Maintainable satellite inertial parameter in-orbit identification method based on flywheel driving

Abstract

The invention discloses a maintainable satellite inertial parameter in-orbit identification method based on flywheel driving, which comprises the following steps: on the basis of establishing a satellite kinetic model, considering the influence of sensor measurement noise and flywheel transmission noise, obtaining an identification equation under an extended Kalman filtering algorithm framework, and combining a Jacobian matrix analytical expression of the identification equation to obtain a maintainable satellite inertial parameter in-orbit identification model; and after the state vector and the covariance matrix at the current moment are obtained through prediction, the corresponding quantity is updated by using the measurement result of the sensor. Compared with a widely applied identification method based on recursive least squares, the identification method based on extended Kalman filtering can utilize statistical information of noise, the anti-interference capability of the method is improved, and a better identification result can still be obtained in the presence of measurement noise. Meanwhile, under the condition that only part of state quantity can be measured, a good identification result can still be obtained.

Description

Technical Field

[0001] The present invention relates to the field of on-orbit service technology in the aerospace field, and in particular to an on-orbit identification method, device, equipment and computer-readable storage medium for inertial parameters of a maintainable satellite based on flywheel drive. Background Art

[0002] On-orbit servicing technology can perform on-orbit module replacement and upgrade operations on repairable satellites. It has good application prospects and has attracted extensive attention from academia and industry at home and abroad. However, due to the influence of on-orbit assembly errors, the satellite center of mass will shift to a certain extent after the module is replaced, which will affect the satellite's attitude dynamics. If it is still controlled according to the original attitude stability law, the control performance will be reduced.

[0003] Repairable satellites often have a high level of research and development and application value. They are mainly capable of performing high-value space missions such as observation, so they have extremely high demands for attitude pointing. The decline in attitude pointing capability will lead to a decline in mission performance and may even lead to mission failure. Therefore, it is necessary to study the inertial parameter identification method for repairable satellites, improve the accuracy of the satellite's dynamic model, and then ensure the effective implementation of observation and communication tasks.

[0004] For satellite inertial parameter identification, the existing research methods mainly rewrite the satellite's attitude dynamics model into a form that is linearly related to the identification parameters, and then use the satellite's own reaction engine to generate thrust, and input the measured satellite motion state parameters into the identification equation for solution. These methods have the following main shortcomings:

[0005] 1) The identification process will consume the satellite’s precious fuel resources, which will affect the satellite’s on-orbit lifespan and reduce the cost-effectiveness;

[0006] 2) The influence of measurement noise is not fully considered, and the corresponding statistical information is not used. The identification accuracy is significantly affected by the measurement noise;

[0007] 3) It requires complete state measurement quantities, and cannot be solved when some sensors fail, which limits the scope of application. Summary of the invention

[0008] The embodiments of the present application aim to overcome the above limitations of the prior art by providing an on-orbit identification method for inertial parameters of a maintainable satellite based on flywheel drive.

[0009] To achieve the above-mentioned purpose, the embodiment of the present application provides an on-orbit identification method of inertial parameters of a repairable satellite based on flywheel drive, comprising the following steps:

[0010] S1. Based on the D'Alembert principle in the form of virtual power, a maintainable satellite dynamics model is established that takes into account the offset between the flywheel system's center of mass and the satellite's center of mass;

[0011] S2, expand the system state vector to a column vector containing the satellite center of mass position and moment of inertia, and derive the identification equation in combination with the extended Kalman filter framework;

[0012] S3. According to the calculation process of the extended Kalman filter and in combination with the satellite dynamics model, the Jacobian matrix analytical expression of the identification equation is obtained, and a corresponding measurement equation is established. The measurement quantity of the measurement equation includes the angular velocity of the flywheel and the motion state of the satellite;

[0013] S4. Discretize the identification equation, perform a state prediction process in combination with the calculation process of Kalman filtering, and update it using the measurement data of the sensor to obtain the identification values ​​of the satellite's center of mass offset and moment of inertia.

[0014] In one embodiment, step S1 includes:

[0015] Assume that the satellite reference center of mass is connected to the inertial reference point via a virtual hinge, and the virtual hinge includes three rotational degrees of freedom and three translational degrees of freedom;

[0016] The satellite dynamics model is established by using the D'Alembert principle in the form of virtual power. The satellite dynamics model is expressed as follows:

[0017]

[0018] Among them, q, denote the generalized coordinates and their first-order and second-order derivatives respectively, θ denotes the inertial parameter to be identified, Z (q,θ) represents the generalized mass matrix, represents the generalized force vector, u represents the control torque on the hinge;

[0019] in, Z (q,θ) and The expression is as follows:

[0020] Z (q,θ)= α T m α +β T J β;

[0021]

[0022] in, α and β It is related to the relative position vector between the satellite and each flywheel and the direction of the flywheel axis.J are all diagonal matrices, where the m diagonal elements are the masses of the satellite and each flywheel, J The diagonal elements are the moments of inertia of the satellite and flywheel in the inertial system, F o is the column vector of the external forces acting on the satellite and the flywheel, M o is the column vector composed of the external torques acting on the satellite and the flywheel, w represents the inertia force of each object, σ and ε represent the inertia moment, F τq Represents a constraint element.

