A model-free integrated approach to guidance and control of exoatmospheric interceptors

Abstract

The present invention relates to the field of spacecraft guidance and control, and discloses a model-free integrated guidance and control method for an exoatmospheric interceptor. First, an integrated guidance and control model for an axially uncontrollable interceptor is constructed. Taking into account the measurement noise and external interference present in exoatmospheric interception, a non-singular fixed-time sliding mode surface is proposed, and on this basis, a fixed-time terminal guidance law and an attitude tracking controller are designed to improve the real-time and robustness of the control system. Finally, the fixed-time stability of the control system is proved based on the Lyapunov theory. The present invention can take into account the attitude and orbit coupling of the interceptor during the interception process, thereby achieving precise strikes on the target in the terminal guidance stage.

Description

Technical Field

[0001] The present invention relates to the field of spacecraft guidance and control, and in particular to a model-free exoatmospheric interceptor guidance and control integration method. Background Art

[0002] Anti-satellite technology will become a key factor in information-based warfare and determine the course of future wars, as the battle for space control unfolds. Target satellites have fixed and easily predictable orbits, and their structures, communications equipment, solar panels, and other components are fragile, making them a viable target for the development and use of anti-satellite weapons. Currently, anti-satellite weapons can be categorized by attack method, including kinetic collision, spraying, laser blinding, and close-range capture. The interception process for a kinetic interceptor involves three stages: programmed guidance, command-based guidance, and autonomous terminal homing. Terminal guidance design directly influences the interceptor's terminal trajectory and intercept accuracy.

[0003] The terminal guidance phase of space interception faces the following challenges: (1) The relative speed between the interceptor and the target is high, and the terminal guidance time is limited; (2) For non-cooperative targets, their motion information is difficult to obtain accurately, and the sensors have measurement errors; (3) The spacecraft will affect the direction of the orbit control engine during attitude adjustment, thereby affecting the interception accuracy; (4) Due to the limitations of the direct force control capability, the interception spacecraft cannot obtain a large overload. In addition, in order to capture the target, the terminal guidance phase needs to ensure that the target is always within the field of view of the spacecraft seeker. Therefore, it is particularly important to design a terminal interception control system that considers the field of view constraint and attitude-orbit coupling and has fast convergence characteristics. Based on this, the present invention proposes a model-free integrated guidance and control method for exoatmospheric interceptors. Summary of the Invention

[0004] The object of the present invention is to provide a model-free integrated guidance and control method for an exoatmospheric interceptor to solve the problems raised in the above background technology.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a model-free exoatmospheric interceptor guidance and control integration method, comprising the following steps:

[0006] Step S1, establishing a relative orbital dynamics model between the intercepting spacecraft and the attacking spacecraft;

[0007] Step S2, establishing a relative attitude dynamics model of the spacecraft;

[0008] Step S3, designing a non-singular fixed-time sliding mode surface based on the singularity problem existing in the terminal sliding mode variable structure control method;

[0009] Step S4: Based on step S3, a fixed-time attitude tracking controller and terminal guidance law based on field of view constraints are designed.

[0010] Preferably, the relative motion relationship between the interceptor and the target spacecraft in step S1 can be expressed as:

[0011]

[0012] Where r = [r x r y r z ] T is the position vector of the interceptor and the target spacecraft in the Earth-centered inertial coordinate system; are the positions of the interceptor spacecraft and the target spacecraft in the Earth-centered inertial coordinate system; μ = 3.986 × 10 14 is the gravitational constant; is the mass of the interceptor spacecraft; It is the control force of the interceptor in the inertial frame; is the unknown disturbance force on the interceptor,

[0013] Define the interceptor's line of sight angle and angular rate relative to the target in the inertial frame:

[0014]

[0015] Among them, q1 and q2 are the line of sight inclination and declination expressed in the inertial system respectively; is the relative distance between the interceptor spacecraft and the target spacecraft,

[0016] Define the state quantity q = [q1 q2] T , combined with the above formula, we have

[0017]

[0018] in, The complete expression is as follows

[0019]

[0020]

[0021]

[0022] Based on the uncontrollable characteristics of the interceptor spacecraft's axial direction, the control of the line of sight angle and angular velocity is achieved by equipping the interceptor spacecraft with engines in the lateral and longitudinal directions.

