A space-time cooperative guidance method considering energy optimization

Abstract

The application discloses a kind of space-time coordination guidance method considering energy optimization, comprising: setting end time constraint;Set guidance instruction expression, including accurate interception item, angle of fall constraint item and time constraint item in guidance instruction;Based on end time constraint, accurate interception item is obtained using optimal control method;Based on accurate interception item, the heading angle of end time is predicted, and angle error is obtained, optimal error dynamics equation is used to eliminate angle error, and angle of fall constraint item is obtained;Based on accurate interception item and time constraint item, end interception time is predicted, and time error is obtained, optimal error dynamics equation is used to eliminate time error, and time constraint item is obtained;According to accurate interception item, angle of fall constraint item and time constraint item, obtain the guidance instruction of vehicle, and vehicle flies according to guidance instruction.The method disclosed in the application is based on optimal error dynamics, while meeting the expected time and angle of fall constraint, the optimal control energy is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of space-time collaborative guidance method considering energy optimization, belong to aircraft control technical field. BACKGROUND

[0002] In many working conditions, aircraft guidance needs to meet both end time constraints and interception time constraints, for example, multi-aircraft terminal constraint intersection docking problem.

[0003] Existing aircraft multi-constraint guidance methods, such as guidance methods based on sliding mode control theory, have high requirements for aircraft acceleration capability and performance in multi-constraint intersection docking.

[0004] Therefore, it is necessary to further study the existing space-time collaborative constraint guidance method to solve the above problems. SUMMARY

[0005] To overcome the above problems, the present application has been studied in depth, and a space-time collaborative guidance method considering energy optimization is proposed, comprising:

[0006] S1, setting end time constraints;

[0007] S2, setting guidance instruction expression, including precise interception term, angle of fall constraint term and time constraint term in guidance instruction;

[0008] S3, based on end time constraints, using optimal control method to obtain precise interception term;

[0009] S4, based on the precise interception term to predict the end time heading angle, and obtain the angle error, using optimal error dynamics equation to eliminate the angle error, and obtain the angle of fall constraint term;

[0010] S5, based on the above precise interception and angle of fall constraint instruction term, predict the remaining flight time, and obtain the time error, using optimal error dynamics equation to eliminate the time error, and obtain the time constraint term;

[0011] S6, according to the precise interception term, angle of fall constraint term and time constraint term, obtain the guidance instruction of aircraft, and the aircraft flies according to the guidance instruction.

[0012] In a preferred embodiment, in S1, the end time constraints include zero-control miss distance constraints, angle of fall constraints and time constraints,

[0013] The zero-control miss distance constraint is expressed as:

[0014] z(r f )=0

[0015] where z denotes the zero-effort miss distance, r f denotes the distance between the vehicle and the target at the terminal time;

[0016] The impact angle constraint is expressed as:

[0017] |θ f | = θ imp

[0018] θ f denotes the heading angle at the terminal time, θ imp denotes the desired terminal heading angle.

[0019] The time constraint is expressed as:

[0020] t f = t d

[0021] t f denotes the terminal time, t d denotes the desired terminal time.

[0022] In one preferred embodiment, in S2, the guidance command expression is expressed as

[0023] a = a P + a IA + a IT

[0024] where a denotes the guidance command, a P denotes the precise intercept term, a IA denotes the impact angle constraint term, a IT denotes the time constraint term.

[0025] In one preferred embodiment, in S3, the optimal control problem is set to minimize the total energy consumption of the flight, expressed as:

[0026]

[0027] z(r f ) = 0

[0028] where J denotes the energy during the flight, r denotes the distance between the vehicle and the target, r0 denotes the initial distance between the vehicle and the target, r f denotes the distance between the vehicle and the target at the terminal time, V denotes the speed of the vehicle, and N denotes a constant.

[0029] In one preferred embodiment, the precise intercept term a P is:

[0030]

[0031] In a preferred embodiment, in S4, the predicted end-time heading angle is represented as:

[0032]

[0033] In a preferred embodiment, the angle error is represented as:

[0034] ε a = θ imp - θ f

[0035] In a preferred embodiment, the impact angle constraint term is represented as:

[0036]

[0037] In a preferred embodiment, in S4, the predicted remaining flight time is represented as:

[0038]

[0039] In a preferred embodiment, the time error is represented as:

[0040] ε t = t d - t go - t

[0041] In a preferred embodiment, the time constraint term is represented as:

[0042]

[0043] In a preferred embodiment, in S6, the guidance command of the aircraft is represented as:

[0044]

[0045] The beneficial effects of the present application include:

[0046] (1) Under the premise of ensuring accurate interception, different impact angles and time constraints can be met.