[0023] In one embodiment, step S2 includes:

[0024] S21. Obtain the matrix form of the satellite dynamics model based on the column vector obtained by expanding the system state vector:

[0025]

[0026] Among them, the generalized coordinates q of the satellite are divided into q1 and q w Two parts, where q1 represents the motion parameters of the satellite body, q w represents the rotation angle of the flywheel;

[0027] S22. For the flywheel drive scenario, the angular acceleration is known, that is, The theoretical value of is known, and the identification equation is obtained by using the integral-inverse hybrid dynamics model as follows:

[0028]

[0029] In one embodiment, step S3 includes:

[0030] S31. Using the chain rule, differentiate the generalized mass matrix Z and the generalized force vector z relative to the generalized coordinates of the system to obtain the following expressions:

[0031]

[0032] S32, calculation and To get the analytical expression of the above formula:

[0033] Opposite direction cosine matrix A j Ask for q l The partial derivative of can be obtained:

[0034]

[0035] in, Determined by the jth joint hinge, it can be calculated by recursive technique

[0036] for and can be written as:

[0037]

[0038] therefore,

[0039]

[0040] because and The joint joint j and its coordinate q j Decided, therefore, and Can be obtained Then it is calculated by recursive method;

[0041] When getting and back, and It can be calculated by the chain rule, and then it can be calculated and

[0042] for It affects ω, σ and ε, so

[0043] For calculation Taking the derivative of the angular velocity with respect to ql, we can obtain:

[0044]

[0045] in, It can be obtained by recursive method;

[0046] for and It can be calculated by Get it directly;

[0047] When calculated and back, It can be obtained by chain derivation rule;

[0048] For the target moment of inertia J'1, replace J with Substitute it into the satellite dynamics model to obtain the corresponding derivative terms;

[0049] For the position vector b1 from the base mass center to the reference point in this system, replace b1' with [1,0,0] T , [0,1,0] T or [0,0,1] T and other b'n Replace with [-1,0,0] T , [0,-1,0] T and [0,0,-1] T To calculate and Where i = x, y, or z;

[0050] Using the chain rule, we get and The analytical expression of the Jacobian matrix of , and then the analytical expression of the identification equation for the state vector x can be obtained;

[0051] S33, establish the measurement equation:

[0052] Assuming that the measurement quantities of the measurement equation include the angular velocity of the flywheel and the motion state of the satellite, in order to analyze the influence of the measurement quantity type on the identification performance, the motion state of the satellite is divided into a first state including a reference center of mass vector and a reference center of mass attitude angle, and a second state including a reference center of mass vector, a reference center of mass velocity, a reference center of mass attitude angle and a reference center of mass angular velocity, and the general formula of the measurement equation is established as follows:

[0053] y(t k )=Hx(t k )+μ;

[0054] Among them, t k =kT, T represents the measurement period, H is a constant matrix, and μ represents the measurement noise.

[0055] In one embodiment, in step S4, the discretization form of the identification equation is as follows:

[0056] x k =f(t k-1 ,x k-1 ,ω k ).

[0057] In one embodiment, in step S4, the prediction process of Kalman filtering is as follows:

[0058] x k|k-1 =f(t k-1 ,x k-1 ,0);

[0059]

[0060] in,

[0061]

[0062] The update process is as follows:

[0063]

[0064] x k|k =x k|k-1 +K k [y k -h(x k|k-1 )];

[0065] P k|k =P k|k-1 -K k H k P k|k-1 .

[0066] To achieve the above purpose, the embodiment of the present application further proposes an on-orbit identification device for inertial parameters of a maintainable satellite based on flywheel drive, comprising:

[0067] The dynamic model building module is used to build a maintainable satellite dynamic model that takes into account the offset between the flywheel system center of mass and the satellite center of mass based on the D'Alembert principle in the form of virtual power.