[0023] The control force in the interceptor spacecraft coordinate system is f c =[f c1 ,f c2 ] T , converted to the inertial system,

[0024] f I =R1f c

[0025] in, R1 is the transformation matrix from the spacecraft body coordinates to the inertial coordinate system. The relative orbital dynamics of the interceptor in the inertial system can be further written as

[0026]

[0027] Preferably, the step S2 uses the modified Rodrigues parameter method to describe the attitude equation of the interception spacecraft:

[0028]

[0029] in, are the Rodrigues parameter and angular velocity of the interceptor spacecraft in the body coordinate system relative to the inertial coordinate system, is the control torque for the interceptor spacecraft, is the disturbance torque, is the moment of inertia of the intercepting spacecraft, the complete expression is as follows

[0030]

[0031] For the intercepting spacecraft, its moment of inertia has the following properties

[0032] J 12 =J 21 ,J 13 =J 31 ,J 23 =J 32

[0033] According to the line of sight inclination and line of sight deflection during the interception process, the conversion matrix from the inertial system to the line of sight represented by the line of sight angle is compared with the conversion matrix from the inertial system to the line of sight represented by the Euler angle, and the expected attitude angle of the interceptor represented by the Euler angle is obtained, and then the expected Rodrigues parameter is obtained, which is expressed as σ d , the specific expression is as follows

[0034]

[0035] For the desired angular velocity, we have

[0036]

[0037] According to the definition of Rodrigues parameter and angular velocity, the relative Rodrigues parameter and relative angular velocity can be calculated.

[0038]

[0039] ω e =ω c -R cs ω d

[0040] Among them, R cs is the coordinate transformation matrix from the sight system to the local system,

[0041] Furthermore, the kinematic and dynamic equations of the relative attitude of the intercepting spacecraft in the inertial system are:

[0042]

[0043] in, Preferably, the specific form of the non-singular fixed-time sliding surface in step S3 is as follows:

[0044]

[0045] Among them, x is the state quantity, is a positive constant, a s ∈(1,2), b s ∈(0,1), a s b s >1,

[0046] The derivative of S with respect to time is

[0047]

[0048] When x approaches zero, due to The above formula can be simplified as

[0049]

[0050] Due to a s >1 and a s b s >1, There will be no singular phenomenon, so the above sliding surface is non-singular.

[0051] When the sliding surface S converges, the system state x also converges. The Lyapunov equation is selected as

[0052]

[0053] The following relationship holds

[0054]

[0055] The convergence of the system state x is proved.

[0056] Preferably: the attitude tracking control in step S4 has a maximum field of view angle of θ due to the limited field of view of the interceptor seeker. max , define L1 = [1,0,0] T is the unit vector of the line of sight, then the angle θ between the line of sight and the centerline of the intercepting spacecraft can be expressed as

[0057]

[0058] To meet the field of view constraints, based on the idea of state transformation, the following variables are defined:

[0059]

[0060] When the conversion variable X s When bounded, Θ is always less than the maximum field of view θ max ,

[0061] Then the following glide surface is designed to achieve the desired attitude σ of the interceptor spacecraft d Tracking

[0062]

[0063] Among them, k1>0, a1∈(1,2), b1∈(0,1) and a1b1>1.