[0047] (2) Compared with other classic guidance methods, less energy consumption and lower acceleration ability are required. BRIEF DESCRIPTION OF DRAWINGS

[0048] Figure 1 A flowchart of a time-space collaborative guidance method considering energy optimization according to a preferred embodiment of the present application is shown;

[0049] Figure 2 The trajectory curve of the aircraft in Example 1 is shown;

[0050] Figure 3 Acceleration curve for the aircraft in Example 1 is shown;

[0051] Figure 4 Yaw angle curve for the aircraft in Example 1 is shown;

[0052] Figure 5 Pitch angle curve for the aircraft in Example 1 is shown;

[0053] Figure 6 Angle error curve for the aircraft in Example 1 is shown;

[0054] Figure 7 Time error curve for the aircraft in Example 1 is shown;

[0055] Figure 8 Remaining flight time curve for the aircraft in Example 1 is shown;

[0056] Figure 9 Control energy curve for the aircraft in Example 1 is shown;

[0057] Figure 10 Trajectory curve for the aircraft in Example 2 is shown;

[0058] Figure 11 Acceleration curve for the aircraft in Example 2 is shown;

[0059] Figure 12 Yaw angle curve for the aircraft in Example 2 is shown;

[0060] Figure 13 Pitch angle curve for the aircraft in Example 2 is shown;

[0061] Figure 14 Angle error curve for the aircraft in Example 2 is shown;

[0062] Figure 15 Time error curve for the aircraft in Example 2 is shown;

[0063] Figure 16 Remaining flight time curve for the aircraft in Example 2 is shown;

[0064] Figure 17 Control energy curve for the aircraft in Example 2 is shown;

[0065] Figure 18 Trajectory curve for the aircraft in Example 3 is shown;

[0066] Figure 19 Acceleration curve for the aircraft in Example 3 is shown;

[0067] Figure 20A heading angle curve of the aircraft in Example 3 is shown;

[0068] Figure 21 A pre-angle curve of the aircraft in Example 3 is shown;

[0069] Figure 22 An angle error curve of the aircraft in Example 3 is shown;

[0070] Figure 23 A time error curve of the aircraft in Example 3 is shown;

[0071] Figure 24 A remaining flight time curve of the aircraft in Example 3 is shown;

[0072] Figure 25 A control energy curve of the aircraft in Example 3 is shown. DETAILED DESCRIPTION

[0073] The application will be further described below in detail with the aid of the drawings and examples. The features and advantages of the application will become more apparent from these descriptions.

[0074] The word "exemplary" is used herein to mean "serving as an example, instance, or illustration." Any implementation described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other implementations. Although various aspects of an implementation can be described herein with reference to a limited number of drawings, these aspects can be modified in various, equivalent ways.

[0075] A time-space cooperative guidance method considering energy optimization is provided according to the application, as shown in the accompanying drawings, comprising: Figure 1

[0076] S1, setting an end time constraint;

[0077] S2, setting a guidance instruction expression, the guidance instruction comprising a precise interception term, a landing angle constraint term and a time constraint term;

[0078] S3, based on the end time constraint, using an optimal control method to obtain the precise interception term;

[0079] S4, based on the precise interception term, predicting the end time heading angle and obtaining the angle error, using an optimal error dynamics equation to eliminate the angle error and obtain the landing angle constraint term;

[0080] S5, based on the above-mentioned precise interception and landing angle constraint instruction terms, predicting the remaining flight time and obtaining the time error, using an optimal error dynamics equation to eliminate the time error and obtain the time constraint term;

[0081] S6, obtaining the guidance instruction of the aircraft according to the precise interception term, the landing angle constraint term and the time constraint term, and the aircraft flying according to the guidance instruction.​

[0082] In S1, the terminal time constraint comprises a zero-control miss distance constraint, a landing angle constraint and a time constraint.

[0083] The zero-control miss distance constraint is expressed as:

[0084] z(r f )=0

[0085] wherein z represents the zero-control miss distance, r f represents the distance between the vehicle and the target at the terminal time.

[0086] Preferably, the terminal time constraint comprises a landing angle constraint, which is expressed as:

[0087] |θ f |=θ imp

[0088] wherein θ f represents the heading angle at the terminal time, and θ imp represents the desired terminal heading angle.