[0068] A derivation module is used to expand the system state vector to a column vector containing the satellite center of mass position and moment of inertia, and derive the identification equation in combination with the extended Kalman filter framework;

[0069] A measurement equation establishment module is used to obtain the Jacobian matrix analytical expression of the identification equation according to the calculation process of the extended Kalman filter and the satellite dynamics model, and establish a corresponding measurement equation, wherein the measurement quantity of the measurement equation includes the angular velocity of the flywheel and the motion state of the satellite;

[0070] The prediction and update module is used to discretize the identification equation, perform a state prediction process in combination with the calculation process of the Kalman filter, and update using the measurement data of the sensor to obtain the identification values ​​of the satellite's center of mass offset and moment of inertia.

[0071] To achieve the above-mentioned purpose, an embodiment of the present application further proposes an on-orbit identification device of inertial parameters of a serviceable satellite based on flywheel drive, comprising a memory, a processor, and an on-orbit identification program of inertial parameters of a serviceable satellite based on flywheel drive stored in the memory and executable on the processor, wherein when the processor executes the on-orbit identification program of inertial parameters of a serviceable satellite based on flywheel drive, the on-orbit identification method of inertial parameters of a serviceable satellite based on flywheel drive as described in any one of the above items is implemented.

[0072] To achieve the above-mentioned purpose, an embodiment of the present application further proposes a computer-readable storage medium, on which is stored an on-orbit identification program for inertial parameters of a repairable satellite based on flywheel drive. When the on-orbit identification program for inertial parameters of a repairable satellite based on flywheel drive is executed by a processor, the on-orbit identification method for inertial parameters of a repairable satellite based on flywheel drive as described in any one of the above items is implemented.

[0073] Compared with the prior art, this application has the following beneficial technical effects:

[0074] Existing satellite inertial parameter identification methods often require the consumption of satellite fuel, which will affect its service life, and do not fully consider the impact of measurement noise, and have poor noise resistance. Aiming at the problem of inertial parameter identification of repairable satellites after module replacement, this application, based on the establishment of a dynamic model that considers the offset between the center of mass of the flywheel system and the center of mass of the satellite, combines the extended Kalman filter method, and can identify the offset and moment of inertia of the satellite center of mass when only the flywheel is driven, and the method has high robustness, adaptability and anti-interference ability. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] 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 or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying creative work.

[0076] Figure 1 It is a module structure diagram of an embodiment of an on-orbit identification device for inertial parameters of a maintainable satellite based on flywheel drive according to the present invention;

[0077] Figure 2 It is a flow chart of an embodiment of an on-orbit identification method of inertial parameters of a maintainable satellite based on flywheel drive according to the present invention;

[0078] Figure 3 To simplify the simulation model diagram;

[0079] Figure 4 For case 1, the error diagram of the center of mass position identification result;

[0080] Figure 5 For case 1, the error diagram of the moment of inertia identification result;

[0081] Figure 6 For case 1, the error diagram of the moment of inertia identification result;

[0082] Figure 7 For case 2, the error diagram of the center of mass position identification result;

[0083] Figure 8 For case 2, the error diagram of the moment of inertia identification result;

[0084] Fig. 9 For case 2, the error diagram of the moment of inertia identification result;

[0085] Fig.10 The module structure diagram of an embodiment of the on-orbit identification device of inertial parameters of a maintainable satellite based on flywheel drive of the present invention.

[0086] The realization of the purpose, functional features and advantages of the present invention will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0087] It should be understood that the specific embodiments described herein are only used to explain the present invention, and are not used to limit the present invention.

[0088] In order to better understand the above technical solution, exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments described herein. On the contrary, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art.

[0089] It should be noted that in the claims, any reference symbols placed between brackets shall not be constructed as limitations to the claims. The presence of "comprising" in the text does not exclude the presence of components or steps not listed in the claims. The quantifier "one" or "an" preceding a component does not exclude the presence of a plurality of such components. The present invention can be implemented by means of hardware comprising several different components and by means of appropriately programmed computers. In a unit claim that lists several means, several of these means may be embodied by the same hardware item. The use of "first", "second", and "third" etc. does not indicate any order, and these words may be interpreted as names.

[0090] like Figure 1 As shown, Figure 1 It is a structural diagram of a server 1 (also called an in-orbit identification device for inertial parameters of a maintainable satellite based on flywheel drive) in a hardware operating environment involved in an embodiment of the present invention.

[0091] The server of the embodiment of the present invention is a device with display function, such as "Internet of Things devices", smart air conditioners, smart lights, smart power supplies with networking functions, AR / VR devices with networking functions, smart speakers, self-driving cars, PCs, smart phones, tablet computers, e-book readers, portable computers, etc.

[0092] like Figure 1 As shown, the server 1 includes: a memory 11, a processor 12 and a network interface 13.

