Model-free external atmospheric interceptor guidance and control integrated method

Abstract

The invention relates to the field of spacecraft guidance and control, and discloses a model-free external atmospheric interceptor guidance and control integrated method, which comprises the following steps of: firstly, constructing an axially uncontrollable interceptor guidance and control integrated model; in consideration of measurement noise and external interference existing in atmospheric external interception, a non-singular fixed-time sliding mode surface is provided, and a fixed-time terminal guidance law and an attitude tracking controller are respectively designed on the basis of the non-singular fixed-time sliding mode surface, so that the real-time performance and robustness of a control system are improved. And finally, the fixed time stability of the control system is proved based on the Lyapunov theory, the attitude and orbit coupling effect of the interceptor in the interception process can be considered, and therefore accurate striking on the target is achieved 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 warfare and determine the direction of war in the fight for space dominance in future wars. The orbit of the target satellite is fixed and easy to predict, and its structure, communication equipment, solar panels and other components are fragile, which provides the possibility for the development and use of anti-satellite weapons. At present, anti-satellite weapons can be divided into kinetic collision, spraying, laser blinding and close-range capture according to the attack method. The interception process of the kinetic interceptor includes three stages: program guidance, command guidance and autonomous terminal guidance. Among them, the terminal guidance design directly affects the terminal trajectory and interception accuracy of the interceptor.

[0003] The terminal guidance stage 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 stage 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 an exoatmospheric interceptor. Summary of the invention

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

[0005] To achieve the above object, 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 of 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, designing a fixed-time attitude tracking controller and terminal guidance law based on field of view constraints on the basis of step S3.

[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 geocentric inertial coordinate system; are the positions of the interceptor and target spacecraft in the geocentric 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 axial characteristics of the interceptor spacecraft, 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 operation equation of the interception spacecraft:

[0028]

[0029] in, denote 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 intercepting 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 transformation matrix from the inertial system to the line of sight represented by the line of sight angle is compared with the transformation 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] Based on the definitions 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] Further, the kinematic and dynamic equations of the relative attitude of the interception 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 angle 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 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 interception spacecraft guidance design in step S4 is the following non-singular fixed time sliding surface

[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 velocity, 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 and 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-orbit coupling characteristics of the interceptor spacecraft, and on this basis establishes a joint system of attitude and orbit;

[0079] The present invention designs a non-singular fixed-time sliding mode surface, and combines the idea of ​​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 process of spacecraft modeling;

[0082] Figure 3 It 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 be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. 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 creative work are within the scope of protection of the present invention.

[0085] Embodiment 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 of 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, designing a fixed-time attitude tracking controller and terminal guidance law based on field of view constraints on the basis of step S3.

[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 geocentric inertial coordinate system; are the positions of the interceptor and target spacecraft in the geocentric 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 axial characteristics, 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, denote 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 intercepting 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, and 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] Based on the definitions 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] Further, 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. In view of the advantages of strong robustness and insensitivity to system parameters of the sliding mode variable structure control method, a non-singular fixed-time sliding mode surface is given 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 angle 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 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 that 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 velocity, 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 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 semi-major axis a at the initial moment is 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 / 6 rad, the argument of perigee w t (0) = 0 rad, true anomaly f t (0) = 0rad, the initial distance between the interceptor and the target spacecraft is R(0) = 50km, and the line of sight angle at the initial moment 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 rad. 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 line of sight angle is set to 1×10 -4 rad, the measurement noise of the line of sight angular velocity 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 get Figure 4 It is not difficult to see from the simulation results in that the interception 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 article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device.

[0166] Although 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 the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A model-free exoatmospheric interceptor guidance and control integration method, characterized in that: The steps include: Step S1, establishing a relative orbital dynamics model of the intercepting spacecraft and the attacking 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 on the basis of step S3.

2. A model-free exoatmospheric interceptor guidance and control integration method according to claim 1, characterized in that: The relative motion relationship between the interceptor 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 and the target spacecraft in the geocentric inertial coordinate system; are the positions of the interceptor and target spacecraft in the geocentric 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. Define the interceptor's line of sight angle and angular rate relative to the target in the inertial frame: 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, Define state quantity q = [q1 q2] T , combined with the above formula, we have in, The complete expression is as follows Based on the uncontrollable axial characteristics of the interceptor spacecraft, 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 in the interceptor spacecraft coordinate system is f c =[f c1 ,f c2 ] T , converted to the inertial system, f I =R1f c 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 3. A model-free exoatmospheric interceptor guidance and control integration method according to claim 2, characterized in that: The step S2 uses the modified Rodrigues parameter method to describe the attitude operation equation of the interception spacecraft: in, denote 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 intercepting 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 line of sight deflection during the interception process, the transformation matrix from the inertial system to the line of sight represented by the line of sight angle is compared with the transformation 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 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 local system, Further, the kinematic and dynamic equations of the relative attitude of the interception spacecraft in the inertial system are: in, 4. A model-free exoatmospheric interceptor guidance and control integration method according to claim 3, 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.

5. A model-free exoatmospheric interceptor guidance and control integration method according to claim 4, characterized in that: 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 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 angle 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 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, r w2 ∈(0,1).

6. A model-free exoatmospheric interceptor guidance and control integration method according to claim 5, characterized in that: The interception spacecraft guidance design in step S4 is 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 of the line of sight angular velocity, 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 and 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 It is stable at a fixed time.

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