Unmanned aerial vehicle flight scheduling method based on stochastic programming

Abstract

The invention discloses an unmanned aerial vehicle flight scheduling method based on stochastic programming, and the method comprises the steps: obtaining the operation time deviation value of an entrance unmanned aerial vehicle and a departure unmanned aerial vehicle; the uncertainty of the running time deviation value of the entering and leaving unmanned aerial vehicles is quantified; and establishing an optimal scheduling random opportunity constraint model of the entering and leaving unmanned aerial vehicles, and calculating the optimal scheduling moment, the sequence, the take-off and landing field and the time slot distribution scheme of the unmanned aerial vehicles by using the uncertainty corresponding to the operation time deviation. According to the invention, a probability distribution method is used to fit the predicted approach time and departure time deviation of the unmanned aerial vehicle in historical operation data; according to the method, an unmanned aerial vehicle optimization scheduling random chance constraint model considering the prediction uncertainty of the approach time and the departure time is established, an unmanned aerial vehicle take-off and landing time sequence closer to the actual situation is generated, the deviation between the predicted take-off and landing time and the actual take-off and landing time can be reduced, the problem of unmanned aerial vehicle delay in the actual operation process is solved, and the unmanned aerial vehicle take-off and landing efficiency is improved. And the effectiveness of the unmanned aerial vehicle scheduling means is enhanced.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of low-altitude unmanned aerial vehicle sequencing and scheduling, and particularly relates to an unmanned aerial vehicle flight scheduling method based on random programming. BACKGROUND

[0002] Currently, the main reasons for unmanned aerial vehicle delay are weather, traffic control, mechanical failure, passenger factors, unmanned aerial vehicle deployment and unmanned aerial vehicle cutting in; some of these reasons can be predicted, and some cannot. The terminal area is an important airspace resource, and the mismatch between demand and capacity is a prominent cause of unmanned aerial vehicle congestion and delay. Unmanned aerial vehicle scheduling optimization is beneficial to fully utilize the available capacity resources of the terminal area and the landing and taking-off field, and reduce unmanned aerial vehicle delay. In actual operation of unmanned aerial vehicles, various factors exist, which lead to uncertainty in the operation time of the unmanned aerial vehicles entering and leaving the field, thereby bringing certain difficulty to the unmanned aerial vehicle operation management decision. Therefore, unmanned aerial vehicle scheduling optimization is helpful to fully utilize the available capacity of the terminal area and the landing and taking-off field, thereby reducing unmanned aerial vehicle delay.

[0003] Trajectory Based Operation (TBO) based on four-dimensional trajectory is based on the four-dimensional trajectory of the aircraft, shares trajectory information among air traffic control departments, airlines and aircraft, realizes trajectory negotiation between pilots and the ground, time constraint negotiation, accurately controls the flight trajectory and interval management of the aircraft, and can improve the time accuracy of the aircraft arriving at the expected point from the minute level to the ten-second level. Through early prediction of the flight trajectory of the aircraft, the conflict in the flight process of the aircraft can be reduced, and the congestion degree of the en route and terminal airspace can be reduced. Therefore, the operation based on the four-dimensional trajectory not only can increase the air traffic flow, but also can make the aircraft fly more smoothly and improve the unmanned aerial vehicle operation status.

[0004] Most related researches are based on deterministic scenarios, and the uncertainty factors affecting the unmanned aerial vehicle operation at the airport have begun to enter the field of view of researchers. More and more unmanned aerial vehicle operation optimization researches considering uncertainty have gradually emerged. The methods for dealing with uncertain optimization problems include random programming method, fuzzy programming method, robust optimization method, etc. The selection of the method depends on the information that can be obtained, the characteristics of the problem and the decision-making angle of the decision maker. The researches on the uncertainty of the entering and leaving time in China mainly focus on the analysis and prediction of unmanned aerial vehicle delay. In recent years, the prediction of unmanned aerial vehicle delay under the influence of weather has been focused on. The researches on the quantification of traffic demand uncertainty at home and abroad mainly focus on the prediction of sector probability traffic demand, and a small number of researches predict the probability traffic demand of the airport.

