Explicit Guidance Method for Anti-interference Fixed-point Landing of Spacecraft

Abstract

The present invention relates to an explicit guidance method for anti-interference fixed-point landing of a spacecraft, comprising: establishing a dynamic model in a LVLH coordinate system; establishing an interference observer, estimating the disturbance online to obtain an anti-interference term, and introducing it into a guidance instruction for compensation to obtain a disturbance-compensated model; constructing a guidance law for the disturbance-compensated model using an optimal principle, and solving the guidance instruction; solving to obtain an analytical range expression, and calculating a thrust correction value to achieve control of the anti-interference fixed-point landing of the spacecraft. The method of the present invention can ensure the guidance accuracy in the presence of uncertain interference, and has the advantages of small calculation amount and being able to achieve fixed-point landing.

Description

Technical Field

[0001] The invention relates to the technical field of spacecraft guidance, navigation and control, and in particular to an explicit guidance method for spacecraft anti-interference fixed-point landing. Background Art

[0002] In order to achieve the extraterrestrial exploration mission, the spacecraft needs to rely on its own power device to achieve the transfer from the orbit to the surface of the target celestial body. This process is called powered descent. The motion parameters of the spacecraft during the powered descent flight, including the three-axis speed, three-axis position and propellant consumption during the descent process, are determined by the guidance law. The guidance command calculates the required thrust and attitude of the spacecraft online to obtain the desired terminal parameters, such as the landing point position and landing speed.

[0003] Polynomial guidance is a commonly used guidance law, which was used in the lunar landing mission of the Apollo program. Its guidance law design did not take into account the optimization of propellant usage and disturbances caused by system uncertainty. When there are disturbances in the system, the guidance accuracy cannot be guaranteed, resulting in a maximum deviation of 7km between the actual landing point and the target landing point.

[0004] PEG (Powered Explicit Guidance) guidance is a constant thrust explicit guidance method derived from the space shuttle. The propellant consumption of this guidance law is suboptimal, but in the process of solving the guidance law, the parameters need to be iteratively solved, which requires a large amount of calculation and cannot effectively adjust the range. Patent CN105253328A improves PEG guidance, adds a process for range prediction, and obtains range adjustment capability by adjusting thrust. However, the range prediction process is iterative, which will further increase the computing power overhead of the PEG algorithm, and also lacks measures to deal with disturbances caused by system uncertainty.

[0005] In future deep space exploration and manned missions, guidance laws are required to ensure that spacecraft can achieve fixed-point landing when there are uncertain disturbances in the system, so as to carry out scientific exploration, build scientific research stations, and deliver supplies in valuable areas. Existing methods still have shortcomings such as high computational overhead, inability to resist interference, and inability to ensure fixed-point landing of spacecraft. Summary of the invention

[0006] In order to overcome the deficiencies in the above-mentioned prior art, the purpose of the present invention is to provide a spacecraft anti-interference fixed-point landing explicit guidance method, which has the advantages of anti-interference, small calculation amount and the ability to achieve fixed-point landing.

[0007] In order to achieve the above-mentioned object of the invention, the technical solution of the present invention is:

[0008] The present invention provides a spacecraft anti-interference fixed-point landing explicit guidance method, comprising:

[0009] Establish the dynamic model in LVLH coordinate system;

[0010] A disturbance observer is established to estimate the disturbance online to obtain the anti-interference term, which is introduced into the guidance command for compensation to obtain the disturbance-compensated model.

[0011] Using the optimal principle to construct a guidance law for the disturbance-compensated model and solve the guidance command;

[0012] The analytical range expression is solved and the thrust correction value is calculated to achieve the anti-interference fixed-point landing control of the spacecraft.

[0013] According to one aspect of the present invention, the step of establishing a kinetic model in a LVLH coordinate system comprises:

[0014] Construct the LVLH coordinate system using the current inertial position and velocity of the spacecraft;

[0015] The dynamic model in the LVLH coordinate system is constructed using the mass, specific impulse and thrust of the spacecraft;

[0016] The kinetic model is rewritten as a strict feedback form with a disturbance term.

