Polynomial guidance method considering inevitable waypoints

Abstract

The invention discloses a polynomial guidance method considering an inevitable waypoint, which comprises the following steps: establishing a polynomial relationship by taking a missile-target distance ratio as an independent variable and a field angle tangent value as a dependent variable, and obtaining a polynomial equation in combination with boundary conditions, the missile-target distance ratio being a ratio of a missile-target distance to an initial distance; a constraint condition is established, and an optimal guidance instruction is obtained in combination with a polynomial equation; and controlling the flight of the aircraft by adopting the optimal guidance instruction. According to the polynomial guidance method considering the inevitable waypoint, introduction of a small-angle linear approximation condition in a guidance system is avoided, and the precision of a track and a guidance instruction under a large-angle nonlinear condition is improved.

Description

Technical Field

[0001] This invention relates to a polynomial guidance method that takes into account necessary waypoints, belonging to the field of aircraft control technology. Background Technology

[0002] Polynomial guidance was first proposed by MIN BM et al. in 2007. Its essence is that it assumes that during the entire guidance process, a certain state variable in the state space is related to another monotonically changing state variable in a polynomial form. At this time, the changes of other states can be quantitatively obtained, thus transforming the original continuous guidance command design into the design of multiple discrete polynomial coefficients. With the initial and final states and various design requirements as constraints, it constitutes a finite-dimensional multi-parameter optimization problem.

[0003] Since state transformations under the polynomial assumption can be analytically represented in functional form, this method can simultaneously integrate various types of constraints, such as landing angle constraints, time constraints, and necessary path constraints. By setting appropriate coefficient dimensions, the problem can be transformed into a solution within the same computational framework, yielding continuous and regular guidance commands. Furthermore, by adjusting the optimization function, certain characteristics of the missile flight process can be planned to obtain the desired guidance performance; in subsequent guidance performance analysis, relevant information can also be quantitatively predicted and directly analyzed. Polynomial guidance exhibits the advantages of simplicity and strong compatibility, making it a good choice for dealing with multi-constraint guidance problems.

[0004] However, most existing studies on polynomial guidance use the remaining flight time or relative coordinates as independent variables. This is because, under the small-angle assumption, the motion model can be linearized into a simplified second-order system near the target-missile line, making the derivation of guidance commands relatively simple. However, on the one hand, the estimation accuracy is insufficient under large-angle conditions, and the guidance commands deviate from the actual needs. If the field of view is incorrectly increased to around 90°, the rate of change of the remaining flight time or relative coordinates tends to 0, which will cause singularity problems. On the other hand, since the polynomial guidance design method requires the independent variables to have strict monotonicity with respect to time during flight, when it is necessary to conduct a flanking attack on the target's rear, the independent variables will change in the opposite direction near the terminal, leading to calculation errors.

[0005] Therefore, it is necessary to conduct more in-depth research on polynomial guidance methods to solve the above problems. Summary of the Invention

[0006] To overcome the above problems, the inventors conducted in-depth research and proposed a polynomial guidance method that considers necessary waypoints, comprising the following steps:

[0007] S1. Establish a polynomial relationship with the projectile-to-target distance ratio as the independent variable and the field of view tangent as the dependent variable, and obtain a polynomial equation by combining the boundary conditions. The projectile-to-target distance ratio refers to the ratio of the projectile-to-target distance to the initial distance.

[0008] S2. Establish constraints and obtain the optimal guidance command by combining polynomial equations.

[0009] S3. The aircraft's flight is controlled by the optimal guidance command.

[0010] In a preferred embodiment, in S1, the polynomial relation is expressed as:

[0011] tanσ(η)=c1η+c2η 2 +…+c n η n

[0012] =[η η 2 …η n C

[0013] Where σ represents the field of view angle, and C = [c1 c2 … c n ] T Let c1, c2, ..., c be the coefficient matrix. n η is a coefficient, η represents the distance ratio between the projectile and the target, and n is the number of polynomial terms that can be set.

[0014] In a preferred embodiment, the boundary conditions refer to the conditions that the aircraft must comply with at the initial and final moments.

[0015] In a preferred embodiment, the obtained polynomial equation is expressed as:

[0016] tanσ0=[1 1 … 1]C

[0017]

[0018] Where λ0 represents the initial line-of-sight angle of the projectile, and θ f σ represents the desired end-collision angle, and σ0 represents the initial field of view angle.