[0005] At present, a prominent cause of terminal area UAV congestion and delay is the mismatch between traffic and capacity, and the long-term effective method to alleviate delay is to expand airport infrastructure and improve overall airspace capacity, which requires a large amount of money and time cost, but this method may not be feasible in some airspace capacity that has reached saturation; and for aircraft with different flight routes, the four-dimensional trajectory information is different, but for a regular UAV, the four-dimensional trajectory information changes every day with weather, load and cruise altitude, resulting in dynamic and uncertain four-dimensional trajectory (4DT) of the aircraft; in addition, in daily operation, various uncertain factors such as weather factors, airline factors, air traffic control intervention and other factors will also cause the UAV operation to have uncertainty, which will bring difficulty to air traffic operation management. SUMMARY

[0006] In view of the above technical problems of the prior art, the purpose of the present application is to provide a UAV flight scheduling method based on random programming, using a probability distribution method to fit the predicted approach time and departure time deviation of the UAV in the historical operation data; a UAV optimization scheduling random chance constraint model considering the uncertainty of approach time and departure time prediction is established to generate a UAV take-off and landing time sequence that is more consistent with the actual occurrence, which can reduce the deviation between the predicted take-off and landing time and the actual take-off and landing time, to solve the UAV delay problem in actual operation and enhance the effectiveness of UAV scheduling means.

[0007] To achieve the above purpose, the technical scheme adopted by the present application is as follows:

[0008] The UAV flight scheduling method based on random programming of the present application comprises the following steps:

[0009] 1) Obtain the operation time deviation value of the approach and departure UAVs;

[0010] 2) Quantify the uncertainty of the operation time deviation value of the approach and departure UAVs;

[0011] 3) Establish an approach and departure UAV optimization scheduling random chance constraint model, and calculate the optimal scheduling time, sequencing, take-off and landing field and time slot allocation scheme of the UAV using the uncertainty corresponding to the operation time deviation.

[0012] Further, the step 1) specifically comprises:

[0013] Obtain the UAV operation data of a certain period of time, extract the predicted take-off and landing time of the approach and departure UAVs and the actual take-off and landing time , and calculate to obtain the operation time deviation value of the UAV , the expression is as follows:

[0014] .

[0015] Further, the step 2) specifically comprises:

[0016] The running time deviation value obtained in step 1) is statistically modeled by using a probability distribution fitting method to quantify the uncertainty of the running time deviation, and the specific process is as follows:

[0017] 21) Construct a running time deviation sample set ;

[0018] 22) Fit the distribution of all deviation data to obtain that all deviation data follow a normal distribution;

[0019] 23) The maximum likelihood estimation method is used to estimate the parameters of the data to obtain the normal distribution parameters: mean and standard deviation ;

[0020] 24) Use the Kolmogorov-Smirnov test to verify the normal distribution result. If the normal distribution result obtained in step 23) passes the test, go to step 25);

[0021] 25) According to the normal distribution result, determine the approach inverse cumulative distribution function and the departure inverse cumulative distribution function , complete the quantification of the approach and departure unmanned aerial vehicle running time deviation value uncertainty, obtain the key parameters describing the deviation distribution characteristics, including: mean , standard deviation , approach inverse cumulative distribution function and departure inverse cumulative distribution function .

[0022] Further, the step 3) specifically comprises:

[0023] An unmanned aerial vehicle optimization scheduling stochastic chance constraint model is constructed with the objective of minimizing the unmanned aerial vehicle delay cost, with the unmanned aerial vehicle sequencing, take-off and landing site allocation, safety interval and time slot scheduling as constraint conditions, and the uncertainty corresponding to the running time deviation value is input into the model for calculation, and the specific process is as follows:

[0024] 31) Construct an unmanned aerial vehicle delay cost minimization objective function;

[0025] The objective function is to minimize the total delay cost, which includes: approach unmanned aerial vehicle delay cost and departure unmanned aerial vehicle delay cost ; the expression of the objective function is as follows:

[0026] ;

[0027] where, is the optimized arrival time of approach drone m, is the planned arrival time of approach drone m, is the operation time deviation of approach drone, is the optimized departure time of departure drone n, is the planned departure time of departure drone n, is the operation time deviation of departure drone n, is the set of approach drones, is the set of departure drones, , , is the unit delay cost of approach drone, is the unit delay cost of departure drone, is to minimize the delay cost of approach and departure drones;

[0028] 32) Set the drone flight sequencing constraint;

[0029] The drone flight sequencing constraint is performed to ensure that any two drones have a unique order on the same landing field, expressed as follows:

[0030] ;

[0031] where, is to indicate that approach drone m is ahead of departure drone n, is to indicate that departure drone n is ahead of approach drone m; indicates that approach drone m is ahead of departure drone n; indicates that approach drone m is behind departure drone n; represents the set of all approach drones and departure drones,

[0032] 33) Set the landing field allocation constraint;

[0033] The landing field allocation constraint is performed to ensure that each drone is allocated only one landing field, expressed as follows:

[0034] ;

[0035] where, represents the set of all available landing fields, is an indication variable, indicating whether drone m is allocated to landing field r, indicates that drone m is allocated to landing field r;