[0093] The memory 11 includes at least one type of readable storage medium, including flash memory, hard disk, multimedia card, card-type memory (e.g., SD or DX memory, etc.), magnetic memory, disk, optical disk, etc. In some embodiments, the memory 11 may be an internal storage unit of the server 1, such as a hard disk of the server 1. In other embodiments, the memory 11 may also be an external storage device of the server 1, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card, etc., equipped on the server 1.

[0094] Furthermore, the memory 11 may also include an internal storage unit of the server 1 and an external storage device. The memory 11 may be used not only to store application software and various data installed on the server 1, such as the code of the flywheel-driven repairable satellite inertial parameter on-orbit identification program 10, but also to temporarily store data that has been output or is to be output.

[0095] In some embodiments, the processor 12 may be a central processing unit (CPU), a controller, a microcontroller, a microprocessor or other data processing chip, used to run program codes or process data stored in the memory 11, such as executing an in-orbit identification program 10 for inertial parameters of a serviceable satellite based on a flywheel drive.

[0096] The network interface 13 may optionally include a standard wired interface, a wireless interface (such as a WI-FI interface), and is generally used to establish a communication connection between the server 1 and other electronic devices.

[0097] The network may be the Internet, a cloud network, a wireless fidelity (Wi-Fi) network, a personal area network (PAN), a local area network (LAN), and / or a metropolitan area network (MAN). Various devices in the network environment may be configured to connect to the communication network according to various wired and wireless communication protocols. Examples of such wired and wireless communication protocols may include, but are not limited to, at least one of the following: Transmission Control Protocol and Internet Protocol (TCP / IP), User Datagram Protocol (UDP), Hypertext Transfer Protocol (HTTP), File Transfer Protocol (FTP), ZigBee, EDGE, IEEE 802.11, Light Fidelity (Li-Fi), 802.16, IEEE 802.11s, IEEE 802.11g, multi-hop communication, wireless access point (AP), device-to-device communication, cellular communication protocol, and / or Bluetooth (Blue Tooth) communication protocol or a combination thereof.

[0098] Optionally, the server may further include a user interface, which may include a display, an input unit such as a keyboard, and an optional user interface may further include a standard wired interface and a wireless interface. Optionally, in some embodiments, the display may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, and an OLED (Organic Light-Emitting Diode) touch device, etc. The display may also be referred to as a display screen or a display unit, which is used to display information processed in the server 1 and to display a visual user interface.

[0099] Figure 1 Only the server 1 having components 11-13 and the flywheel-driven maintainable satellite inertial parameter on-orbit identification program 10 is shown. It can be understood by those skilled in the art that Figure 1 The structure shown does not constitute a limitation on the server 1, and may include fewer or more components than shown in the figure, or combine certain components, or arrange the components differently.

[0100] In this embodiment, the processor 12 may be used to call the flywheel-driven maintainable satellite inertial parameter on-orbit identification program stored in the memory 11, and perform the following operations:

[0101] S1. Based on the D'Alembert principle in the form of virtual power, a maintainable satellite dynamics model is established that takes into account the offset between the flywheel system's center of mass and the satellite's center of mass;

[0102] S2, expand the system state vector to a column vector containing the satellite center of mass position and moment of inertia, and derive the identification equation in combination with the extended Kalman filter framework;

[0103] S3. According to the calculation process of the extended Kalman filter and in combination with the satellite dynamics model, the Jacobian matrix analytical expression of the identification equation is obtained, and a corresponding measurement equation is established. The measurement quantity of the measurement equation includes the angular velocity of the flywheel and the motion state of the satellite;

[0104] S4. Discretize the identification equation, perform a state prediction process in combination with the calculation process of Kalman filtering, and update it using the measurement data of the sensor to obtain the identification values ​​of the satellite's center of mass offset and moment of inertia.

[0105] Based on the hardware architecture of the above-mentioned flywheel-driven on-orbit identification device for inertial parameters of a maintainable satellite, an embodiment of the flywheel-driven on-orbit identification method for inertial parameters of a maintainable satellite is proposed.

[0106] Reference Figure 2 , Figure 2 This is an embodiment of the on-orbit identification method of inertial parameters of a serviceable satellite based on flywheel drive of the present invention. The on-orbit identification method of inertial parameters of a serviceable satellite based on flywheel drive comprises the following steps:

[0107] S1. Based on the D'Alembert principle in the form of virtual power, a maintainable satellite dynamics model is established that takes into account the offset between the flywheel system's center of mass and the satellite's center of mass;

[0108] S2, expand the system state vector to a column vector containing the satellite center of mass position and moment of inertia, and derive the identification equation in combination with the extended Kalman filter framework;

[0109] S3. According to the calculation process of the extended Kalman filter and in combination with the satellite dynamics model, the Jacobian matrix analytical expression of the identification equation is obtained, and a corresponding measurement equation is established. The measurement quantity of the measurement equation includes the angular velocity of the flywheel and the motion state of the satellite;

[0110] S4. Discretize the identification equation, perform a state prediction process in combination with the calculation process of Kalman filtering, and update it using the measurement data of the sensor to obtain the identification values ​​of the satellite's center of mass offset and moment of inertia.

