment k,the angle between φi(k)and the desired angle can be denoted as

Note that Eq.(14)is significant only when Eq.(15)is met.The reason is as follows:Eq.(14)just ensures the optimal path at the moment k but does not consider the optimality of path in the following moments.Besides,Eq.(15)always makes the aircraft taxi heading to the catapult and turn as soon as possible.On this basis,aircraft can reach the catapult quickly with Eq.(14).

The objective function of path planning for aircraft No.i is a combination of above three items.It is expressed as

where ω1,ω2and ω3are the weights of each item.Different weights reflect different requirements during the path planning process.

3.5.Optimization model

Solving the mission planning problem is a continuous decisionmaking process.The idea of rolling optimization is introduced to obtain the series of control instruction and the state of aircraft.Here the discrete time interval[k,k+H-1]is considered;H is the number of discrete moment.The series of control instruction and the state of aircraft No.i are expressed as

According to Eq.(16),the objection function in discrete time interval[k,k+H-1]can be expressed as

Note that the optimization model has distributed architecture,and the taxiing path of aircraft No.i is only relevant to the local decision variable Ui,so the scale of problem is greatly reduced.When solving the problem,local planners communicate with others and get the current state information of other taxiing aircraft.Then the control instruction is generated using the distributed path planning algorithm.

4.Distributed path planning algorithm based on asynchronous planning strategy

An asynchronous planning strategy is developed to generate non-conflict paths and avoid the deadlock and the Buckets effect.Taxiing paths must be planned online to respond to dynamic environment effectively and determine the state of aircraft at each moment.Here Particle Swarm Optimization(PSO)algorithm is used to solve the distributed rolling optimization model.

4.1.Asynchronous planning strategy for online planning

The most straightforward approach to decentralize multiaircraft path planning is to allow all local planners to continuously plan their own paths subject to constraints imposed by the other local planners'paths.Here the idea of Model Predictive Control(MPC)is introduced to judge the feasibility of path in advance.Based on this thinking,it is not suitable for all the local planners working synchronously,because it can lead to deadlock.

An asynchronous planning strategy based on token passing is proposed in this paper.The idea of token-passing for mutual exclusion and access control is widespread in distributed computer systems.In the token passing strategy,a token is used to control which local planner can access the shared information,i.e.,which local planner is allowed to plan at this moment.Here the dynamic token-passing strategy is developed to satisfy the state change of aircraft.

At each sampling time k,local planner agents firstly compute the specified information and broadcast these values as bids to be the token holder.Then the coordination agent determines the token holder and the order of passing the token.All local planner agents are involved in the token holder determination process.The principle and flow of token holder determination are presented in Fig.4.

Note that if none of the aircraft which one local planner is in charge of is taxiing,the local planner is not included in the candidate token holder list.The state of corresponding aircraft can be updated before the process of token holder determination because these aircraft will not get involved in collision.In Fig.4,the local planner having the most remaining launch tasks is given the token because of the Buckets effect:the mission time consumption of the corresponding catapult is the longest and needs to be optimized according to Eq.(12).The same is true when one considers the distance between the taxiing aircraft and the catapult.In general,the token holder can deal with less constraints when one plans taxiing path,so it is more likely to result in a more optimal path.Note that the validity of the token holder is limited to a specific sampling time k,and in the next moment,all the local planners will bid for the token holder again.

Fig.4 Process of token holder determination.

After the token holder is determined,taxiing paths will be generated according to the order.The asynchronous planning strategy can avoid the deadlock and guarantee the safety of aircraft.

4.2.Solution of distributed optimization problem

The distributed path planning problem is a many-objective optimization problem with two variables in mathematical essence.Here the normal PSO algorithm is used to accelerate the convergence.The control instruction vi(k)and θi(k)are optimized at each sampling time k,and then the state of aircraft can be updated according to the motion equations(from Eqs.(6)to(8)).In the normal PSO algorithm,the control instruction is updated according to the following equations:

Ueg(l)(e=1,2,...,Np;g=1,2,...,Nd;l=1,2,...,Niter)represents the control instruction of the gth dimension of the eth particle at the lth iteration.Npis the number of particle,Ndis the number of particle dimension(in this case,Ndrefers to the length of predictive information),and Niteris the maximum number of iteration. ΔUeg(l) is the increment of control instruction.Besides,is inertia weight,c1and c2are acceleration constants,and rand1 and rand2 are random number obeyed uniform distribution in interval[0,1].Note that when an aircraft taxies,the constraint of taxiing velocity,deflection angle of nose wheel and the maximum angular velocity of nose wheel must be met.If the updated Ueg(l+1)violates any one of those constraints,it will be modified as the closest threshold.