[0036] 34) Set safety separation constraints;

[0037] Perform approach inter-UAV safety separation constraints as follows:

[0038] ;

[0039] where, is the optimized arrival time of the approach UAV m, is the optimized arrival time of the departure UAV n, is the minimum safety time slot between the approach UAV m and the departure UAV n, is a positive number set for proper constraints;

[0040] Perform departure inter-UAV safety separation constraints as follows:

[0041] ;

[0042] where, is the optimized departure time of the departure UAV m, is the optimized departure time of the departure UAV n, is the minimum safety time slot between the departure UAV m and n;

[0043] Perform approach and departure inter-UAV safety separation constraints as follows:

[0044] ;

[0045] where, is the safety separation between the approach UAV m and the departure UAV n;

[0046] Perform departure and approach inter-UAV safety separation constraints as follows:

[0047] ;

[0048] where, is the safety separation between the departure UAV n and the approach UAV m;

[0049] 35) Set stochastic chance constraints;

[0050] Approach UAV m stochastic chance constraints are as follows:

[0051] ;

[0052] where, is the approach confidence level; is the expected arrival time of the approach UAV m, is the operational time deviation of the approach UAV m;

[0053] The random chance constraint for the departure UAV n is as follows:

[0054] ;

[0055] where, is the departure confidence level; is the predicted departure time of the departure UAV n, is the operation time deviation of the departure UAV n;

[0056] Extract the operation time deviation of the arrival UAV and the operation time deviation of the departure UAV , and fit the probability distribution to the deviation data to obtain the normal distribution parameters: mean and standard deviation ;

[0057] The random chance constraint expression for the arrival UAV is as follows:

[0058] ;

[0059] The random chance constraint expression for the departure UAV is as follows:

[0060] ;

[0061] Using the arrival inverse cumulative distribution function , the arrival confidence level is converted into a deterministic constant, and the deterministic constraint of the arrival UAV is as follows:

[0062] ;

[0063] Using the departure inverse cumulative distribution function , the departure confidence level is converted into a deterministic constant, and the deterministic constraint of the departure UAV is as follows:

[0064] ;

[0065] 36) Set the time slot scheduling constraint;

[0066] Perform time slot allocation constraint, the expression is as follows:

[0067] ;

[0068] where, , indicates whether the UAV m is allocated to the time slot , if the UAV m is allocated to the time slot , then =1; denotes all the UAVs set;

[0069] Intra-slot runtime constraint is performed to ensure the optimized takeoff and landing time of the UAVs within the allocated time slot, expressed as follows:

[0070]

[0071] wherein, denotes the set of time slots, which represents the discretization of the entire scheduling period into a set of time slots; denotes the time slot start time, denotes the length of each time slot, denotes the optimized runtime of the UAV m;

[0072] Slot capacity constraint is performed to prevent multiple UAVs from being scheduled within the same time slot, expressed as follows:

[0073]

[0074] 37) Constructing the random chance-constrained model for the optimized scheduling of the arrival and departure UAVs;

[0075] Integrating the objective function and the constraints constructed in steps 31) to 36) into the random chance-constrained model for the optimized scheduling of the arrival and departure UAVs, and obtaining the optimal scheduling time, sequence, takeoff and landing field, and time slot allocation scheme of the UAVs by solving the model;

[0076] The objective function of the random chance-constrained model for the optimized scheduling of the arrival and departure UAVs is as follows:

[0077]

[0078] wherein, denotes the delay cost of the arrival UAVs; denotes the delay cost of the departure UAVs; denotes the total delay cost target value, denotes the minimum value of the delay cost of the arrival and departure UAVs; denotes the unit delay cost of the arrival UAVs; denotes the unit delay cost of the departure UAVs; denotes the optimized arrival time of the arrival UAV m; denotes the planned arrival time of the arrival UAV m; denotes the optimized takeoff time of the departure UAV n; denotes the planned takeoff time of the departure UAV n; denotes the arrival confidence level a deterministic constant obtained by converting the inverse cumulative distribution function, used to offset the safety interval requirement; ​​​Indicates the confidence level for exiting the market. The deterministic constants obtained through the transformation of the inverse cumulative distribution function.

[0079] Furthermore, the stochastic chance constraints for the optimized scheduling of arriving and departing UAVs in step 37) include:

[0080] 371) The drone sorting constraints are as follows:

[0081] ;

[0082] in, As an indicator variable, if drone m is listed before drone n, then Otherwise, it is 0; As an indicator variable, if drone n is listed before drone m, then Otherwise, it is 0; This represents the set of all drones. In the drone sorting constraint, for any two drones on the same landing field, it is guaranteed that one of them must be listed before the other.

