An integrated control method for long-distance pursuit and close-range rendezvous of small spacecraft

Abstract

The present invention relates to an integrated control method for long-distance pursuit and close-range rendezvous of small spacecraft, belonging to the field of aerospace engineering technology. This method considers the orbital dynamics equation of the small spacecraft and environmental disturbances, and establishes the dynamic models of the target spacecraft and the chasing spacecraft; designs a nonlinear model predictive control framework to achieve the motion control of the chasing spacecraft, so that the satellite can achieve rendezvous control with the chasing target while ensuring the actuator saturation constraint; and further uses the fuzzy logic method to fuzzily classify the relative distance between the two spacecraft, and uses the model predictive control plus fuzzy logic tuning parameter controller to control the chasing spacecraft, so that the spacecraft can automatically adjust the weights of position, speed and thrust at long and short distances, and achieve the integrated control of long-distance pursuit and close-range rendezvous of the spacecraft.

Description

Technical Field

[0001] The present invention belongs to the technical field of aerospace engineering, and particularly relates to an integrated control method for long-distance pursuit and short-distance rendezvous of small spacecrafts. Background Technique

[0002] The long-distance pursuit and short-distance rendezvous of spacecrafts are important space activities, providing technical support for the development of China's aerospace industry. In recent years, with the continuous development of science and technology, the spacecraft rendezvous and docking technology has also been continuously evolving. The spacecraft rendezvous technology is mainly used to control and monitor the relative positions and motion states of two or more spacecrafts in space to achieve various mission objectives, such as manned spaceflight, space exploration, satellite repair and maintenance, etc. This technology can ensure the safe operation between spacecrafts and enable them to precisely converge, dock, separate or capture in orbit. Therefore, for the wide application of spacecraft tracking and docking technology, the algorithm of its controller is very important.

[0003] For the rendezvous and docking process of spacecrafts, there are mainly the following algorithm classifications: ground guidance, space guidance, approach-approach, and approach-hop. The spacecraft rendezvous and docking generally include the following steps: 1) Launch: Two or more spacecrafts need to be launched into predetermined orbits respectively, and ensure that their relative positions and velocities meet the mission requirements. 2) Close-range flight: The spacecrafts approach each other in orbit and start close-range flight. In this stage, it is necessary to accurately measure and correct parameters such as the position, velocity and attitude of the spacecrafts to ensure that they can converge smoothly. 3) Approach and capture: When the spacecrafts approach each other and reach the convergence distance, it is necessary to control the speed and attitude through propellants to make one spacecraft stationary relative to the other spacecraft. Then, the capture between spacecrafts can be carried out through a robotic arm or other devices. 4) Guidance code alignment: After the spacecrafts are captured, it is necessary to perform guidance code alignment to complete the docking process. The guidance code is a signal sent by the target spacecraft for guiding and controlling the docking process. After the above complex process, it is possible for the spacecrafts to achieve accurate docking, so the control strategy therein is very important.

[0004] Based on the above summary and investigation of various research methods, the present invention makes an integrated control direction for long-distance pursuit and close-range rendezvous of spacecraft based on model predictive control. By using an MPC controller to predict the next state, the spacecraft can intuitively handle a multivariable constraint system in a complex non-linear space environment, and can well solve the optimal control problem of pursuit and rendezvous in this design. When the two spacecraft are at a relatively long distance, since the requirements for position and velocity are not very high, the focus of the controller is energy conservation. When the two spacecraft are in a state of approaching rendezvous, the requirements for position and velocity become very high, and at this time the requirement for energy conservation is not so strict. Therefore, the present invention adjusts each parameter in the MPC by means of fuzzy logic to achieve automatic recognition of the far and near distances by the controller to automatically adjust the parameter weights, so as to achieve the ideal effect at different distances.

[0005] However, MPC also has its own limitations. When using model predictive control to solve non-linear optimal control problems, there are mainly the following two aspects of deficiencies: 1) From the perspective of the algorithm, it is only applicable to slow dynamic processes and environments with high-performance computers, which poses a challenge to ordinary local controllers. 2) From the perspective of application, there are not many applications for non-linear processes. These shortcomings hinder the development of MPC in practical applications, and its applications in the aerospace field are extremely rare. Summary of the Invention

[0006] The purpose of the present invention is to solve the problem of realizing the control objectives of two stages with a single controller when a spacecraft is in long-distance pursuit and close-range rendezvous. A method for integrated control of long-distance pursuit and close-range rendezvous of a small spacecraft is provided. By fuzzifying the relative distance between the two spacecraft and adjusting the weight matrix parameters of the controller, the same controller can be used in the two stages of long-distance pursuit and close-range rendezvous, and the weight problems of position, velocity and thrust can be automatically controlled and switched when the tracking spacecraft switches from long distance to close distance, thereby significantly improving the safety of the spacecraft and achieving the expected control objectives.