[0064] Combining the interceptor spacecraft attitude tracking model and the non-singular sliding mode surface, a fixed-time sliding mode controller can be designed as follows:

[0065]

[0066] Among them, k w1 ,k w2 is a positive constant, r w1 >1,

[0067] Preferably, the model-free exoatmospheric interceptor guidance and control integration method is characterized in that the interceptor spacecraft guidance in step S4 is designed as follows:

[0068]

[0069] Among them, q * is the desired approach angle, k2>0, a2∈(1,2), b2∈(0,1) and a2b2>1. The design of the sliding surface S2 not only considers the zeroing of the line of sight angular rate, but also ensures that the line of sight angle can track the desired approach angle q * ,

[0070] According to the relative orbit model of the interceptor spacecraft and the target spacecraft, the following non-singular fixed-time sliding mode guidance law is designed:

[0071]

[0072] Among them, k q1 ,k q2 is a positive constant, r q1 >1,

[0073] In terms of stability proof, the Lyapunov equation is selected as

[0074]

[0075]

[0076] Through the above formula, we can finally explain the system state It is stable at a fixed time.

[0077] Compared with the prior art, the present invention has the following beneficial effects:

[0078] The present invention fully considers the attitude and orbit coupling characteristics of the interceptor spacecraft and establishes a joint system of attitude and orbit on this basis;

[0079] The present invention designs a non-singular fixed-time sliding mode surface, and combines the idea of the parallel approach method to design a fixed-time terminal guidance law and a fixed-time sliding mode attitude tracking controller, which ensures the robustness of the spacecraft system to external disturbances, model uncertainty and measurement noise, and has engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 is a flow chart of the present invention;

[0081] Figure 2 It is the coordinate system and vector definition in the spacecraft modeling process;

[0082] Figure 3 This is a schematic diagram of the attitude control and orbit control engine layout;

[0083] Figure 4 are the simulation results of the guidance law and attitude tracking controller. DETAILED DESCRIPTION

[0084] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0085] Example 1

[0086] See also Figure 1 , the flowchart of the present invention shown in the figure, a model-free exoatmospheric interceptor guidance and control integration method, comprising the following steps:

[0087] Step S1, establishing a relative orbital dynamics model between the intercepting spacecraft and the attacking spacecraft;

[0088] Step S2, establishing a relative attitude dynamics model of the spacecraft;

[0089] Step S3, designing a non-singular fixed-time sliding mode surface based on the singularity problem existing in the terminal sliding mode variable structure control method;

[0090] Step S4: Based on step S3, a fixed-time attitude tracking controller and terminal guidance law based on field of view constraints are designed.

[0091] In this embodiment, Figure 2 As shown, only when considering the two-body problem of the interceptor and the target spacecraft, the relative motion relationship between the two is established:

[0092]

[0093] Where r = [r x r y r z ] T is the position vector of the interceptor and the target spacecraft in the Earth-centered inertial coordinate system; are the positions of the interceptor spacecraft and the target spacecraft in the Earth-centered inertial coordinate system; μ = 3.986 × 10 14 is the gravitational constant; is the mass of the interceptor spacecraft; It is the control force of the interceptor in the inertial frame; The unknown disturbance force acting on the interceptor.

[0094] Define the interceptor's line of sight angle and angular rate relative to the target in the inertial frame:

[0095]

[0096] Among them, q1 and q2 are the line of sight inclination and declination expressed in the inertial system respectively; is the relative distance between the interceptor spacecraft and the target spacecraft.

[0097] Define the state quantity q = [q1 q2] T . Combining the above formula, we have

[0098]

[0099] in, The complete expression is as follows

[0100]

[0101] Since the interceptor spacecraft has uncontrollable characteristics in its axial direction, such as Figure 3 As shown, it is possible to consider equipping the interceptor spacecraft with engines in the lateral and longitudinal directions to achieve control of the line of sight angle and angular rate.

[0102] Assume that the control force in the interceptor spacecraft coordinate system is f c =[f c1 ,f c2 ] T , converted to the inertial system, we have

[0103] f I =R1f c

[0104] in, R1 is the transformation matrix from the spacecraft body coordinates to the inertial coordinate system. The relative orbital dynamics of the interceptor in the inertial system can be further written as

[0105]

[0106] In the second step, the modified Rodrigues parameter method is used to describe the attitude equations of the interceptor spacecraft:

[0107]

[0108] in, are the Rodrigues parameter and angular velocity of the interceptor spacecraft in the body coordinate system relative to the inertial coordinate system, respectively. is the control torque for the interceptor spacecraft, is the disturbance torque, is the moment of inertia of the intercepting spacecraft, the complete expression is as follows