In Eq.(20),Peg(l)is the control instruction corresponding to the personal best value of the eth particle.Pgb(l)is the control instruction corresponding to the global best value.The fitness value of each particle is calculated by Eq.(23)as follows:

When collision happens at any moment of the discrete time interval[k,k+ND-1],the fitness value of particle is set to Γ.Γ is a positive real number which has larger magnitudes than the value in Eq.(19).It means that the taxiing path which cannot avoid the obstacles must be excluded.In other cases,the algorithm selects the particle minimizing the objective function in Eq.(19).

4.3.Flow of distributed path planning algorithm

Fig.5 Flow of decision-making process of local planner j at sampling time k.

In rolling optimization process,the coordination agent firstly determines the token holder and the order of passing the token.Then the token holder calculates the optimal control instruction series using the PSO algorithm and passes the token to the next token holder.After all local planners generate the optimal control instruction series,the aircraft execute the first item only.At the sampling time k,the flow of the distributed path planning algorithm performed by local planner j(j=1,2,3,4)is presented in Fig.5.

In Fig.5,the four levels of the distributed planning architecture are marked in the corresponding parts.Note that if local planner j is not the last token holder,the token must be passed to the next holder.Then the next token holder performs the flow in Fig.5 again.After all local planners have updated the state of aircraft,an iteration of the path planning algorithm ends.The distributed path planning algorithm will not be terminated until the overall launch mission is completed.

5.Experimental studies

The experiment is conducted under the given launch plan determined by the commander on the Nimitz-class aircraft carrier.The simulation environment is Windows 7 and Matlab R2009a.Two scenarios are considered,and the mission planning problem is solved by the proposed approach called Mission Planning Approach for Carrier Aircraft Launching(MPACAL).The first scenario is basic;two aircraft start to taxi simultaneously towards their destinations.Under the distributed planning architecture,asynchronous planning strategy is adopted in the path planning algorithm, and its validity is verified by comparing to the synchronous planning strategy.In the second scenario,14 aircraft are involved in the launch mission.Comparison is made among the Isolated Architecture Based Method(IABM),the Centralized Architecture Based Method(CABM)and the MPACAL method.

5.1.Scenario 1:mission of 2 aircraft launched at 2 catapults

The setup of this scenario is presented in Fig.6.According to the launch plan,A I and A II are assigned to launch at C1and C2respectively.They start to taxi simultaneously and are likely to collide with each other if there is no interaction between them.Coordination is needed to guarantee the efficiency and safety of launch mission.The parameter settings are presented in Table 1.Note that the parameters of PSO in this paper are set according to the experience of Ref.27.

Fig.6 Setup of scenario 1.

Table 1 Parameter settings of path planning algorithm in scenario 1(1 ft=0.3048 m).

Firstly,the synchronous planning strategy is adopted.The result is presented in Fig.7.

The two aircraft only change their positions when t=1 s.In the rest of time,using their predictive information,they stay still and wait the other to go first.The deadlock makes the launch mission unable to be completed.

Fig.7 State of A I and A II(from t=0 s to t=10 s)using synchronous planning strategy.

Fig.8 State of A I and A II(from t=0 s to t=9 s)using asynchronous planning strategy.

Fig. 9 Velocity instructions of local planners using asynchronous planning strategy.

Fig. 10 Complete taxiing paths of A I and A II using asynchronous planning strategy.

Next,the asynchronous planning strategy will be applied.The principle of token holder determination is named the longer distance-based token passing and has been explained in Section 4.1.The results are presented in Figs.8 and 9.

Using the longer distance-based token passing principle,A II stops at the moment t=4 s,because local planner 1 is the first token holder at that moment,local planner 2 must take into account the state of A I both at the moment t=3 s and t=4 s when planning.Using the predictive information,local planner 2 judges that if A II goes on taxiing,A I and A II will collide with each other at the next moment.Therefore,A II stops and restarts at the moment t=9 s.Finally,both A I and A II spend 33 s to reach the corresponding catapult.