[0019] In a preferred embodiment, in S2, the constraint conditions include a necessary waypoint constraint, which is expressed in terms of field of view and missile-target distance.

[0020] In a preferred embodiment, the necessary waypoint constraint is set as follows:

[0021]

[0022] Where, λ i η represents the line-of-sight angle of the missile at the i-th necessary waypoint.i This represents the missile-to-target distance ratio at the i-th necessary waypoint.

[0023] In a preferred embodiment, the constraints further include the aircraft terminal angle of attack, field of view, and acceleration constraints.

[0024] In a preferred embodiment, the terminal angle of attack, field of view, and acceleration constraints of the aircraft are expressed as follows:

[0025]

[0026] In a preferred embodiment, constraints are combined with polynomial equations to obtain a system of linear equations. Solving the system of linear equations yields the optimal guidance command. The system of linear equations is expressed as follows:

[0027] PC = Q

[0028] in,

[0029] n is the number of polynomial terms that can be set, and m represents the total number of waypoints that must be passed.

[0030] In a preferred embodiment, when solving for the guidance commands for the positions of necessary waypoints based on the linear equation system, the current necessary waypoint positions are discarded, and only the remaining unreached necessary waypoints and terminal conditions are used to generate the corresponding guidance commands. New constraints are added to limit the variation range of the guidance commands. These new constraints are set as follows:

[0031] a -1 =a real

[0032] Among them, a -1 This represents the guidance command corresponding to the coefficient matrix C at time t=0 of the previous calculation step, a real This indicates the guidance command actually used in the previous calculation step.

[0033] The beneficial effects of this invention include:

[0034] (1) Compared with previous studies on the constraints of necessary points, the guidance method proposed in this invention does not use complex optimization algorithms, but transforms the problem into simple linear constraints. It requires less computation, can realize online real-time computation, and has the ability to adaptively adjust.

[0035] (2) The guidance method proposed in this invention does not use a switching strategy to decompose a problem into multiple problems to be satisfied separately, but can keep each constraint condition as a whole problem to be solved, thus preserving the parsability of the guidance process;

[0036] (3) Compared with previous polynomial guidance research, the guidance method of this invention avoids the introduction of small-angle linear approximation conditions in the guidance system by designing polynomial assumptions, and improves the accuracy of trajectory and guidance commands under large-angle nonlinear conditions. Attached Figure Description

[0037] Figure 1 A schematic flowchart of a polynomial guidance method considering necessary waypoints according to a preferred embodiment of the present invention is shown.

[0038] Figure 2 The simulation results of the aircraft's flight trajectory in Example 1 are shown;

[0039] Figure 3 The simulation results of aircraft overload in Example 1 are shown;

[0040] Figure 4 The simulation results of the aircraft's track angle change in Example 1 are shown;

[0041] Figure 5 The simulation results of the distance between the aircraft and each necessary point of passage and the terminal miss distance are shown in Example 1. Detailed Implementation

[0042] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Through these descriptions, the features and advantages of the present invention will become clearer and more apparent.

[0043] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments. Although various aspects of embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless specifically indicated otherwise.

[0044] According to the present invention, a polynomial guidance method considering necessary waypoints is provided, such as... Figure 1 As shown, it includes the following steps:

[0045] S1. Establish a polynomial relationship with the ratio of projectile to target distance as the independent variable and the tangent of the field of view as the dependent variable, and obtain the polynomial equation by combining the boundary conditions;

[0046] S2. Establish constraints and obtain the optimal guidance command by combining polynomial equations.

[0047] S3. The aircraft's flight is controlled by the optimal guidance command.

[0048] In S1, the projectile-to-target distance ratio refers to the ratio of the projectile-to-target distance R to the initial distance R0. Using the projectile-to-target distance ratio as the independent variable ensures the monotonicity of the independent variable.

[0049] Using the tangent of the field of view as the dependent variable makes it easier to handle constraints.

[0050] The polynomial relation is expressed as:

[0051] tanσ(η)=c1η+c2η 2 +…+c n η n

[0052] =[η η 2 …η n C

[0053] Where σ represents the field of view angle, and C = [c1 c2 … c n ] T Let c1, c2, ..., c be the coefficient matrix. n η is a coefficient, η represents the distance ratio between the projectile and the target, and n is the number of polynomial terms that can be set.