[0109]

[0110] For the intercepting spacecraft, its moment of inertia has the following properties

[0111] J 12 =J 21 ,J 13 =J 31 ,J 23 =J 32

[0112] According to the line of sight inclination and line of sight deflection during the interception process, the conversion matrix from the inertial system to the line of sight represented by the line of sight angle is compared with the conversion matrix from the inertial system to the line of sight represented by the Euler angle. The expected attitude angle of the interceptor represented by the Euler angle can be obtained, and then the expected Rodrigues parameter can be obtained, which is expressed as σ d The specific expression is as follows

[0113]

[0114] For the desired angular velocity, we have

[0115]

[0116] According to the definition of Rodrigues parameter and angular velocity, the relative Rodrigues parameter and relative angular velocity can be calculated.

[0117]

[0118] ω e =ω c -R cs ω d

[0119] Among them, R cs is the coordinate transformation matrix from the sight system to this system.

[0120] Furthermore, the kinematic and dynamic equations of the relative attitude of the intercepting spacecraft in the inertial system are obtained as follows:

[0121]

[0122] in,

[0123] During the terminal interception process, the intercepting spacecraft will be affected by external interference and model uncertainty. Given that the sliding mode variable structure control method has the advantages of strong robustness and insensitivity to system parameters, a non-singular fixed-time sliding mode surface is proposed here. The specific form is as follows:

[0124]

[0125] Among them, x is the state quantity, is a positive constant, a s ∈(1,2), b s ∈(0,1), a s b s >1.

[0126] The derivative of S with respect to time is

[0127]

[0128] When x approaches zero, due to The above formula can be simplified as

[0129]

[0130] Considering a s >1 and a s b s >1, No singular phenomenon will occur, so the designed sliding surface is non-singular.

[0131] When the sliding surface S converges, the system state x also converges. The Lyapunov equation is selected as

[0132]

[0133] The following relationship holds

[0134]

[0135] The convergence of the system state x is proved.

[0136] In terms of attitude tracking control, considering the limited field of view of the interceptor seeker, its maximum field of view angle is θ max . Define L1 = [1,0,0] T is the unit vector of the line of sight, then the angle θ between the line of sight and the centerline of the intercepting spacecraft can be expressed as

[0137]

[0138] In order to meet the field of view constraints, based on the idea of state transformation, the following variables are defined

[0139]

[0140] When the conversion variable X s When bounded, Θ is always less than the maximum field of view θ max .

[0141] Then the following glide surface is designed to achieve the desired attitude σ of the interceptor spacecraft d Tracking

[0142]

[0143] Among them, k1>0, a1∈(1,2), b1∈(0,1) and a1b1>1.

[0144] Combining the interceptor spacecraft attitude tracking model and the non-singular sliding mode surface, a fixed-time sliding mode controller can be designed as follows:

[0145]

[0146] Among them, k w1 ,k w2 is a positive constant, r w1 >1,

[0147] In terms of stability proof, the Lyapunov equation is selected as

[0148]

[0149]

[0150] Through the above formula, we can finally explain the system state σ e ,ω e It can converge within a fixed time, and the field of view angle always meets the constraints during the posture tracking process.

[0151] In terms of interception spacecraft guidance, the following non-singular fixed-time sliding mode surface is designed

[0152]

[0153] Among them, q * is the desired approach angle, k2>0, a2∈(1,2), b2∈(0,1) and a2b2>1. In addition to considering the zeroing of the line of sight angular rate, the sliding surface S2 also ensures that the line of sight angle can track the desired approach angle q * .

[0154] According to the relative orbit model of the interceptor spacecraft and the target spacecraft, the following non-singular fixed-time sliding mode guidance law can be designed:

[0155]

[0156] Among them, k q1 ,k q2 is a positive constant, r q1 >1,

[0157] In terms of stability proof, the Lyapunov equation is selected as

[0158]

[0159] Through the above formula, we can finally explain the system state It is stable at a fixed time.