[0089] Preferably, the terminal time constraint further comprises a time constraint, which is expressed as:

[0090] t f =t d

[0091] wherein t f represents the terminal time, and t d represents the desired terminal time.

[0092] In S2, a guidance command expression is set, which comprises a precise interception term, a landing angle constraint term and a time constraint term.

[0093] Preferably, the guidance command expression is expressed as

[0094] a=a P +a IA +a IT

[0095] wherein a represents the guidance command, a P represents the precise interception term, a IA represents the landing angle constraint term, and a IT represents the time constraint term.

[0096] In the present application, the precise interception term is set to ensure that the vehicle can achieve precise interception, the landing angle constraint term is set to ensure that the vehicle can meet the landing angle constraint, and the time constraint term is set to ensure that the vehicle can meet the time constraint.

[0097] In the application, by setting the precise interception term, the angle of fall constraint term and the time constraint term, the guidance instruction can meet the precise interception condition, the specific angle of fall constraint and the time constraint.

[0098] In S3, the precise interception term a P Based on the optimal control method.

[0099] Further, in the optimal control method, based on the end time constraint, the optimal control problem is set to minimize the total energy consumption of flight, which is expressed as:

[0100]

[0101] z(r f )=0

[0102] Wherein, J represents the energy in the flight process, r represents the distance between the aircraft and the target, r0 represents the initial distance between the aircraft and the target, r f represents the distance between the aircraft and the target at the end time, V represents the speed of the aircraft, and N represents a constant.

[0103] According to the above optimal control problem, the precise interception term a P :

[0104]

[0105] In S4, the end time heading angle is predicted based on the precise interception term, the angle error is obtained, the optimal error dynamics equation is used to eliminate the angle error, and the angle of fall constraint term is obtained.

[0106] Unlike the traditional relative motion equation, in the application, the relative motion equation is expressed as:

[0107]

[0108]

[0109] Wherein, λ represents the line of sight angle of the aircraft.

[0110] The traditional relative motion equation is generally expressed as:

[0111]

[0112] In the application, based on the guidance feature that the distance r between the aircraft and the target decreases with time, the geometric relationship is obtained:

[0113] η=θ-λ

[0114] η∈(-(π / 2),(π / 2))

[0115] Using the above geometric relationships, the traditional relative motion equations are reduced in dimension to obtain the aforementioned relative motion equations.

[0116] Furthermore, based on precise interception item a P Substituting into the equations of relative motion, we get:

[0117]

[0118] Integrating both sides of the equation, we get:

[0119] θ f -θ(r)=N(λ f -λ(r))

[0120] By combining precise interception parameters, the terminal heading angle is predicted and obtained:

[0121]

[0122] The angle error ε a Represented as:

[0123] ε a =θ imp -θ f

[0124] The optimal error dynamics equation is expressed as:

[0125]

[0126] Where K is a constant whose value satisfies K≥1.

[0127] Based on the optimal error dynamics equation, the angle error ε can be obtained. a The parsing expression:

[0128]

[0129] Where, ε a0 This represents the angle error at the initial moment.

[0130] Furthermore, by differentiating the angle error, we obtain:

[0131]

[0132] Comprehensive angular error εa The analytical expression is used to obtain the landing angle constraint term a. IA :

[0133]

[0134] In S5, based on the above-mentioned accurate interception and impact angle constraint instruction item, the remaining flight time is predicted, the time error is obtained, the optimal error dynamics equation is used to eliminate the time error, and the time constraint item is obtained;

[0135] Based on the accurate interception item a P And the impact angle constraint instruction item a IA , the derivative of the pre-angle relative to the angle error can be obtained by substituting the relative motion equation:

[0136]

[0137] Assuming that the pre-angle is small during flight, tanη≈η is satisfied, and the above formula is approximately:

[0138]

[0139] Integrating both sides of the equation can obtain:

[0140]

[0141] The remaining flight time expression is:

[0142]

[0143] Based on the accurate interception item a P And the impact angle constraint instruction item a IA , the remaining flight time estimation expression is obtained:

[0144]

[0145] Deriving the equation with respect to time t can obtain:

[0146]

[0147] Assuming that the pre-angle η is small during flight, cosη≈1-η 2 / 2, sinη≈η is satisfied, and the following can be obtained:

[0148]

[0149] For ease of writing, let

[0150] The time error ε t is expressed as:

[0151] ε t =t d -t go -t

[0152] The optimal error dynamics equation is expressed as:

[0153]

[0154] wherein M is a constant, and the value of M satisfies M≥1.