[0054] The boundary conditions refer to the conditions that the spacecraft must meet at the initial and final moments, and are expressed as:

[0055] R(t0)=R0, λ(t0)=λ0, σ(t0)=σ0;

[0056] R(t f )=0,λ(t f )=θ f ,σ(t f ) = 0

[0057] Where t0 represents the initial time, t f Let R() represent the relative distance between the projectile and the target as a function of time, λ() represent the line-of-sight angle between the projectile and the target as a function of time, σ() represent the field of view angle as a function of time, R0 represent the relative distance between the projectile and the target at the initial time, λ0 represent the line-of-sight angle between the projectile and the target at the initial time, and θ represent the terminal time. f σ represents the desired end-collision angle, and σ0 represents the initial field of view angle.

[0058] Furthermore, the state vector is set according to the polynomial relation.

[0059]

[0060] Establish the state space:

[0061]

[0062] in, V represents the rate of change of the state vector with respect to η. m a represents the speed of the aircraft. m This indicates the normal overload of the aircraft.

[0063] Based on the boundary conditions, the state vectors at the initial and final times have:

[0064]

[0065] Where X(1) represents the initial state vector value and X(0) represents the terminal state vector value.

[0066] Combining the state space, we obtain the polynomial equation, which is expressed as:

[0067] tanσ0=[1 1 … 1]C

[0068]

[0069] Where λ0 represents the initial line-of-sight angle of the projectile, and θ f Let σ0 represent the desired end-collision angle, σ0 represent the initial field of view angle, and C = [c1 c2 … c3]. n ] T Let c1, c2, ..., c be the coefficient matrix. n is a coefficient.

[0070] In S2, the constraints include waypoint constraints, which are expressed in terms of field of view and missile-target distance:

[0071]

[0072] Where t1, t2, ..., t m This represents the time it takes for the aircraft to reach different waypoints, where m represents the total number of waypoints, and R1, R2, ..., R... m The relative distances between missiles and targets at different necessary waypoints are represented by λ1, λ2, ..., λ. m The line-of-sight angle of the missile at different necessary waypoints.

[0073] Based on the state space, the necessary waypoint constraints are set as follows:

[0074]

[0075] Where, λ i η represents the line-of-sight angle of the missile at the i-th necessary waypoint. i This represents the missile-to-target distance ratio at the i-th necessary waypoint.

[0076] The constraints also include constraints on the aircraft's terminal angle of attack, field of view, and acceleration, expressed as follows:

[0077]

[0078] Among them, a m(0) indicates that the normal overload of the aircraft at the terminal moment.

[0079] Combining the state space, the terminal angle of attack, field of view, and acceleration constraints of the aircraft are expressed as follows:

[0080]

[0081] According to the present invention, constraints are combined with polynomial equations to obtain a system of linear equations, and the optimal guidance command is obtained by solving the system of linear equations.

[0082] The system of linear equations can be expressed as:

[0083]

[0084] It can be abbreviated as PC = Q

[0085] in,

[0086] n is the number of polynomial terms that can be set, and m represents the total number of waypoints that must be passed.

[0087] The linear equations proposed in this invention can analytically represent the guidance process without linear approximation. Compared with the polynomial guidance of the linearized model, it has higher computational accuracy, can cope with large track angle changes, can constrain the field of view to not approach 90°, avoid singularity problems, and only has requirements on the initial velocity direction of the target, enabling all-round strikes on the target at the terminal.

[0088] It can be proven through theoretical derivation that the equation has a solution, and the coefficient matrix C can be obtained:

[0089] C = P -1 Q

[0090] Preferably, to enable the guidance commands to have real-time adaptive adjustment capabilities to cope with possible interference, target maneuvers, and other situations during flight, the current position can always be regarded as the guidance starting point and the coefficient matrix can be recalculated at each step.

[0091] σ→σ0, λ→λ0,

[0092] By combining the polynomial equations and letting n = m + 3, we can obtain the precise value of the guidance command required by the aircraft at the starting point, i.e., η = 1, which can be expressed as:

[0093]

[0094] in

[0095]

[0096] tanσ=[1 1 … 1]P -1 Q

[0097] The inventors discovered that although the guidance commands for the entire flight process can be obtained directly by solving a system of linear equations, the coefficient matrix C and the corresponding guidance commands tend to diverge when the flight passes through a necessary waypoint. Overload will cause drastic jumps, which seriously affect the smoothness of the guidance trajectory and the controllability of the projectile.