[0017] According to one aspect of the present invention, the LVLH coordinate system is:

[0018]

[0019] in, are the three-axis unit vectors of the LVLH coordinate system, is the current inertial position of the spacecraft, is the speed of the spacecraft;

[0020] The kinetic model is:

[0021]

[0022]

[0023]

[0024]

[0025]

[0026]

[0027] Among them, x, y, z are the three-axis position coordinates of the spacecraft in the LVLH coordinate system, u, v, w are the three-axis velocity coordinates of the spacecraft in the LVLH coordinate system, r is the distance, r m is the radius of the central celestial body, θ and ψ are the pitch angle and yaw angle of the spacecraft respectively, m0 is the mass of the spacecraft, I sp is the specific impulse, T is the thrust, and the definition in V e =I sp g.

[0028] According to one aspect of the present invention, the establishment of a disturbance observer, online estimation of disturbance to obtain an anti-interference term, and introduction of the anti-interference term into a guidance instruction for compensation, comprises:

[0029] defining a deviation of desired dynamics from actual dynamics and using the deviation to establish a disturbance observer;

[0030] The disturbance observer is used to estimate the disturbance of the position and velocity of the spacecraft in real time online, and the anti-interference term is obtained by the output estimation value and the dynamic inverse principle calculation;

[0031] The anti-interference term is introduced into the guidance instruction, the dynamic model is simplified, and a disturbance-compensated model is obtained.

[0032] According to one aspect of the present invention, the anti-interference term a i,d for:

[0033]

[0034] Among them, x, y, z are the three-axis position coordinates of the spacecraft in the LVLH coordinate system, u, v, w are the three-axis velocity coordinates of the spacecraft in the LVLH coordinate system, is the estimated value of the disturbance observer output.

[0035] According to one aspect of the present invention, the method of constructing a guidance law for the disturbance-compensated model using an optimal principle and solving guidance instructions comprises:

[0036] Construct Hamiltonian function and use the optimal principle to derive the optimal guidance law in the composite control law;

[0037] The optimal guidance law and the anti-interference term are comprehensively utilized to obtain a composite control law, and the guidance command is obtained by inverse solution.

[0038] According to one aspect of the present invention, the guidance instruction includes a pitch angle and a yaw angle of the spacecraft.

[0039] According to one aspect of the present invention, the solving to obtain the analytical range expression and calculating the thrust correction value comprises:

[0040] Obtain the current position, velocity and thrust of the spacecraft, solve the analytical range expression corresponding to the guidance law, and predict the final range of the spacecraft at any time;

[0041] The relationship between the current range and target range of the spacecraft is used to calculate the thrust correction value, which is used as the thrust input for the next guidance cycle to achieve anti-interference fixed-point landing control of the spacecraft.

[0042] According to one aspect of the invention, the calculation of the thrust correction value takes into account the variable thrust capability of the spacecraft engine.

[0043] Beneficial effects:

[0044] According to one solution of the present invention, a unified estimation is performed on the uncertain parameters in the dynamic model, such as mass, specific impulse, thrust size, etc., through a disturbance observer, and these are compensated in the design of a composite guidance law (or composite control law), thereby ensuring the guidance accuracy in the presence of uncertain interference.

[0045] According to one solution of the present invention, by reasonably simplifying the dynamic model, there is no need to run an iterative method to solve the guidance parameters in the process of solving the optimal guidance law, thereby reducing the computing power overhead, enhancing the real-time performance of the algorithm, and facilitating on-orbit implementation.

[0046] According to one solution of the present invention, by constructing an accurate analytical range expression, there is no need to use numerical methods to estimate the range, which further enhances the real-time performance of the algorithm. Accurate control of the range can be achieved by dynamically adjusting the thrust through the relationship between thrust and range.