[0083] 372) The constraints for the allocation of takeoff and landing fields are as follows:

[0084] ;

[0085] in, As an indicator variable, if the UAV m is assigned to the takeoff and landing field r, then Otherwise, it is 0; This represents the set of all available takeoff and landing sites; the takeoff and landing site allocation constraints must ensure that each UAV is assigned to only one takeoff and landing site;

[0086] 373) The safety interval constraints are as follows:

[0087] ;

[0088] in, This indicates the optimized arrival time of the approaching drone m. The optimized arrival time for the approaching drone n, The minimum safe time slot between the approaching drones m and n, A positive number is set to be used for appropriate constraints; when hour Taking 0 means the constraint is strictly enforced; when hour Set to 1, relax the constraints, and let A represent the set of all incoming drones; the safety interval constraint must ensure that the optimized arrival time interval is not less than the specified minimum safety time slot;

[0089] 374) The time constraints within a time slot are as follows:

[0090] ;

[0091] ;

[0092] wherein, is the start time of the time slot, is the length of each time slot, represents the optimal operation time of the unmanned aerial vehicle m; is an indicator variable, which represents whether the unmanned aerial vehicle m is assigned to the time slot , if the unmanned aerial vehicle m is assigned to the time slot , then =1; represents the set of all unmanned aerial vehicles; is a large positive number, which makes the constraint unconstrained when ; is the set of time slots; the operation time constraint in the time slot represents that the start time determined to be assigned to the time slot t is not higher than the optimal time of the unmanned aerial vehicle m and the optimal operation time of the unmanned aerial vehicle m does not exceed the end time determined to be assigned to the time slot t.

[0093] The beneficial effects of the present application are:

[0094] 1. The present application uses historical data to obtain uncertainty parameters that truly reflect operation deviation through normal distribution fitting, so that the scheduling optimization is more in line with the actual operation law.

[0095] 2. In the present application, the random chance constraint converts operation uncertainty into specific numerical constraints, which guarantees that the take-off and landing time of the unmanned aerial vehicle meets the safety requirements under the preset confidence level, greatly reduces the probability of delay occurrence, and ensures the flight safety of the unmanned aerial vehicle.

[0096] 3. The present application comprehensively considers the sequencing of the unmanned aerial vehicle, the allocation of the take-off and landing site, the safety interval and the time slot scheduling, realizes the scientific allocation of the take-off and landing site resources, and ensures the flight safety.

[0097] 4. In the present application, the model parameters can be flexibly adjusted according to different take-off and landing sites and operation environments, and have high universality and application value. BRIEF DESCRIPTION OF DRAWINGS

[0098] Figure 1 is the principle diagram of the method of the present application. DETAILED DESCRIPTION

[0099] In order to facilitate the understanding of those skilled in the art, the present application will be further described below in conjunction with the embodiments and the drawings. The content mentioned in the embodiments is not a limitation of the present application.

[0100] Referring to Figure 1As shown, a random programming-based UAV flight scheduling method of the application has the following steps:

[0101] 1) Obtain the operation time deviation value of the approaching and departing UAVs; specifically including:

[0102] Obtain the UAV operation data in a certain time period, extract the expected take-off and landing time of the approaching and departing UAVs and the actual take-off and landing time , and calculate to obtain the operation time deviation value of the UAV , which is expressed as follows:

[0103] .

[0104] 2) Quantify the uncertainty of the operation time deviation value of the approaching and departing UAVs; specifically including:

[0105] The operation time deviation value obtained in step 1) is statistically modeled by using a probability distribution fitting method to quantify the uncertainty of the operation time deviation, and the specific process is as follows:

[0106] 21) Construct an operation time deviation sample set ;

[0107] 22) Perform distribution fitting on all deviation data to obtain that all deviation data follow a normal distribution;

[0108] 23) Perform parameter estimation on the data by using the maximum likelihood estimation method to obtain the normal distribution parameters: mean and standard deviation ;

[0109] 24) Verify the normal distribution result by using the Kolmogorov-Smirnov test. If the normal distribution result obtained in step 23) passes the test, proceed to step 25);

[0110] 25) According to the normal distribution result, determine the approaching inverse cumulative distribution function and the departing inverse cumulative distribution function , complete the quantification of the operation time deviation value uncertainty of the approaching and departing UAVs, and obtain the key parameters describing the deviation distribution characteristics, including: mean , standard deviation , approaching inverse cumulative distribution function and departing inverse cumulative distribution function .