[0098] In this invention, during the process of solving for the guidance commands based on the linear equations to determine the positions of necessary waypoints, the current necessary waypoint positions are discarded, and only the remaining unreached necessary waypoints and terminal conditions are used to generate the corresponding guidance commands. Simultaneously, to avoid abrupt changes in guidance commands due to changes in guidance conditions, new constraints are added to limit the range of variation in guidance commands.

[0099] The new constraint is set as follows:

[0100] a -1 =a real

[0101] Among them, a -1 This represents the guidance command corresponding to the coefficient matrix C at time t=0 of the previous calculation step, a real This indicates the guidance command actually used in the previous calculation step.

[0102] The new constraints are transformed into a linear relationship, expressed as:

[0103]

[0104] Where, σ -1 This represents the field of view state at the previous calculation step.

[0105] More preferably, to add constraints, n = m + 4 is set, and the current target state is no longer used as the initial state, but the target state of the previous calculation step is used as the initial state.

[0106] After adding new constraints, solving the polynomial equation yields the optimal guidance command, expressed as:

[0107]

[0108] tanσ=[η0 η0 2 …η0 n ]P -1 Q

[0109] Where η0 represents the ratio of the missile-target distance at the current moment to the missile-target distance at the previous calculation step.

[0110] It should be understood that the various forms of processes shown above can be used to rearrange, add, or delete steps. For example, the steps described in this disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.

[0111] Example

[0112] Example 1

[0113] The simulation process includes the following steps:

[0114] S1. Establish a polynomial relationship with the projectile-to-target distance ratio as the independent variable and the field of view tangent as the dependent variable, and obtain a polynomial equation by combining the boundary conditions. The projectile-to-target distance ratio refers to the ratio of the projectile-to-target distance to the initial distance.

[0115] S2. Establish constraints and obtain the optimal guidance command by combining polynomial equations.

[0116] S3. The aircraft's flight is controlled by the optimal guidance command.

[0117] The obtained polynomial equation is expressed as

[0118] tanσ0=[1 1 … 1]C

[0119]

[0120] Where λ0 represents the initial line-of-sight angle of the projectile, and θ f σ represents the desired end-collision angle, and σ0 represents the initial field of view angle.

[0121] In S2, the constraints include the necessary waypoint constraints, which are expressed in terms of field of view and missile-target distance.

[0122] The necessary waypoint constraint is set as follows:

[0123]

[0124] The constraints also include constraints on the aircraft's terminal angle of attack, field of view, and acceleration, expressed as follows:

[0125]

[0126] By combining constraints with polynomial equations, a system of linear equations is obtained. Solving this system yields the optimal guidance command. The system of linear equations is expressed as follows:

[0127] PC = Q

[0128] in,

[0129] The guidance command for the aircraft at the starting point is:

[0130]

[0131] in

[0132]

[0133] tanσ=[1 1 … 1]P -1 Q

[0134] When solving for guidance commands based on the linear equations to determine the positions of necessary waypoints, the current necessary waypoint positions are discarded, and only the remaining unreached necessary waypoints and terminal conditions are used to generate the corresponding guidance commands. New constraints are added to limit the variation range of the guidance commands. These new constraints are set as follows:

[0135] a -1 =a real

[0136] Among them, a -1 This represents the guidance command corresponding to the coefficient matrix C at time t=0 of the previous calculation step, a real This indicates the guidance command actually used in the previous calculation step.

[0137] After adding new constraints, solving the polynomial equation yields the optimal guidance command, expressed as:

[0138]

[0139] tanσ=[η0 η0 2 …η0 n ]P -1 Q

[0140] Where η0 represents the ratio of the missile-target distance at the current moment to the missile-target distance at the previous calculation step.

[0141] During the simulation, the parameter settings are shown in Table 1;

[0142] Table 1

[0143] parameter Value Aircraft speed (m / s) 500 Initial position (m) (0，10000) Target location (m) (10000，0) Initial angle of attack (°) 30 Terminal angle of attack (°) -150 Maximum overload (m / s^2) 100 Number of necessary waypoints m 5 Location of the necessary waypoint: 1 m (5000.11000) Location of the necessary waypoint: 2m (8000.11000) Location of the necessary waypoint: 3m (10000.10000) The location of the necessary waypoint is 4 meters away. (12000.7000) The location of the necessary waypoint is 5 meters away. (13000.3000) Number of terms n in a polynomial 5

[0144] The simulation results are shown in Table 2-5, where Figure 2 The simulation results of the aircraft's flight trajectory Figure 3 The results of the aircraft overload simulation are as follows. Figure 4 The simulation results show the changes in the aircraft's trajectory angle. Figure 5 This refers to the distances between the aircraft and each necessary transit point, as well as the terminal miss distance.