[0047] According to one scheme of the present invention, the spacecraft anti-interference fixed-point landing explicit guidance method can realize precise range control, integrate optimal guidance and interference observation, and ensure that the position control accuracy is better than 100m in the presence of mass and engine specific impulse uncertainty disturbances. The solution process also avoids the iterative calculation of guidance law parameters and range estimation, reduces the computational overhead, and improves the real-time performance of the algorithm. It has the advantages of anti-interference, small calculation amount, and the ability to achieve fixed-point landing. This makes the method mainly used to achieve fixed-point landing of aircraft or spacecraft with uncertain model parameters on extraterrestrial bodies, and can be applied to fixed-point landing and exploration missions on the moon and other deep space bodies without atmosphere, and has broad application prospects and value. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0049] Figure 1 A flowchart for implementing an explicit guidance method for anti-interference fixed-point landing of a spacecraft provided by an embodiment of the present invention is schematically shown;

[0050] Figure 2 Schematically showing a pitch angle curve diagram provided by an embodiment of the present invention;

[0051] Figure 3 A yaw angle curve diagram provided by an embodiment of the present invention is schematically shown;

[0052] Figure 4 A schematic diagram of a three-axis speed curve provided by an embodiment of the present invention is shown;

[0053] Figure 5 A schematic diagram of a three-axis position curve provided by an embodiment of the present invention is shown;

[0054] Figure 6 The thrust curve diagram provided by the embodiment of the present invention is schematically shown. DETAILED DESCRIPTION

[0055] The description of the embodiments of this specification should be combined with the corresponding drawings, which should be considered as part of the complete specification. In the drawings, the shape or thickness of the embodiments may be enlarged and indicated for simplification or convenience. Furthermore, the parts of each structure in the drawings will be described separately. It is worth noting that the elements not shown in the drawings or not described in words are in a form known to ordinary technicians in the relevant technical field.

[0056] The description of the embodiments herein and any reference to directions and orientations are only for the convenience of description and are not to be construed as any limitation on the scope of protection of the present invention. The following description of the preferred embodiments may involve combinations of features, which may exist independently or in combination, and the present invention is not particularly limited to the preferred embodiments. The scope of the present invention is defined by the claims.

[0057] like Figure 1 As shown, the specific implementation steps of a spacecraft anti-interference fixed-point landing explicit guidance method provided by an embodiment of the present invention include:

[0058] Step 100, establishing a dynamic model in the LVLH coordinate system.

[0059] In one embodiment, the specific implementation process of establishing the dynamic model in the LVLH coordinate system in step 100 includes:

[0060] Step 101, constructing an LVLH coordinate system using the current inertial position and velocity of the spacecraft. The LVLH coordinate system is as follows:

[0061]

[0062] in, are the three-axis unit vectors of the LVLH coordinate system, is the current inertial position of the spacecraft, is the speed of the spacecraft.

[0063] Step 102, constructing a dynamic model in the LVLH coordinate system using the mass, specific impulse and thrust of the spacecraft, the dynamic model is the following formula (2):

[0064]

[0065]

[0066]

[0067]

[0068]

[0069]

[0070] Among them, x, y, z are the three-axis position coordinates of the spacecraft in the LVLH coordinate system, u, v, w are the three-axis velocity coordinates of the spacecraft in the LVLH coordinate system, r is the distance, r m is the radius of the central celestial body, θ and ψ are the pitch angle and yaw angle of the spacecraft (i.e., the guidance command input to be designed), m0 is the mass of the spacecraft, I sp is the specific impulse, T is the thrust, and the definition in V e =I sp g.

[0071] Step 103: rewrite the dynamic model into a strict feedback form with a disturbance term.