[0111] Specifically, step S1 includes:

[0112] To simplify the modeling, it is assumed that the satellite reference center of mass is connected to the inertial reference point through a virtual hinge. The virtual hinge has a total of 6 degrees of freedom, including 3 rotational degrees of freedom and 3 translational degrees of freedom. The introduction of the virtual hinge is only for the convenience of dynamic modeling and will not have any effect on the dynamic characteristics of the system. Combined with the D'Alembert principle in the form of virtual power, the dynamic model of the satellite can be written as:

[0113]

[0114] Among them, q, denote the generalized coordinates and their first-order and second-order derivatives respectively, θ denotes the inertial parameter to be identified, Z (q,θ) represents the generalized mass matrix, represents the generalized force vector, and u represents the control torque on the hinge.

[0115] Z (q,θ) and The specific expression is:

[0116] Z (q,θ)= α T m α +β T J β(2);

[0117]

[0118] in, α and β It is related to the relative position vector between the satellite and each flywheel and the direction of the flywheel axis. J are all diagonal matrices, where the m diagonal elements are the masses of the satellite and each flywheel, J The diagonal element is the moment of inertia of the satellite and flywheel in the inertial system. o is the column vector of the external forces acting on the satellite and the flywheel, M o is the column vector composed of the external torques acting on the satellite and the flywheel, w represents the inertial force of each object, σ and ε represent the inertial torque, F τq Represents a constraint element.

[0119] Specifically, step S2 includes:

[0120] S21. Obtain the matrix form of the satellite dynamics model based on the column vector obtained by expanding the system state vector:

[0121]

[0122] Among them, the generalized coordinates q of the satellite are divided into q1 and q w There are two parts, q1 represents the motion parameters of the satellite body, and q w Indicates the rotation angle of the flywheel.

[0123] S22. For the flywheel drive scenario, the angular acceleration is known, that is, The theoretical value of is known, and using the integral-inverse hybrid dynamics model, the identification equation is obtained as follows:

[0124]

[0125] Specifically, step S3 includes:

[0126] S31. Using the chain rule, differentiate the generalized mass matrix Z and the generalized force vector z relative to the generalized coordinates of the system to obtain the following expressions:

[0127]

[0128] S32, considering α, β, F a ,w,M a , σ and ε, and calculate and To get the analytical expression of the above formula:

[0129] Opposite direction cosine matrix A j Ask for q l The partial derivative of can be obtained:

[0130]

[0131] in, It is determined only by the jth joint hinge, so it can be calculated by recursive technique

[0132] for and can be written as:

[0133]

[0134] therefore,

[0135]

[0136] because and The joint joint j and its coordinate q j Decide, and Can be obtained Then it is calculated by recursion.

[0137] when and After getting, considering the specific definition, and It can be calculated by the chain rule. Then, it can be calculated and

[0138] for It affects ω, σ and ε, so

[0139] For calculation The angular velocity Taking the derivative, we can get:

[0140] in, It can be obtained by recursive method.

[0141] for and Considering its definition, we can calculate Get it directly.

[0142] When the calculation is and after, It can also be obtained by the chain rule.

[0143] In addition to the system generalized coordinates q and its derivatives In addition, the inertial parameter θ will also affect the motion.

[0144] The moment of inertia J'1 only affects the matrix J, so we only need to replace J with Substituting into the dynamic model, the corresponding derivative term can be obtained. For the position vector b1 from the center of mass of the base to the reference point in this system, it appears in α and w in a linear form. Therefore, it is only necessary to replace b1' with [1,0,0] T , [0,1,0] T or [0,0,1] T and others n 'Replace with [-1,0,0] T , [0,-1,0] T and [0,0,-1] T To calculate and i=x,y,orz.

[0145] Using the chain rule, we can get and The analytical expression of the Jacobian matrix of can then be used to obtain the analytical expression of the identification equation for the state vector x.

[0146] S33, establish the measurement equation:

[0147] Assuming that the measurement quantities of the measurement equation include the angular velocity of the flywheel and the motion state of the satellite, in order to analyze the influence of the measurement quantity type on the identification performance, the motion state of the satellite is divided into a first state including the reference center of mass vector and the reference center of mass attitude angle, and a second state including the reference center of mass vector, the reference center of mass velocity, the reference center of mass attitude angle and the reference center of mass angular velocity. The general formula of the measurement equation can be written as:

[0148] y(tk )=Hx(t k )+μ(12);

[0149] Among them, t k =kT, T represents the measurement period, H is a constant matrix, and μ represents the measurement noise.