[0145] from Figure 2-5 It can be seen that the aircraft can achieve the predetermined guidance target, accurately pass through each necessary waypoint, hit the target with the expected terminal collision angle, and the terminal overload converges to near 0.

[0146] During the simulation, with a simulation duration of approximately 45.24 seconds and a simulation step size of 0.001 seconds, the average simulation time was approximately 2.57 seconds, indicating that the method can achieve online real-time computation.

[0147] The present invention has been described above with reference to preferred embodiments; however, these embodiments are merely exemplary and illustrative. Various substitutions and modifications can be made to the present invention based on these embodiments, all of which fall within the scope of protection of the present invention.

Claims

1. A polynomial guidance method considering necessary waypoints, characterized in that, Includes the following steps: S1. Establish a polynomial relationship with the projectile-to-target distance ratio as the independent variable and the field of view tangent as the dependent variable, and obtain a polynomial equation by combining the boundary conditions. The projectile-to-target distance ratio refers to the ratio of the projectile-to-target distance to the initial distance. S2. Establish constraints and obtain the optimal guidance command by combining polynomial equations. S3. The aircraft's flight is controlled by the optimal guidance command.

2. The polynomial guidance method considering necessary waypoints according to claim 1, characterized in that, In S1, the polynomial relation is expressed as: tanσ(η)=c1η+c2η 2 +…+c n or n =[hh 2 …or n ]C Where σ represents the field of view angle, and C = [c1 c2…c n ] T Let c1, c2, ..., c be the coefficient matrix. n η is a coefficient, η represents the distance ratio between the projectile and the target, and n is the number of polynomial terms that can be set.

3. The polynomial guidance method considering necessary waypoints according to claim 1, characterized in that, The boundary conditions refer to the conditions that the aircraft must abide by at the initial and final moments.

4. The polynomial guidance method considering necessary waypoints according to claim 2, characterized in that, The obtained polynomial equation is expressed as tanσ0=[1 1…1]C Where λ0 represents the initial line-of-sight angle of the projectile, and θ f σ represents the desired end-collision angle, and σ0 represents the initial field of view angle.

5. The polynomial guidance method considering necessary waypoints according to claim 1, characterized in that, In S2, the constraints include the necessary waypoint constraints, which are expressed in terms of field of view and missile-target distance.

6. The polynomial guidance method considering necessary waypoints according to claim 5, characterized in that, The necessary waypoint constraint is set as follows: Where, λ i η represents the line-of-sight angle of the missile at the i-th necessary waypoint. i This represents the missile-to-target distance ratio at the i-th necessary waypoint.

7. The polynomial guidance method considering necessary waypoints according to claim 1, characterized in that, The constraints also include constraints on the aircraft's terminal angle of attack, field of view, and acceleration.

8. The polynomial guidance method considering necessary waypoints according to claim 7, characterized in that, The terminal angle of attack, field of view, and acceleration constraints of the aircraft are expressed as follows:

9. The polynomial guidance method considering necessary waypoints according to claim 1, characterized in that, By combining constraints with polynomial equations, a system of linear equations is obtained. Solving this system yields the optimal guidance command. The system of linear equations is expressed as follows: PC = Q in, n is the number of polynomial terms that can be set, and m represents the total number of waypoints that must be passed.

10. The polynomial guidance method considering necessary waypoints according to claim 1, characterized in that, When solving for guidance commands based on the linear equations to determine the positions of necessary waypoints, the current necessary waypoint positions are discarded, and only the remaining unreached necessary waypoints and terminal conditions are used to generate the corresponding guidance commands. New constraints are added to limit the variation range of the guidance commands. These new constraints are set as follows: a -1 =a real Among them, a -1 This represents the guidance command corresponding to the coefficient matrix C at time t=0 of the previous calculation step, a rea l This indicates the guidance command actually used in the previous calculation step.

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