[0072] For a powered descent mission of a spacecraft, usually r→r m , g→g m , and the lateral position velocity is small, formula (2) is rewritten as the following formula (3):

[0073]

[0074]

[0075]

[0076]

[0077]

[0078]

[0079] Among them, d x ,d u ,d y ,d v ,d w ,d z is the total disturbance term of the model deviation caused by all approximate assumptions and actual model parameter errors (such as specific impulse, mass, etc.), i (θ,ψ)=a i,opt +a i,d , (i=u,v,w) is the total control input in composite form, a i,opt is the optimal guidance law component, which is used to achieve the guidance target and will be solved in the subsequent steps. i,d It is the anti-interference component, which is used to offset various deviation disturbances of the system and will be solved by the interference observer in the subsequent steps.

[0080] Step 200, establish a disturbance observer, perform online estimation on the disturbance to obtain an anti-interference term, and introduce it into the guidance instruction for compensation to obtain a disturbance-compensated model.

[0081] In one embodiment, the specific implementation process of establishing a disturbance observer in step 200, performing online estimation of disturbance to obtain anti-interference terms, and introducing the anti-interference terms into the guidance instructions for compensation includes:

[0082] Step 201, define the deviation between the expected dynamics and the actual dynamics, and use the deviation to establish a disturbance observer. The deviation is the following formula (4):

[0083]

[0084] Step 202: Use the disturbance observer to estimate the disturbance of the position and velocity of the spacecraft in real time online, and calculate the anti-interference term from the output estimate value and the dynamic inverse principle.

[0085] The estimation of the disturbance of the three-axis position coordinates x, y, and z of the spacecraft is as follows:

[0086]

[0087]

[0088] The estimation of the disturbance of the three-axis velocity coordinates u, v, w of the spacecraft is as follows:

[0089]

[0090]

[0091] The estimated value of the above disturbance observer output is The actual disturbance d i A good estimate is made and the disturbance observer estimation error is input-output stable.

[0092] Anti-disturbance term a in the composite control law i,d It is the following formula (7):

[0093]

[0094] Step 203, introducing the anti-interference term into the guidance instruction, simplifying the dynamic model, and obtaining a disturbance-compensated model.

[0095] The spacecraft anti-interference fixed-point landing explicit guidance method disclosed in the embodiment of the present invention makes a unified estimate of the uncertainty parameters in the dynamic model, such as mass, specific impulse, thrust size, etc., through the interference observer, and compensates for them in the design of the composite guidance law (or composite control law), thereby ensuring the guidance accuracy in the presence of uncertain interference. At the same time, through the reasonable simplification of the dynamic model, it is not necessary to run the iterative method to solve the guidance parameters in the process of solving the optimal guidance law, thereby reducing the computing power overhead, enhancing the real-time performance of the algorithm, and facilitating on-orbit implementation.

[0096] Step 300, constructing a guidance law for the disturbance-compensated model using an optimal principle, and solving guidance instructions.

[0097] In one embodiment, in step 300, the guidance law is constructed for the disturbance-compensated model using the optimal principle, and the specific implementation process of solving the guidance instruction includes:

[0098] Step 301, constructing a Hamiltonian function, and using the optimal principle to derive the optimal guidance law in the composite control law, that is, the guidance part in the composite control law.

[0099] Specifically, the terminal constraint condition is constructed as follows:

[0100] G(t)=λ T Ψ(t)

[0101] =λ1(yy tf)+λ2(zz tf )+λ3(uu tf )+λ4(vv tf )+λ5(ww tf )

[0102] The optimal guidance of propellant under constant thrust is equivalent to the shortest time guidance, so the performance function of formula (9) can be constructed as follows:

[0103]

[0104] Then we get the Hamiltonian of the following formula (10):

[0105]

[0106] Among them, p is the oblique variable, p * For its corresponding weight.

[0107] Depend on With transversality condition The oblique variable integral can be solved.

[0108] t f represents the waiting time, as shown in formula (11):

[0109] t f =α[1-exp(-V x / V e )]

[0110] Apply the small angle assumption and normalize the oblique variables The following formula (12) can be obtained:

[0111]

[0112] in, C2, C3 are corresponding integral constants.