[0150] Specifically, step S4 includes:

[0151] By selecting an appropriate method, the discrete form of the identification equation can be written as:

[0152] x k =f(t k-1 ,x k-1 ,ω k )(13);

[0153] The corresponding filter prediction process is:

[0154] x k|k-1 =f(t k-1 ,x k-1 ,0) (14);

[0155]

[0156] in,

[0157]

[0158] The update process is:

[0159]

[0160] x k|k =x k|k-1 +K k [y k -h(x k|k-1 )] (19);

[0161] P k|k =P k|k-1 -K k H k P k|k-1 (20).

[0162] Combined with the analytical expression of the Jacobian matrix of the dynamic model studied previously, the above equations can be solved.

[0163] Considering the characteristics of the extended Kalman filter, it has good anti-interference ability and can still obtain good estimation results when measurement noise exists. At the same time, it can still provide good estimation results when only part of all state quantities are measurable. Therefore, compared with the traditional identification method based on recursive least squares, the method proposed in this patent has better robustness.

[0164] In order to better illustrate the purpose and advantages of the present invention, the following Figures 3 to 9 The present invention is further described with examples:

[0165] Assume that there is a deviation vector between the satellite mass center and the flywheel system mass center, such as Figure 3 As shown, this deviation will also bring uncertainty to the satellite body's moment of inertia. In order to better demonstrate the characteristics and advantages of the proposed method, this patent simulates and analyzes two situations based on the measured values, as follows:

[0166] like Figures 4 to 6 As shown, case 1: the measured quantities include the satellite's reference point (i.e., reference center of mass) vector, velocity, attitude angle, angular velocity, and flywheel rotation angular velocity;

[0167] like Figures 7 to 9 As shown, case 2: the measured quantities only include the satellite's reference point vector, attitude angle and flywheel rotation angular velocity.

[0168] Step 1: First, a dynamic model considering the center of mass offset is established according to the D'Alembert principle based on the virtual power form, as shown in equations (1)-(3). The initial state of the system including the satellite reference point position, velocity, attitude angle and angular velocity and the initial value of the identification parameter is used as the initial state value of the filter, and the initial covariance matrix is ​​determined according to the error range of the corresponding parameters;

[0169] Step 2: The ideal motion of the flywheel during the identification process, i.e. It is known that according to the identification equation obtained by equation (5), the state quantity and covariance matrix prediction are first calculated according to equations (13)-(17). In the calculation process, the Jacobian matrix analytical expression represented by equations (6)-(11) is needed.

[0170] Step 3: After the state quantity and covariance matrix at the corresponding moment are predicted, the update calculation is performed in combination with the physical quantity measured by the sensor, as shown in equations (18)-(20). After the update process is completed, the iterative calculation of step 2 is performed until the simulation ends.

[0171] The values ​​of the system parameters used in the above embodiment are shown in Table 1 below.

[0172]

[0173]

[0174] Table 1 Simulation parameters.

[0175] It can be understood that the on-orbit identification method of inertial parameters of a maintainable satellite based on flywheel drive of the present application utilizes the dynamic coupling characteristics caused by the offset between the satellite center of mass and the flywheel system center of mass, and combines with the extended Kalman filter algorithm to achieve high-precision inertial parameter identification of a maintainable satellite after module replacement by only using flywheel drive when only part of the state quantity is measurable and measurement noise exists. At the same time, it can also avoid fuel consumption and improve the on-orbit period.

[0176] Therefore, compared with the prior art, the present invention has the following beneficial technical effects:

[0177] Existing satellite inertial parameter identification methods often require the consumption of satellite fuel, which will affect its service life, and do not fully consider the impact of measurement noise, and have poor noise resistance. Aiming at the problem of inertial parameter identification of repairable satellites after module replacement, this application, based on the establishment of a dynamic model that considers the offset between the center of mass of the flywheel system and the center of mass of the satellite, combines the extended Kalman filter method, and can identify the offset and moment of inertia of the satellite center of mass when only the flywheel is driven, and the method has high robustness, adaptability and anti-interference ability.