[0111] 3) Establish an optimal scheduling random chance constraint model for the approaching and departing UAVs, and calculate the optimal scheduling time, sequence, take-off and landing field and time slot allocation scheme of the UAVs by using the uncertainty corresponding to the operation time deviation.

[0112] wherein, the step 3) specifically comprises:

[0113] A random chance constraint model of the UAV optimization scheduling is constructed with the objective of minimizing the UAV delay cost, with the UAV sequencing, landing site allocation, safety interval and time slot scheduling as constraint conditions, and the uncertainty corresponding to the running time deviation value is input into the model for calculation, specifically as follows:

[0114] 31) Constructing a UAV delay cost minimization objective function;

[0115] The objective function is to minimize the total delay cost, which includes: approach UAV delay cost and departure UAV delay cost ; The objective function expression is as follows:

[0116] ;

[0117] wherein, is the optimized arrival time of approach UAV m, is the planned arrival time of approach UAV m, is the running time deviation of approach UAV, is the optimized take-off time of departure UAV n, is the planned take-off time of departure UAV n, is the running time deviation of departure UAV n, is the set of approach UAVs, is the set of departure UAVs, , , is the unit delay cost of approach UAV, is the unit delay cost of departure UAV, is the minimum approach and departure UAV delay cost;

[0118] 32) Setting the UAV flight sequencing constraint;

[0119] The UAV flight sequencing constraint is performed to ensure that any two UAVs have a unique sequence on the same landing site, and the expression is as follows:

[0120] ;

[0121] wherein, is to indicate that approach UAV m is in front of departure UAV n, is to indicate that departure UAV n is in front of approach UAV m; indicates that approach UAV m is in front of departure UAV n; represents that the approaching UAV m is behind the departing UAV n; represents the set of all approaching and departing UAVs,

[0122] 33) Set the landing site assignment constraints;

[0123] The landing site assignment constraints are performed to ensure that each UAV is assigned only one landing site, expressed as follows:

[0124] ;

[0125] where, represents the set of all available landing sites, is an indicator variable that represents whether the UAV m is assigned to the landing site r, represents that the UAV m is assigned to the landing site r;

[0126] 34) Set the safety interval constraints;

[0127] The safety interval constraints between approaching UAVs are performed as follows:

[0128] ;

[0129] where, is the optimized arrival time of the approaching UAV m, is the optimized arrival time of the departing UAV n, is the minimum safety time slot between the approaching UAV m and the departing UAV n, is a positive number set to perform appropriate constraints;

[0130] The safety interval constraints between departing UAVs are performed as follows:

[0131] ;

[0132] where, is the optimized departure time of the departing UAV m, is the optimized departure time of the departing UAV n, is the minimum safety time slot between the departing UAV m and n;

[0133] The safety interval constraints between approaching and departing UAVs are performed as follows:

[0134] ;

[0135] where, is the safety interval between the approaching UAV m and the departing UAV n;

[0136] The safety interval constraints between departing and approaching UAVs are performed as follows:

[0137] ;

[0138] wherein, is the safety separation between the approaching UAV n and the departing UAV m;

[0139] 35) setting a random chance constraint;

[0140] The approaching UAV m random chance constraint is as follows:

[0141] ;

[0142] wherein, is the approaching confidence level; is the expected arrival time of the approaching UAV m, is the operation time deviation of the approaching UAV m;

[0143] The departing UAV n random chance constraint is as follows:

[0144] ;

[0145] wherein, is the departing confidence level; is the expected takeoff time of the departing UAV n, is the operation time deviation of the departing UAV n;

[0146] Extracting the operation time deviation of the approaching UAV and the operation time deviation of the departing UAV , and fitting the deviation data with a probability distribution to obtain the normal distribution parameters: mean and standard deviation ;

[0147] The approaching UAV random chance constraint expression is as follows:

[0148] ;

[0149] The departing UAV random chance constraint expression is as follows:

[0150] ;

[0151] Using the approaching inverse cumulative distribution function , the approaching confidence level is converted into a deterministic constant, and the approaching UAV deterministic constraint is as follows:

[0152] ;

[0153] Using the departing inverse cumulative distribution function , the departing confidence level The deterministic constant is converted to get the off-site UAV deterministic constraint as follows:

[0154] ;

[0155] 36) Set the time slot scheduling constraint;

[0156] The time slot allocation constraint is performed, and the expression is as follows:

[0157] ;

[0158] wherein, , indicates whether the UAV m is allocated to the time slot , if the UAV m is allocated to the time slot , then =1; indicates the set of all UAVs;

[0159] The time slot internal running time constraint is performed to ensure that the optimized take-off and landing time of the UAV is located within the allocated time slot, and the expression is as follows:

[0160] ;