[0113] The current position is x0, y0, z0, and the current velocity is u0, v0, w0, then the corresponding spacecraft terminal position deviation Y, Z and terminal velocity deviation V can be calculated. x ,V y ,V z , which is the following formula (13):

[0114] V x =u f -u0,V y =v f -v0+g m t f -F,V z =w f-w0

[0115]

[0116] in, I* are all integral variables, which can be solved by yourself and will not be explained in detail.

[0117] It can be solved by the following formula (14) and formula (15):

[0118]

[0119]

[0120] Where S, L, Q, and J are integral constants, as shown in formula (16):

[0121]

[0122] The optimal guidance law component in the composite control law can be expressed as follows:

[0123]

[0124] Step 302, comprehensively utilizing the optimal guidance law and the anti-interference term to obtain a composite control law, and inversely solving the law to obtain a guidance instruction.

[0125] Specifically, a i (θ,ψ)=a i,opt +a i,d , (i=x, y, z) are substituted into the above formula (7) and formula (17) respectively to obtain the composite control law. Then the guidance command is obtained by inversely solving the following formula (18), specifically the attitude guidance command, including the pitch angle θ and the yaw angle ψ,

[0126]

[0127] Step 400, solving the analytical range expression and calculating the thrust correction value to achieve the control of the spacecraft's anti-interference fixed-point landing.

[0128] In one embodiment, the specific implementation process of solving the analytical range expression and calculating the thrust correction value in step 400 includes:

[0129] Step 401, obtain the current position, speed and thrust of the spacecraft, solve the analytical range expression corresponding to the guidance law, and predict the final range of the spacecraft at any time.

[0130] Specifically, the analytical range expression obtained by directly integrating the above formula (3) is the following formula (19):

[0131]

[0132] in, The range can be adjusted by adjusting T. The larger T is, the shorter the corresponding range is.

[0133] Step 402, using the relationship between the current range and the target range of the spacecraft to calculate the thrust correction value, which is used as the thrust input for the next guidance cycle to achieve the anti-interference fixed-point landing control of the spacecraft.

[0134] Specifically, the difference between the range under the current thrust and the target range is defined as δx = x r -x tf , we can get T k+1 =T k +δT, where T k is the thrust value at the current moment, T k+1 is the thrust value at the next moment, δT is the thrust correction value or thrust adjustment value, and is determined by the relationship between the expected range and the predicted range, as shown in the following formula (20):

[0135]

[0136] Among them, k>0 is an adjustable control parameter, k a is the variable thrust rate, which is determined by the engine characteristics of the spacecraft. Furthermore, the calculation of the thrust correction value δT takes into account the variable thrust capability of the spacecraft engine.

[0137] The spacecraft anti-interference fixed-point landing explicit guidance method disclosed in the embodiment of the present invention constructs an accurate analytical range expression, without the need to use numerical methods to estimate the range, further enhancing the real-time performance of the algorithm. The thrust can be dynamically adjusted through the relationship between thrust and range to achieve precise control of the range.

[0138] A simulation example is used to verify the spacecraft anti-interference fixed-point landing explicit guidance method proposed in an embodiment of the present invention. For example, the initial mass of the aircraft is 10,000 kg, the initial altitude is 12,000 m, the initial speed is [1300 00] m / s, and the target terminal position is [200 5 5] km, that is, the range is 200 km, the target altitude is 5 km, and the horizontal range is 5 km. The target terminal speed is [50-10 0] m / s. The guidance accuracy requirements are that the three-axis position accuracy is better than 100 m, and the three-axis speed accuracy is better than 1 m / s.

[0139] According to the engine performance indicators, the initial thrust is taken as 40kN, the specific impulse is 300s, and the variable thrust rate is less than 500N / s. Considering the common deviations of current engines, the simulation considers a 1% deviation of the specific impulse and a 1% deviation of the mass, which can cover the deviation range.