[0178] In addition, refer to Fig.10 The embodiment of the present invention further proposes an on-orbit identification device for inertial parameters of a maintainable satellite based on flywheel drive, and the on-orbit identification device for inertial parameters of a maintainable satellite based on flywheel drive comprises:

[0179] A dynamic model building module 110 is used to build a maintainable satellite dynamic model taking into account the offset between the mass center of the flywheel system and the mass center of the satellite based on the D'Alembert principle in the form of virtual power;

[0180] A derivation module 120, for expanding the system state vector to a column vector including the satellite center of mass position and moment of inertia, and deriving the identification equation in combination with the extended Kalman filter framework;

[0181] A measurement equation establishment module 130 is used to obtain the Jacobian matrix analytical expression of the identification equation according to the calculation process of the extended Kalman filter in combination with the satellite dynamics model, and establish a corresponding measurement equation, wherein the measurement quantity of the measurement equation includes the angular velocity of the flywheel and the motion state of the satellite;

[0182] The prediction and update module 140 is used to discretize the identification equation, perform a state prediction process in combination with the calculation process of the Kalman filter, and update using the measurement data of the sensor to obtain the identification values ​​of the satellite's center of mass offset and moment of inertia.

[0183] Among them, the steps implemented by each functional module of the on-orbit identification device of inertial parameters of a repairable satellite based on flywheel drive can refer to the various embodiments of the on-orbit identification method of inertial parameters of a repairable satellite based on flywheel drive of the present invention, and will not be repeated here.

[0184] In addition, the embodiment of the present invention further proposes a computer-readable storage medium, which may be any one or any combination of a hard disk, a multimedia card, an SD card, a flash memory card, an SMC, a read-only memory (ROM), an erasable programmable read-only memory (EPROM), a portable compact disk read-only memory (CD-ROM), a USB memory, etc. The computer-readable storage medium includes an on-orbit identification program 10 for inertial parameters of a repairable satellite based on flywheel drive. The specific implementation of the computer-readable storage medium of the present invention is substantially the same as the specific implementation of the on-orbit identification method for inertial parameters of a repairable satellite based on flywheel drive and the server 1, which will not be described in detail.

[0185] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0186] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0187] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1A function specified in one or more boxes.

[0188] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0189] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0190] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A flywheel-driven on-orbit identification method for inertial parameters of a maintainable satellite, characterized in that: The following steps are involved: S1. Based on the D'Alembert principle in the form of virtual power, a maintainable satellite dynamics model is established that takes into account the offset between the flywheel system center of mass and the satellite center of mass; S2, expand the system state vector to a column vector containing the satellite center of mass position and moment of inertia, and derive the identification equation in combination with the extended Kalman filter framework; S3. According to the calculation process of the extended Kalman filter and in combination with the satellite dynamics model, the Jacobian matrix analytical expression of the identification equation is obtained, and a corresponding measurement equation is established. The measurement quantity of the measurement equation includes the angular velocity of the flywheel and the motion state of the satellite; S4. Discretize the identification equation, perform a state prediction process in combination with the calculation process of Kalman filtering, and update it using the measurement data of the sensor to obtain the identification values ​​of the satellite's center of mass offset and moment of inertia.

2. The flywheel-driven on-orbit identification method for inertial parameters of a maintainable satellite according to claim 1, characterized in that: Step S1 includes: Assume that the satellite reference center of mass is connected to the inertial reference point via a virtual hinge, and the virtual hinge includes three rotational degrees of freedom and three translational degrees of freedom; The satellite dynamics model is established by using the D'Alembert principle in the form of virtual power. The satellite dynamics model is expressed as follows: Among them, q, denote the generalized coordinates and their first-order and second-order derivatives respectively, θ denotes the inertial parameter to be identified, Z (q,θ) represents the generalized mass matrix, represents the generalized force vector, u represents the control torque on the hinge; in, Z (q,θ) and The expression is as follows: Z (q,θ)= α T m α +b T J b; in, α and β It is related to the relative position vector between the satellite and each flywheel and the direction of the flywheel axis. J are all diagonal matrices, where the m diagonal elements are the masses of the satellite and each flywheel, J The diagonal elements are the moments of inertia of the satellite and flywheel in the inertial system, F o is the column vector of the external forces acting on the satellite and the flywheel, M o is the column vector composed of the external torques acting on the satellite and the flywheel, w represents the inertial force of each object, σ and ε represent the inertial torque, F τq Represents a constraint element.