[0161] wherein, is a set of time slots, indicating that the entire scheduling period is discretely divided into a set of time slots; is the time slot start time, is the length of each time slot, is the optimized running time of the UAV m;

[0162] The time slot capacity limit is performed to prevent multiple UAVs from being arranged in the same time slot, and the expression is as follows:

[0163] ;

[0164] 37) Construct the random chance constraint model of the approach and off-site UAV optimization scheduling;

[0165] The objective function and constraint conditions constructed in steps 31) to 36) are integrated into the random chance constraint model of the approach and off-site UAV optimization scheduling, and by solving the model, the optimal scheduling time, sequence, take-off and landing site, and time slot allocation scheme of the UAV are obtained;

[0166] The objective function of the random chance constraint model of the approach and off-site UAV optimization scheduling is as follows:

[0167] ;

[0168] wherein, indicates the delay cost of the approach UAV;

[0169] denotes the delay cost of the departure UAVs; denotes the total delay cost target value, denotes the minimum value of the arrival and departure UAVs delay cost; is the unit delay cost of the arrival UAVs; is the unit delay cost of the departure UAVs; denotes the optimized arrival time of the arrival UAV m; denotes the planned arrival time of the arrival UAV m; denotes the optimized departure time of the departure UAV n; denotes the planned departure time of the departure UAV n; denotes the arrival confidence level is a certainty constant obtained by converting the inverse cumulative distribution function, used to offset the safety interval requirement; denotes the departure confidence level is a certainty constant obtained by converting the inverse cumulative distribution function.

[0170] Specifically, the random chance constraint conditions of the arrival and departure UAVs in the step 37) include:

[0171] 371) The UAV sequencing constraint is as follows:

[0172] ;

[0173] wherein, is an indicator variable, if the UAV m is sequenced before the UAV n, then , otherwise 0; is an indicator variable, if the UAV n is sequenced before the UAV m, then , otherwise 0; denotes the set of all UAVs; in the UAV sequencing constraint, for any two UAVs on the same landing field, it is ensured that one of them is sequenced before the other;

[0174] 372) The landing field allocation constraint is as follows:

[0175] ;

[0176] wherein, is an indicator variable, if the UAV m is allocated to the landing field r, then , otherwise 0; denotes the set of all available landing fields; the landing field allocation constraint needs to ensure that each UAV is allocated to only one landing field;

[0177] 373) The safety interval constraint is as follows:

[0178] ;

[0179] wherein, denotes the optimized arrival time of the approaching UAV m, denotes the optimized arrival time of the approaching UAV n, denotes the minimum safety time slot between the approaching UAV m and n, denotes a positive number set for proper constraint; when 0 is taken, the constraint is strictly implemented; when 1 is taken, the constraint is relaxed, and A denotes the set of all approaching UAVs; the safety interval constraint needs to ensure that the interval between the optimized arrival times is not less than the specified minimum safety time slot; 374) The time-in-slot constraint is as follows:

[0180] 374) The time-in-slot constraint is as follows:

[0181] ;

[0182] ;

[0183] wherein, denotes the start time of the time slot, denotes the length of each time slot, denotes the optimized running time of the UAV m; denotes an indicator variable, which indicates whether the UAV m is assigned to the time slot , if the UAV m is assigned to the time slot , then =1; denotes the set of all UAVs; denotes a sufficiently large positive number, which makes the constraint have no effect when ; denotes the set of time slots; the time-in-slot constraint indicates that the start time assigned to the time slot t is not higher than the optimized time of the UAV m, and the optimized running time of the UAV m does not exceed the end time assigned to the time slot t.

[0184] The present application has many specific application approaches, and the above description is only the preferred embodiment of the present application. It should be pointed out that, for ordinary skilled in the art, without departing from the principles of the present application, a number of improvements can be made, and these improvements should also be considered as the protection scope of the present application.​