[0160] Finally, the effectiveness and superiority of the algorithm are verified through Matlab simulation. Some of the parameters used in the simulation are as follows:

[0161] The maximum thrust of the interceptor spacecraft's orbital control engine is fmax =[350,350] T N, the maximum torque of the attitude control engine is [0.25, 1.5, 1.5] T N·m, the mass and moment of inertia of the interceptor spacecraft are m c =25kg, J=diag([0.0049,0.45,0.45])kg·m 2 The mass of the target spacecraft is 1425.6 kg, and its initial semi-major axis a t (0) = 7078 km, eccentricity e t =0.01, right ascension of ascending node Ω t (0) = 0 rad, orbital inclination i t (0) = π / 6rad, argument of perigee w t (0) = 0rad, true anomaly f t (0) = 0rad, the initial distance between the interceptor spacecraft and the target spacecraft is R(0) = 50km, and the initial sight angle is q(0) = [0.001ε r ,0.6435+0.001ε r ] T rad, the expected value of the approach angle is q * =[0,0.6435] T The initial modified Rodrigues parameter of the interceptor spacecraft is set to σ c (0) = [0.2, 0.2, 0.45] T , the initial angular velocity is ω c (0) = 0.01 × [2, -2, 2] T rad / s. In the simulation, due to the measurement noise and field of view constraints of the seeker, the measurement noise of the sight angle is set to 1×10 -4 rad, the measurement noise of the line of sight angular rate is 1×10 -5 rad / s, the maximum field of view semi-cone angle of the seeker is 30 degrees, and the external disturbance to the spacecraft is set to

[0162]

[0163] in, represents the orbital angular velocity of the target spacecraft. The control parameters are selected as follows: a1=1.2,b1=0.9,k1=0.5,k w1 =k w2 =4, r w1 =1.1, r w2 =0.8, a2=1.2, b2=0.95, k2=0.05, k q1 =k q2 =0.6, rq1 =1.4, r q2 =0.65.

[0164] According to the above parameters, we can get Figure 4 From the simulation results in , it is not difficult to see that the interceptor spacecraft can intercept the target. Even in the presence of initial alignment error and measurement error, in terms of attitude tracking, the algorithm in the present invention can ensure faster convergence speed and higher convergence accuracy, and the field of view constraint of the seeker is always met. Therefore, the effectiveness of the control algorithm in the present invention is verified.

[0165] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that includes a list of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus.

[0166] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A model-free integrated guidance and control method for exoatmospheric interception spacecraft, characterized in that: The steps include: Step S1, establishing a relative orbital dynamics model between the interceptor spacecraft and the target spacecraft; Step S2, establishing a relative attitude dynamics model of the spacecraft; Step S3, designing a non-singular fixed-time sliding mode surface based on the singularity problem existing in the terminal sliding mode variable structure control method; Step S4, designing a fixed-time attitude tracking controller and terminal guidance law based on field of view constraints based on step S3; The step S2 uses the modified Rodrigues parameter method to describe the attitude operation equation of the interception spacecraft: Among them, σ c , are the Rodrigues parameter and angular velocity of the interceptor spacecraft in the body coordinate system relative to the inertial coordinate system, is the control torque for the interceptor spacecraft, is the disturbance torque, is the moment of inertia of the intercepting spacecraft, the complete expression is as follows For the intercepting spacecraft, its moment of inertia has the following properties I 12 =J 21 ,J 13 =J 31 ,J 23 =J 32 According to the line of sight inclination and deflection during the interception process, the transformation matrix from the inertial coordinate system to the line of sight represented by the line of sight angle is compared with the transformation matrix from the inertial coordinate system to the line of sight represented by the Euler angle, and the expected attitude angle of the interception spacecraft represented by the Euler angle is obtained, and then the expected Rodrigues parameter is obtained, which is expressed as σ d , the specific expression is as follows For the desired angular velocity, we have According to the definition of Rodrigues parameter and angular velocity, the relative Rodrigues parameter and relative angular velocity can be calculated. oh e =ω c -R cs oh d Among them, R cs is the coordinate transformation matrix from the sight system to the body coordinate system, Furthermore, the kinematic and dynamic equations of the relative attitude of the intercepting spacecraft in the inertial coordinate system are: in, The attitude tracking control in step S4 has a maximum field of view angle of θ due to the limited field of view of the interceptor spacecraft seeker. max , define L1 = [1,0,0] T is the unit vector of the line of sight, then the angle θ between the line of sight and the centerline of the intercepting spacecraft can be expressed as To meet the field of view constraints, based on the idea of state transformation, the following variables are defined: When the conversion variable X s When bounded, Θ is always less than the maximum field of view θ max , Then the following glide surface is designed to achieve the desired attitude σ of the interceptor spacecraft d Tracking Among them, k1>0, a1∈(1,2), b1∈(0,1) and a1b1>1; Combining the interceptor spacecraft attitude tracking model and the non-singular sliding mode surface, a fixed-time sliding mode controller can be designed as follows: Among them, k w1 ,k w2 is a positive constant, r w1 >1, ; Define the line-of-sight angle and angular rate of the interceptor spacecraft relative to the target spacecraft in the inertial coordinate system: Among them, q1 and q2 are the line of sight inclination and declination expressed in the inertial coordinate system respectively; is the relative distance between the interceptor spacecraft and the target spacecraft.