3. The flywheel-driven on-orbit identification method for inertial parameters of a maintainable satellite according to claim 2, characterized in that: Step S2 includes: S21. Obtain the matrix form of the satellite dynamics model based on the column vector obtained by expanding the system state vector: Among them, the generalized coordinates q of the satellite are divided into q1 and q w Two parts, where q1 represents the motion parameters of the satellite body, q w represents the rotation angle of the flywheel; S22. For the flywheel drive scenario, the angular acceleration is known, that is, The theoretical value of is known, and the identification equation is obtained by using the integral-inverse hybrid dynamics model as follows:

4. The on-orbit identification method of inertial parameters of a maintainable satellite based on flywheel drive as claimed in claim 3, characterized in that: Step S3 includes: S31. Using the chain rule, differentiate the generalized mass matrix Z and the generalized force vector z relative to the generalized coordinates of the system to obtain the following expressions: S32, calculation and To get the analytical expression of the above formula: Opposite direction cosine matrix A j Ask for q l The partial derivative of can be obtained: in, Determined by the jth joint hinge, it can be calculated by recursive technique for and can be written as: therefore, because and The joint joint j and its coordinate q j Decided, therefore, and Can be obtained Then it is calculated by recursive method; When getting and back, and It can be calculated by the chain rule, and then it can be calculated and for It affects ω, σ and ε, so For calculation The angular velocity Taking the derivative, we can get: in, It can be obtained by recursive method; for and It can be calculated by Get it directly; When calculated and back, It can be obtained by chain derivation rule; For the target moment of inertia J′1, replace J with Substitute it into the satellite dynamics model to obtain the corresponding derivative terms; For the position vector b1 from the base mass center to the reference point in this system, replace b1' with [1,0,0] T , [0,1,0] T or [0,0,1] T and others n 'Replace with [-1,0,0] T , [0,-1,0] T and [0,0,-1] T To calculate and Where i = x, y, or z; Using the chain rule, we get and The analytical expression of the Jacobian matrix of , and then the analytical expression of the identification equation for the state vector x can be obtained; S33, establish the measurement equation: Assuming that the measurement quantities of the measurement equation include the angular velocity of the flywheel and the motion state of the satellite, in order to analyze the influence of the measurement quantity type on the identification performance, the motion state of the satellite is divided into a first state including a reference center of mass vector and a reference center of mass attitude angle, and a second state including a reference center of mass vector, a reference center of mass velocity, a reference center of mass attitude angle and a reference center of mass angular velocity, and the general formula of the measurement equation is established as follows: y(t k )=Hx(t k )+μ; Among them, t k =kT, T represents the measurement period, H is a constant matrix, and μ represents the measurement noise.

5. The on-orbit identification method of inertial parameters of a maintainable satellite based on flywheel drive as claimed in claim 4, characterized in that: In step S4, the discretization form of the identification equation is as follows: x k =f(t k-1 ,x k-1 ,ω k )。 6. The on-orbit identification method of inertial parameters of a maintainable satellite based on flywheel drive as claimed in claim 5, characterized in that: In step S4, the prediction process of Kalman filtering is as follows: x k|k-1 =f(t k-1 ,x k-1 ,0); in, The update process is as follows: x k|k =x k|k-1 +K k [y k -h(x k|k-1 )]; P k|k =P k|k-1 -K k H k P k|k-1 。 7. A flywheel-driven on-orbit identification device for inertial parameters of a maintainable satellite, characterized in that: include: The dynamic model building module is used to build a maintainable satellite dynamic model that takes into account the offset between the flywheel system center of mass and the satellite center of mass based on the D'Alembert principle in the form of virtual power. A derivation module is used to expand the system state vector to a column vector containing the satellite center of mass position and moment of inertia, and derive the identification equation in combination with the extended Kalman filter framework; A measurement equation establishment module is used to obtain the Jacobian matrix analytical expression of the identification equation according to the calculation process of the extended Kalman filter and the satellite dynamics model, and establish a corresponding measurement equation, wherein the measurement quantity of the measurement equation includes the angular velocity of the flywheel and the motion state of the satellite; The prediction and update module is used to discretize the identification equation, perform a state prediction process in combination with the calculation process of the Kalman filter, and update using the measurement data of the sensor to obtain the identification values ​​of the satellite's center of mass offset and moment of inertia.

8. A flywheel-driven inertial parameter on-orbit identification device for a maintainable satellite, characterized in that: The invention comprises a memory, a processor and an on-orbit identification program of inertial parameters of a serviceable satellite based on flywheel drive which is stored in the memory and can be run on the processor. When the processor executes the on-orbit identification program of inertial parameters of a serviceable satellite based on flywheel drive, the on-orbit identification method of inertial parameters of a serviceable satellite based on flywheel drive as described in any one of claims 1 to 6 is implemented.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores an on-orbit identification program for inertial parameters of a serviceable satellite based on flywheel drive. When the on-orbit identification program for inertial parameters of a serviceable satellite based on flywheel drive is executed by a processor, the on-orbit identification method for inertial parameters of a serviceable satellite based on flywheel drive as described in any one of claims 1 to 6 is implemented.

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