Claims

1. A method for scheduling unmanned aerial vehicle (UAV) flight based on stochastic programming, characterized in that, The steps are as follows: 1) Obtain the operation time deviation value of the approach and departure unmanned aerial vehicles; 2) Quantify the uncertainty of the operation time deviation value of the approach and departure unmanned aerial vehicles; 3) Establish an optimal scheduling stochastic chance constraint model for the approach and departure unmanned aerial vehicles, and calculate the optimal scheduling time, sequence, take-off and landing site, and time slot allocation scheme of the unmanned aerial vehicles by using the uncertainty of the operation time deviation. 2.The random planning based UAV flight scheduling method of claim 1, wherein, The step 1) specifically includes: Obtain the unmanned aerial vehicle operation data in a certain period of time, extract the expected take-off and landing time of the unmanned aerial vehicle and the actual take-off and landing time , and calculate to obtain the operation time deviation value of the unmanned aerial vehicle , and the expression is as follows: 。 3.The random planning based UAV flight scheduling method of claim 2, wherein, The step 2) specifically includes: The operation time deviation value obtained in step 1) is statistically modeled by using a probability distribution fitting method to quantify the uncertainty of the operation time deviation, and the specific process is as follows: 21) Constructing a set of run-time bias samples ; 22) Perform distribution fitting on all deviation data to obtain that all deviation data follow a normal distribution; 23) Parameters estimation of data by using maximum likelihood estimation method, get normal distribution parameters: mean and standard deviation ; 24) Verify the normal distribution result by using Kolmogorov-Smirnov test, if the normal distribution result obtained in step 23) passes the test, then go to step 25); 25) Determine the approach inverse cumulative distribution function from the normal distribution result and the departure inverse cumulative distribution function , complete the quantification of the approach, departure UAV operation time deviation value uncertainty, get the key parameters describing the deviation distribution characteristics, including: mean , standard deviation , approach inverse cumulative distribution function and the departure inverse cumulative distribution function .

4. The random planning based UAV flight scheduling method of claim 3, wherein, The step 3) specifically includes: An optimal scheduling stochastic chance constraint model for the unmanned aerial vehicles is constructed, with the minimum unmanned aerial vehicle delay cost as the target, and the unmanned aerial vehicle sequence, take-off and landing site allocation, safety interval, and time slot scheduling as the constraint conditions, and the uncertainty corresponding to the operation time deviation value is input into the model for calculation, and the specific process is as follows: 31) Construct a minimum unmanned aerial vehicle delay cost objective function; The objective function is to minimize the total delay cost, which includes: approach UAV delay cost and departure UAV delay cost The objective function expression is as follows: ； wherein, is the optimized arrival time for the approach unmanned aircraft m, is the planned arrival time for the approach unmanned aircraft m, is the operating time deviation for the approach unmanned aircraft, is the optimized departure time for the departure unmanned aircraft n, is the planned departure time for the departure unmanned aircraft n, is the operating time deviation for the departure unmanned aircraft n, is the set of approach unmanned aircraft, is the set of departure unmanned aircraft, , , is the unit delay cost for the approach unmanned aircraft, is the unit delay cost for the departure unmanned aircraft, is the minimum approach and departure unmanned aircraft delay cost; 32) Set the unmanned aerial vehicle flight sequence constraint; The unmanned aerial vehicle flight sequence constraint is performed to ensure that any two unmanned aerial vehicles have a unique sequence on the same take-off and landing site, and the expression is as follows: ； wherein, to represent the case where the approach drone m is in front of the departure drone n, to represent the case where the departure drone n is in front of the approach drone m; to represent the case where the approach drone m is in front of the departure drone n; to represent the case where the approach drone m is behind the departure drone n; representing the set of all approach drones and departure drones, 33) Set the take-off and landing site allocation constraint; The take-off and landing site allocation constraint is performed to ensure that each unmanned aerial vehicle is allocated only one take-off and landing site, and the expression is as follows: ； wherein, denotes the set of all available landing sites, is an indicator variable denoting whether the drone m is assigned to the landing site r, denotes that the drone m is assigned to the landing site r; 34) Set the safety interval constraint; The safety interval constraint between the approach unmanned aerial vehicles is performed as follows: ； wherein, is the optimized arrival time of the inbound drone m, is the optimized arrival time of the outbound drone n, is the minimum safety time slot between the inbound drone m and the outbound drone n, is a positive number set for making proper constraints; The safety interval constraint between the departure unmanned aerial vehicles is performed as follows: ； wherein, toptakeoffm is the optimized take-off time of the unmanned aircraft m, toptakeoffn is the optimized take-off time of the unmanned aircraft n, tmin is the minimum safety time slot between the unmanned aircraft m and n; The safety interval constraint between the approach and departure unmanned aerial vehicles is performed as follows: ； wherein, is the safety separation between the approaching drone m and the departing drone n; The safety interval constraint between the departure and approach unmanned aerial vehicles is performed as follows: ； wherein, is the safety separation between the approaching drone n and the departing drone m; 35) Set the stochastic chance constraint; The approach unmanned aerial vehicle m stochastic chance constraint is as follows: ； wherein, is an approach confidence level; is a predicted arrival time of the approach drone m, is a run time deviation of the approach drone m; The departure unmanned aerial vehicle n stochastic chance constraint is as follows: ； wherein, is a departure confidence level; is a predicted takeoff time of the departure UAV n, is a run time deviation of the departure UAV n; Extracting run time deviation of incoming drones and outgoing drones and fitting a probability distribution to the deviation data to obtain normal distribution parameters: mean and standard deviation ; The approach unmanned aerial vehicle stochastic chance constraint expression is as follows: ； The departure unmanned aerial vehicle stochastic chance constraint expression is as follows: ； Utilizing an approach inverse cumulative distribution function The approach confidence level is converted to a deterministic constant, resulting in the following approach UAV deterministic constraint: ； Utilizing an offsite inverse cumulative distribution function The offsite confidence level is converted to a deterministic constant, resulting in the offsite drone deterministic constraint as follows: ； 36) Set the time slot scheduling constraint; The time slot allocation constraint is performed, and the expression is as follows: ； wherein , indicates whether the drone m is assigned to the time slot , if the drone m is assigned to the time slot then = 1; The time slot internal operation time constraint is performed to ensure that the optimal take-off and landing time of the unmanned aerial vehicle is located within the allocated time slot, and the expression is as follows: ； wherein, is a set of time slots, representing the entire scheduling period is discretely divided into a plurality of time slots; is a time slot start time, is a length of each time slot, is an optimal operation time of the unmanned aerial vehicle m; The time slot capacity limit is performed to prevent multiple unmanned aerial vehicles from being arranged in the same time slot, and the expression is as follows: ； 37) Construct the approach and departure unmanned aerial vehicle optimal scheduling stochastic chance constraint model; The objective function and constraint conditions constructed in steps 31) to 36) are integrated into the approach and departure unmanned aerial vehicle optimal scheduling stochastic chance constraint model, and by solving the model, the optimal scheduling time, sequence, take-off and landing site, and time slot allocation scheme of the unmanned aerial vehicles are obtained; The objective function of the approach and departure unmanned aerial vehicle optimal scheduling stochastic chance constraint model is as follows: ； wherein, represents the delay cost of the approach drone; represents the delay cost of the departure UAV; represents the total delay cost target value, represents the minimum value of the arrival and departure UAV delay cost; is the unit delay cost of the arrival UAV; is the unit delay cost of the departure UAV; represents the optimized arrival time of the arrival UAV m; is the planned arrival time of the arrival UAV m; is the optimized departure time of the departure UAV n; is the planned departure time of the departure UAV n; represents the arrival confidence level a certainty constant obtained by conversion through the inverse cumulative distribution function, used to offset the safety interval requirement; represents the departure confidence level a certainty constant obtained by conversion through the inverse cumulative distribution function.