Compared to the synchronous planning strategy,the asynchronous planning strategy is able to strengthen the interaction among local planners and avoid the deadlock in planning.This is because the local planners(except for the first token holder)have mastered the real state of aircraft(for the next moment).Therefore,the local planners use more real information rather than predictive information to plan the path.In the synchronous planning strategy,more predictive information is taken into account,and it may cause the deadlock and make the launch mission unable to be completed.Therefore,the synchronous planning strategy is not suitable for solving the proposed mission planning problem and the asynchronous planning strategy results in a higher possibility of generating more optimal paths.The complete taxiing paths of A I and A II are shown in Fig.10.

Next,the convergence of the PSO algorithm which is used to obtain the taxiing paths will be discussed.Note that the maximum iteration times is set as 50 in this scenario,and the convergence times for each step of path planning is shown in Fig.11.

It can be seen from Fig.11 that in most of the steps,the PSO algorithm can converge within 20 times of iterations,which are fast and satisfy the demand of online planning.Note that the values of convergence times are 0 at some steps because the aircraft is still at those moments,and the corresponding convergence times is set as 0.

5.2.Scenario 2:mission planning for 14 aircraft launched at 4 catapults

A more complicated scenario was designed to test the validity of the MPACAL method.There are 14 aircraft parking on the flight deck.The diagram of the experimental model and the given launch plan are shown in Fig.12 and Table 2.

Fig.11 Convergence times of A I and A II in each step of path planning.

Note that the launch plan is determined by the command center on the carrier,and the determination of launch plan is a decision-making problem belonging to upper level of flight deck operation.The launch plan information is the input level of the distributed architecture,and the launch position and order of each aircraft are included.For example,the order of aircraft launching at C1is A4,A6and A5.The values of most parameters are the same as those in scenario 1.The settings of other parameters in scenario 2 are listed in Table 3,and the values of Tvortex,Tpreand Tlaunchtake Ref.28as a reference.

According to the launch plan and parameter setting,the IABM,the CABM and the MPACAL are used to solve the mission planning problem.Note that,in the centralized architecture,the objective function of taxiing path is written as

The control instruction ziand the state siof each aircraft can be obtained by solving Eq.(24).The constraints and parameter setting are the same when the above three methods are adopted.The three methods were independently run ten times under the same initial conditions.The results are summarized in Table 4.

TCC1 means the Time Consumption on C1.The same is true for TCC2,TCC3 and TCC4.OTC is short for‘‘Overall Consumption Time”,and ETEI denotes the Elapsed Time of Each Iteration in path planning algorithm.In Table 4,the results of TCC1,TCC2,TCC3,TCC4,OTC and ETEI are the average of ten independent runs.The results denoted by percentage are the probabilities that the corresponding event happens in ten independent runs.The best results of each item among the three methods are in bold.

Fig.12 Setting up of Scenario 2.

Table 2 Launch position and order of each aircraft.

Table 3 Parameter settings in Scenario 2.

Table 4 Comparison among IABM, CABM and DCMPAAL.

Note that TCC1,TCC2,TCC3 and TCC 4 are intermediate results to show the workload of catapult,and the final results,i.e.OTC,can be obtained by selecting the maximum among the four intermediate results in one independent run.Compared to IABM and CABM,aircraft can finish the launch mission successfully and safely using the MPACAL method.Aircraft collide with others or are influenced by the vortex flow effect with high probability when IABM is used,as shown in Fig.13.

In Fig.13,A7is taxiing to C3and has a collision with A5when t=9 s regardless of the current state of other aircraft.The aircraft influenced by the vortex flow effect are for the same reason.This is because,in the isolated architecture,each sub-planner plans the taxiing path for a single aircraft.Lacking of communication with other independent sub-planners will make the launch mission unsafe,thus resulting in collision and vortex flow effect.

Different from the experiment results of IABM,aircraft fail to reach the destination using the CABM.The best result in ten independent runs is presented in Fig.14.

In the experiments,the terminal condition of path planning for each aircraft is set that the distance between the aircraft and the destination is less than 2 ft in the x direction.In Fig.14,the final positions of 7 aircraft deviate from the destination,and all wrong paths miss the destinations in the y direction.The reason is that,in the centralized architecture,a single objective function is used to generate taxiing path for each aircraft.However,different attentions are paid in different stages of taxiing.For example,ω1and ω2are set larger values when the distance between the taxiing aircraft and the destination is relatively long;ω3is set a larger value to make sure the nose of aircraft align the runway when aircraft is near the destination.Therefore,when one taxiing aircraft is near the destination,a larger value of ω3will lead to the fact that other taxiing aircraft make their noses align the runway in advance.In general,aircraft are in different stages of taxiing,so it is very hard to coordinate the state of each aircraft with the CABM.