[0007] To achieve the above object, the technical solution of the present invention is: a method for integrated control of long-distance pursuit and close-range rendezvous of a small spacecraft, including the following steps:

[0008] Step S1: Design a nine-state variable tracking spacecraft dynamics model based on position, velocity and thrust, establish the operation trajectory of the target spacecraft and establish the target spacecraft dynamics model;

[0009] Step S2: Define the controller to be designed for the integrated control of long-distance pursuit and close-range rendezvous of the spacecraft, design an MPC controller according to the model predictive control method, and observe the simulation diagram of the fuel cumulative consumption through simulation;

[0010] Step S3: Use the MATMPC toolbox to implement the integrated control of the MPC controller for the long-distance pursuit and close-range rendezvous of the spacecraft. Then, use fuzzy logic to adjust the parameters to obtain an optimized MPC controller, and conduct a simulation to observe the simulation diagram of the cumulative fuel consumption.

[0011] In an embodiment of the present invention, the specific content of the step S1 includes: defining the state variables and control variables of the tracking spacecraft model, establishing the dynamic equation and control equation of the tracking spacecraft, and establishing the dynamic model of the target spacecraft according to the trajectory of the target spacecraft to be designed.

[0012] In an embodiment of the present invention, the specific content of the step S2 includes: from the dynamic model of the tracking spacecraft, the dynamic model of the target spacecraft, and the MATMPC toolbox established in step S1, combining the difference between the future predicted state and the reference trajectory and the control variable into an optimization problem cost function, and realizing the trajectory tracking of the target spacecraft through rolling optimization.

[0013] In an embodiment of the present invention, the specific content of the step S3 includes: from the dynamic model of the tracking spacecraft, the dynamic model of the target spacecraft, and the MATMPC toolbox established in step S1, combining the difference between the future predicted state and the reference trajectory and the control variable into an optimization problem cost function, and through rolling optimization, adding fuzzy logic, and adjusting the weight matrix parameters of the MPC controller by fuzzifying the relative distance between the tracking spacecraft and the target spacecraft, so as to realize the trajectory tracking of the target spacecraft.

[0014] In an embodiment of the present invention, the specific implementation steps of the step S1 are as follows:

[0015] Step S11: Dynamic modeling of the tracking spacecraft:

[0016] A) Characteristics of the tracking spacecraft

[0017] The tracking spacecraft is a small spacecraft, and the moments of inertia of each main axis of the tracking spacecraft are expressed as:

[0018]

[0019]

[0020]

[0021] where m is the mass of the small spacecraft, Z represents the moment of inertia, and a, b, c are the dimensions of the small spacecraft;

[0022] B) System dynamics of the tracking spacecraft

[0023] Assume that the earth is a perfect sphere, then the acceleration of the tracking spacecraft is as follows:

[0024]

[0025] μ is the gravitational parameter of the Earth, is the position vector of the object in the Earth inertial coordinate system, and r is the radius of the Earth;

[0026] In fact, the Earth is an ellipsoid, so its gravitational field is asymmetric. By superimposing additional harmonic terms to simulate the oblateness of the Earth, a more accurate simulation approximation is given. The mathematical form of the acceleration at this time is as follows:

[0027]

[0028]

[0029]

[0030] B is a constant representing the oblateness of the Earth, R is the equatorial radius of the Earth, and x, y, and z are used to describe the position of the spacecraft on the x, y, and z axes of the geocentric equatorial inertial coordinate system;

[0031] C) Tracking spacecraft system dynamics modeling

[0032] Establish a tracking spacecraft system model and only study the dynamics of the position. Therefore, there are 9 state variables, which are as follows:

[0033] There are 3 position state variables (x, y, z) in the geocentric equatorial inertial coordinate system;

[0034] There are 3 velocity state variables (v x , v y , v z ) in the geocentric equatorial inertial coordinate system;

[0035] There are 3 control state variables (T x , T y , T z ) in the geocentric equatorial inertial coordinate system;

[0036] In the MATMPC toolbox, the dynamics of the tracking spacecraft are defined by writing the derivative equations of each state; the acceleration of the tracking spacecraft only considers the gravity from the Earth and the force from the thruster;

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046] Denote the derivatives of x, y, and z. Denote v x , v y , v z . The derivative of T x,ECI Denote the thrust in the x - direction in the Earth - centered inertial coordinate system ECI. Denote the derivatives of the thrust in the x, y, and z directions of the chaser spacecraft. c1, c2, and c3 denote the control quantities in the x, y, and z directions of the chaser spacecraft.