5. The random planning based UAV flight scheduling method of claim 4, wherein, The approach and departure unmanned aerial vehicle optimal scheduling stochastic chance constraint conditions in step 37) include: 371) The unmanned aerial vehicle sequence constraint is as follows: ； wherein, is an indicator variable that is 1 if drone m precedes drone n in the ordering, and 0 otherwise; is an indicator variable that is 1 if drone n precedes drone m in the ordering, and 0 otherwise; is an indicator variable that is 1 if drone m precedes drone n in the ordering, and 0 otherwise; is an indicator variable that is 1 if drone n precedes drone m in the ordering, and 0 otherwise; denotes the set of all drones; in the drone ordering constraint, for any two drones on the same landing site, it is guaranteed that one of them precedes the other in the ordering; 372) The take-off and landing site allocation constraint is as follows: ； wherein, is an indicator variable, if the drone m is assigned to the landing site r, otherwise 0; denotes the set of all available landing sites; the landing site assignment constraint needs to ensure that each drone is assigned to only one landing site; 373) The safety interval constraint is as follows: ； in, This indicates the optimized arrival time of the approaching drone m. The optimized arrival time of the approaching drone n, The minimum safe time slot between the approaching drones m and n, A positive number is set to be used for appropriate constraints; when hour Taking 0 means the constraint is strictly enforced; when hour Set to 1, relax the constraints, and let A represent the set of all incoming drones; the safety interval constraint must ensure that the optimized arrival time interval is not less than the specified minimum safety time slot; 374)The in-slot run-time constraints are as follows: ； ； wherein, is the start time of the time slot, is the length of each time slot, denotes the optimized running time of the drone m; is an indicator variable denoting whether the drone m is assigned to the time slot , if the drone m is assigned to the time slot , then = 1; is a sufficiently large positive number, when the constraint has no effect; is the set of time slots; the running time constraint within a time slot means that the optimized time of the drone m and the optimized running time of the drone m are determined such that the start time assigned to the time slot t is not higher than the optimized time of the drone m and the optimized running time of the drone m does not exceed the end time assigned to the time slot t.

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