2. The model-free integrated guidance and control method for exoatmospheric interception spacecraft according to claim 1, characterized in that: The relative motion relationship between the interceptor spacecraft and the target spacecraft in step S1 can be expressed as: Where r = [r x r y r z ] T is the position vector of the interceptor spacecraft and the target spacecraft in the inertial coordinate system; r c , are the positions of the interceptor spacecraft and the target spacecraft in the inertial coordinate system respectively; μ=3.986×10 14 is the gravitational constant; is the mass of the interceptor spacecraft; It is the control force of the intercepting spacecraft in the inertial coordinate system; To intercept the unknown disturbance force on the spacecraft, Define the state quantity q = [q1 q2] T , combined with the above formula, we have in, The complete expression is as follows Based on the uncontrollable characteristics of the interceptor spacecraft's axial direction, the control of the line of sight angle and angular velocity is achieved by equipping the interceptor spacecraft with engines in the lateral and longitudinal directions. The control force on the interceptor spacecraft coordinate system is f c =[f c1 ,f c2 ] T , converted to the inertial coordinate system, f I =R1f c in, R1 is the transformation matrix from the spacecraft body coordinate system to the inertial coordinate system. The relative orbital dynamics of the interceptor spacecraft in the inertial coordinate system can be further written as 3. The model-free integrated guidance and control method for exoatmospheric interception spacecraft according to claim 2, characterized in that: The specific form of the non-singular fixed-time sliding surface in step S3 is as follows Among them, x is the state quantity, is a positive constant, a s ∈(1,2), b s ∈(0,1), a s b s >1, The derivative of S with respect to time is When x approaches zero, due to The above formula can be simplified as Due to a s >1 and a s b s >1, There will be no singular phenomenon, so the above sliding surface is non-singular. When the sliding surface S converges, the system state x also converges. The Lyapunov equation is selected as The following relationship holds The convergence of the system state x is proved.

4. The model-free integrated guidance and control method for exoatmospheric interception spacecraft according to claim 3, characterized in that: The interception spacecraft guidance in step S4 is designed as follows: Among them, q * is the desired approach angle, k2>0, a2∈(1,2), b2∈(0,1) and a2b2>1. The design of the sliding surface S2 not only considers the zeroing angular rate, but also ensures that the line of sight angle can track the desired approach angle q * , According to the relative orbit model of the interceptor spacecraft and the target spacecraft, the following non-singular fixed-time sliding mode guidance law is designed: Among them, k q1 ,k q2 is a positive constant, r q1 >1, In terms of stability proof, the Lyapunov equation is selected as Through the above formula, we can finally explain the system state q e , It is stable at a fixed time.

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