[0140] like Figures 2 to 6 As shown, the simulation results in the figure verify the good performance of the guidance law in the method of the present invention, which can ensure that all six terminal states including the range are accurately satisfied under the condition of uncertainty disturbance, among which the three-axis position control accuracy is better than 60m, and the three-axis speed control accuracy is better than 0.4m / s. Since the iterative solution calculation process is cancelled, the simulation can achieve 200 times of ultra-real-time calculation in the test platform win7+i5-9400+MATLAB2019 environment, meeting the application requirements.

[0141] The serial numbers of the above-mentioned steps involved in the method of the present invention do not mean the order of execution of the method. The execution order of each step should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the implementation mode of the present invention.

[0142] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A spacecraft anti-interference fixed-point landing explicit guidance method, comprising: Establish the dynamic model in LVLH coordinate system; A disturbance observer is established to estimate the disturbance online to obtain the anti-interference term, which is introduced into the guidance command for compensation to obtain the disturbance-compensated model. Using the optimal principle to construct a guidance law for the disturbance-compensated model and solve the guidance command; Solve the analytical range expression and calculate the thrust correction value to achieve the anti-interference fixed-point landing control of the spacecraft; The method of establishing a kinetic model in the LVLH coordinate system comprises: Construct the LVLH coordinate system using the current inertial position and velocity of the spacecraft; The dynamic model in the LVLH coordinate system is constructed using the mass, specific impulse and thrust of the spacecraft; The kinetic model is rewritten into a strict feedback form with a disturbance term; The LVLH coordinate system is: in, are the three-axis unit vectors of the LVLH coordinate system, is the current inertial position of the spacecraft, is the speed of the spacecraft; The kinetic model is: Among them, x, y, z are the three-axis position coordinates of the spacecraft in the LVLH coordinate system, u, v, w are the three-axis velocity coordinates of the spacecraft in the LVLH coordinate system, r is the distance, r m is the radius of the central celestial body, θ and ψ are the pitch angle and yaw angle of the spacecraft respectively, m0 is the mass of the spacecraft, I sp is the specific impulse, T is the thrust, and the definition in V e =I sp g; The establishment of the interference observer, online estimation of the disturbance to obtain the anti-interference term, and introduction of the anti-interference term into the guidance instruction for compensation, includes: defining a deviation of desired dynamics from actual dynamics and using the deviation to establish a disturbance observer; The disturbance observer is used to estimate the disturbance of the position and velocity of the spacecraft in real time online, and the anti-interference term is obtained by the output estimation value and the dynamic inverse principle calculation; Introducing the anti-interference term into the guidance instruction, simplifying the dynamic model, and obtaining a disturbance-compensated model; The anti-interference term a i,d for: Among them, x, y, z are the three-axis position coordinates of the spacecraft in the LVLH coordinate system, u, v, w are the three-axis velocity coordinates of the spacecraft in the LVLH coordinate system, is the estimated value of the disturbance observer output.

2. The method according to claim 1, characterized in that The method of constructing a guidance law for the disturbance-compensated model using the optimal principle and solving guidance instructions comprises: Construct Hamiltonian function and use the optimal principle to derive the optimal guidance law in the composite control law; The optimal guidance law and the anti-interference term are comprehensively utilized to obtain a composite control law, and the guidance command is obtained by inverse solution.

3. The method according to claim 2, characterized in that The guidance instructions include the pitch angle and yaw angle of the spacecraft.

4. The method according to claim 1, characterized in that: The solution obtains the analytical range expression and calculates the thrust correction value, including: Obtain the current position, velocity and thrust of the spacecraft, solve the analytical range expression corresponding to the guidance law, and predict the final range of the spacecraft at any time; The relationship between the current range and target range of the spacecraft is used to calculate the thrust correction value, which is used as the thrust input for the next guidance cycle to achieve anti-interference fixed-point landing control of the spacecraft.

5. The method according to claim 1, characterized in that The thrust correction value is calculated taking into account the variable thrust capability of the spacecraft engine.

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