Fig.13 Collision happens when t=9 s using IABM.

Fig.14 The best results with centralized architecture.

Among the three methods,the OTC is approximately the same,and the ETEI of CABM is the longest,which is a disadvantage in real-time planning.To sum up,the launch mission can be completed efficiently and safely with the MPACAL method,while aircraft fail to complete the launch mission with the IABM and CABM.The proposed MPACAL method shows its advantages in avoiding the collision,the influence of vortex flow effect and the deviation from the destination.Besides,compared to the CABM,the MPACAL method has shorter computational time and is suitable for online planning.

5.3.Detailed results and discussion of scenario 2 with MPACAL method

The above results show the deficiency of two planning architectures.The best result using the MPACAL method in ten independent runs is represented in Figs.15 and 16.They are the taxiing paths and the time histories of aircraft respectively.

Fig.15 The best result of taxiing paths using MPACAL.

Fig.16 Time histories of aircraft corresponding to Fig.9.

In Fig.15,all aircraft can taxi to the catapult.According to Fig.16,aircraft go through four stages before finishing the launch tasks.Note that the aircraft starts to taxi immediately when the former one launching at the same catapult finishes launching.This practice saves the mission time consumption and realizes the coordination among the launch tasks belonging to the same catapult.As a whole,most aircraft begin the launching process immediately when the preparation on catapult is completed.Exceptionally,A7,A8and A10launching at C3wait extra time because A14finishes the preparation on catapult one second earlier than A7,and A7must wait before the influence of vortex flow dies away.The same circumstance happens to A8and A10.The distributed planning architecture has advantage in coordinating the launch tasks belonging to different catapults and ensures the safety of launch mission.Besides,four aircraft taxiing to four different catapults start simultaneously when t=0 s,and the mission time consumptions from C1to C4are 521 s,476 s,621 s and 605 s respectively,which are approximate and reasonable in balancing the workload and the use efficiency among catapults.In summary,the overall mission time consumption for 14 aircraft is 621 s(the average time for each aircraft is 44.4 s)and satisfies the requirement of the time consumptions for a wave of sortie mentioned in Ref.29(the time interval between two consecutive launch tasks is about 39 s with the success rate of 50%).

For a single aircraft,the taxiing time only accounts for a small proportion of the launch task time consumption.Aircraft usually have to wait in the original parking position and on the catapult.These two processes occupy most of the launch task time and are fixed in the operation of launch task.3,30Therefore,the optimization of taxiing path does not make a big contribution to the efficiency improvement of a single aircraft's launch task.Compared to the IABM and CABM,the efficiency and safety of launch mission for multi-aircraft are enhanced mainly by the coordination,e.g.collision,taxiing path,vortex flow effect and crowd effect.Under the current work efficiency of catapult,the proposed distributed planning architecture and MPACAL method are able to shorten the overall mission time consumption and guarantee the mission safety.

Fig.17 State of aircraft when t=15,200,400,600 s.

In Fig.15,the taxiing paths only show two-dimensional information about the paths of aircraft. To display the dynamic state of aircraft on the flight deck,the states of aircraft at some particular moments are presented in Fig.17.

When t=15 s,the flight deck is busy.A4,A1,A7and A14are taxiing towards their destinations respectively.As time goes on,more and more aircraft finish launching,and the flight deck becomes empty gradually.When t=600 s,A10and A11remain and are making preparations on catapults.To sum up,the states of aircraft are in accordance with the time histories shown in Fig.16.More details of the launch mission are provided and make a supplement to the results.

6.Conclusions

(1)A novel distributed planning architecture is proposed to deal with the mission planning problem for a team of carrier aircraft launching in this paper.

(2)The mathematical model for mission planning is established based on the constraints in different levels of the distributed planning architecture.

(3)The distributed path planning algorithm is developed,and an asynchronous planning strategy which can avoid the deadlock and Buckets effect is adopted.

(4)The results show that the distributed planning architecture has advantages in coordinating the launch tasks not only belonging to the same catapult but also when all different catapults are considered.