[0155] According to the optimal error dynamics equation, an analytical expression of the angle error εt can be obtained as follows:

[0156]

[0157] wherein ε t0 is the time error at the initial time.

[0158] Further, by taking the derivative of the time error, we can obtain:

[0159]

[0160] By combining the analytical expression of the residual error ε t , the time constraint term a IT is obtained as follows:

[0161]

[0162] To avoid the phenomenon of command divergence when δ→0, an auxiliary function Ψ(|δ|) is added, which satisfies:

[0163]

[0164] By combining the auxiliary function, the time constraint term a IT is obtained as follows:

[0165]

[0166] S6, according to the precise interception term, the angle of fall constraint term and the bias term, the guidance command of the spacecraft is obtained, which is expressed as:

[0167]

[0168] It should be understood that the various forms of the flow shown above can be used to reorder, add or delete steps. For example, each step described in the present disclosure can be executed in parallel, sequentially or in a different order, as long as the desired results of the technical solutions of the present disclosure can be achieved, which is not limited herein.

[0169] Embodiment

[0170] Embodiment 1

[0171] The guidance simulation experiment is carried out, including:

[0172] S1, setting the end time constraint;

[0173] S2, set the guidance instruction expression, the guidance instruction includes the accurate interception item, the landing angle constraint item and the time constraint item;

[0174] S3, based on the terminal time constraint, the optimal control method is adopted to obtain the accurate interception item;

[0175] S4, based on the accurate interception item, the terminal time heading angle is predicted, and the angle error is obtained, the optimal error dynamics equation is used to eliminate the angle error, and the landing angle constraint item is obtained;

[0176] S5, based on the above accurate interception and landing angle constraint instruction item, the remaining flight time is predicted, and the time error is obtained, the optimal error dynamics equation is used to eliminate the time error, and the time constraint item is obtained;

[0177] S6, according to the accurate interception item, the landing angle constraint item and the time constraint item, the guidance instruction of the aircraft is obtained, and the aircraft flies according to the guidance instruction.

[0178] In S1, the terminal time constraint includes zero control off-target quantity constraint, landing angle constraint and time constraint,

[0179] The zero control off-target quantity constraint is expressed as:

[0180] z(r f )=0

[0181] The landing angle constraint is expressed as:

[0182] |θ f |=θ imp

[0183] The time constraint is expressed as:

[0184] t f =t d

[0185] In S2, the guidance instruction expression is expressed as

[0186] a=a P +a IA +a IT

[0187] In S3, the optimal control problem is set to minimize the total energy consumption of flight, which is expressed as:

[0188]

[0189] z(r f )=0

[0190] The accurate interception item a P obtained is:

[0191]

[0192] In S4, the predicted end-time heading angle is represented as:

[0193]

[0194] The angle error is represented as:

[0195] ε a = θ imp - θ f

[0196] The time constraint term is represented as:

[0197]

[0198] In S5, the predicted remaining flight time is represented as:

[0199]

[0200] The time error is represented as:

[0201] ε t = t d - t go - t

[0202] The time constraint term is represented as:

[0203]

[0204] In S6, the guidance command of the aircraft is represented as:

[0205]

[0206] In the simulation process, N = 3, K = 2, M = 2, and δ0= 10° in the auxiliary function. The impact of different time constraints on the aircraft is verified by selecting the impact angle constraint θ imp as 90°. The simulation results are shown in FIGS. 1-8. Figures 2-9

[0207] wherein, Figure 2 FIG. 1 shows the trajectory curve of the aircraft, Figure 3 FIG. 2 shows the acceleration curve of the aircraft, Figure 4 FIG. 3 shows the heading angle curve of the aircraft, Figure 5 FIG. 4 shows the pre-angle curve of the aircraft, Figure 6 FIG. 5 shows the angle error curve of the aircraft, Figure 7 FIG. 6 shows the time error curve of the aircraft, Figure 8 FIG. 7 shows the remaining flight time curve of the aircraft, Figure 9 and FIG. 8 shows the control energy curve of the aircraft. From Figures 2-9 ​As can be seen, the aircraft can guarantee perfect interception under different time constraints, meet specific angle of impact constraints, and the guidance commands are always bounded throughout the flight.

[0208] Example 2

[0209] The same experiment as in Example 1 was conducted, except that the time constraint was set to 35 seconds and the landing angle constraint to θ during the simulation. imp The effects of different field-of-view constraints on the aircraft were verified by selecting 80°, 90°, 100°, 110°, and 120° respectively. The simulation results are as follows: Figures 10-17 As shown.

[0210] in, Figure 10 The trajectory curve of the aircraft is shown. Figure 11 The acceleration curve of the aircraft is shown. Figure 12 The heading angle curve of the aircraft is shown. Figure 13 The aircraft's lead angle curve is shown. Figure 14 The angular error curve of the aircraft is shown. Figure 15 The time error curve of the aircraft is shown. Figure 16 The remaining flight time curve of the aircraft is shown. Figure 17 The control energy curve of the aircraft is shown.

[0211] from Figures 10-17 As can be seen, considering different angles of impact, the aircraft can achieve precise interception while meeting specific time constraints. Throughout the entire flight process, the guidance commands remain bounded.

[0212] Example 3

[0213] The same experiment as in Example 1 was conducted, except that during the simulation, four aircraft were set to intercept the same target, the target's location was (10000m, 0m), the speed of the four aircraft was 400m / s, the desired time constraint was 35 seconds, and the initial states of the four aircraft were shown in Table 1:

[0214]

[0215]

[0216] Figure 18 The trajectory curve of the aircraft is shown. Figure 19 The acceleration curve of the aircraft is shown. Figure 20 The heading angle curve of the aircraft is shown. Figure 21 The aircraft's lead angle curve is shown. Figure 22 The angular error curve of the aircraft is shown. Figure 23 The time error curve of the aircraft is shown.Figure 24 a remaining flight time curve of the aircraft is shown, Figure 25 a control energy curve of the aircraft is shown.

[0217] It can be seen from Figures 18-25 that in the case of four aircrafts intercepting the same target, the four aircrafts can achieve accurate interception of the same target for different initial conditions, meet the preset time constraint and the expected impact angle constraint. Throughout the flight process, the guidance instruction always remains bounded. At the end time, the angle error and the time error converge to zero.

[0218] The above describes the present application in combination with the preferred embodiments, but these embodiments are only exemplary and serve only to illustrate. On this basis, various substitutions and improvements can be made to the present application, which all fall within the protection scope of the present application.

Claims

1. A space-time cooperative guidance method considering energy optimization, characterized in that, The method comprises the following steps: S1, setting an end time constraint; S2, setting a guidance instruction expression, the guidance instruction comprising a precise interception term, a landing angle constraint term and a time constraint term; S3, based on the end time constraint, a precise interception term is obtained by using an optimal control method; S4, based on the precise interception term, a heading angle at the end time is predicted, an angle error is obtained, an optimal error dynamics equation is used to eliminate the angle error, and a landing angle constraint term is obtained; S5, based on the precise interception term and the landing angle constraint term, a remaining flight time is predicted, a time error is obtained, an optimal error dynamics equation is used to eliminate the time error, and a time constraint term is obtained; S6, according to the precise interception term, the landing angle constraint term and the time constraint term, a guidance instruction of a spacecraft is obtained, and the spacecraft flies according to the guidance instruction; In S2, the guidance instruction expression is expressed as: ； wherein, represents a guidance command, represents a precise interception term, represents a fall angle constraint term, represents a time constraint term; In S3, an optimal control problem is set with the minimum total energy consumption of flight as the target, and is expressed as: ； wherein, represents the energy during flight, represents the distance between the aircraft and the target, represents the initial distance between the aircraft and the target, represents the distance between the aircraft and the target at the terminal time instant, represents the speed of the aircraft, represents a constant, represents the zero-control miss distance, represents the distance between the aircraft and the target at the terminal time instant; In S3, the acquired accurate interception item is: ； wherein denotes the rake angle; In S4, the landing angle constraint term is expressed as: ； wherein is a constant, is an angular error; In S5, the time constraint term is expressed as: ； ； ； wherein , is an auxiliary function, is a constant, is a time error.

2. The time-space cooperative guidance method considering energy optimization according to claim 1, characterized in that, In S1, the end time constraint comprises a zero-control miss distance constraint, a landing angle constraint and a time constraint, The zero-control miss distance constraint is expressed as: ； The landing angle constraint is expressed as: ； a heading angle representing the terminal time, a desired terminal heading angle; The time constraint is expressed as: ； representing a terminal time, representing a desired terminal time.

3. The time-space cooperative guidance method considering energy optimization according to claim 1, characterized in that, In S4, the prediction of the heading angle at the end time is expressed as: 。 4. The time-space cooperative guidance method considering energy optimization according to claim 1, characterized in that, In S4, the angle error is expressed as: 。

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