[0047] Step S12: Trajectory planning of the target spacecraft:

[0048] Set the initial position and velocity of the target spacecraft as: [6678; 0; 0; 0; 6.69; 3.862], and set its trajectory to rotate around the Earth once. Its trajectory expression is as follows:

[0049] v a = 7.7247(20)

[0050]

[0051] x m = x0 * cos(w * (t + T * n))(22)

[0052]

[0053]

[0054]

[0055]

[0056]

[0057] Among them, v a Denote the total velocity of the target spacecraft. The three position quantities of the target spacecraft are x m , y m , z m , and the three velocity quantities are v xm, v ym , v zm , where x0 is the initial x - direction position of the target spacecraft, y0 is the initial y - direction position of the target spacecraft, z0 is the initial z - direction position of the target spacecraft, w represents the angular velocity of the target spacecraft, t is the current time, T is the simulation sampling time, n is the current step number, and the step size N = 100; the dynamic model of the target spacecraft is established by the above equations.

[0058] In an embodiment of the present invention, the specific implementation steps of step S2 are as follows:

[0059] Step S21, design the MATMPC toolbox:

[0060] MATMPC is a collection of MATLAB functions, including standard functions and MEX functions; MATMPC is divided into two parts: the model generation part and the simulation part;

[0061] (1) Model generation part

[0062] The model generation function uses a user - defined dynamic model and, using automatic differentiation in CasADi, generates C code for the model analytical function and its derivative;

[0063] (2) Simulation part

[0064] The simulation function is used to run a closed - loop NMPC simulation in MATLAB; it starts from initializing the controller options, data, and memory defined in the MATLAB structure format; the NMPC controller in MATMPC is a MATLAB function that calls multiple modules, which are MEX functions, and they share the same data and memory structure created during initialization;

[0065] Step S22, design the MPC controller:

[0066] Assume the current state is x(t), and the optimal control problem to be solved at time t is expressed as

[0067]

[0068]

[0069] 0 = x k+1 -φ k (x k , u k ), k = 0, 1,......, N - 1, (30)

[0070] r 1k ≤r k (x k , u k )≤r 2k, k = 0, 1,......, N - 1, (31)

[0071] r 1N ≤ r N (x N ) ≤ r 2N , (32)

[0072] wherein, is the measured value of the current state, x0 is the given value of the current state, W represents the constraint of the optimal control problem of the tracking spacecraft, and W N represents the constraint of the optimal control problem of the target spacecraft. Equation (31) is the constraint on the running path of the tracking spacecraft, and r k represents the running radius of the tracking spacecraft, and r 1k and r 2k are the upper and lower limits of r k respectively. Equation (32) is the running path constraint of the target spacecraft, and the parameter meanings are the same as those in Equation (31). When k = 0, 1,......, N, the system state x k is defined at the discrete point t k . When k = 0, 1,......, N - 1, the control input u k is a piecewise constant; h k (x k , u k ) represents the position of the tracking spacecraft, and h N (x N ) represents the position of the target spacecraft; Equation (30) represents a continuity constraint, where φ k (x k , u k ) is a numerical integration operator;

[0073] The control action should allow a trade - off between the speed, position of the rendezvous mission and the minimization of the related fuel consumption. The W matrix is the matrix that weighs these three factors. By simply adjusting the corresponding parameters in the W matrix, the weights of the three factors can be adjusted to achieve good control effects;

[0074] The optimal control problem is formulated by applying multiple - shooting to the optimal control problem over the prediction horizon T = [t0, t f , where t0 and t f are the upper and lower limits of the prediction horizon of the model predictive control. N is divided into [t0, t1,......, t N , and t N represents the time at the Nth moment.

[0075] In an embodiment of the present invention, the specific implementation steps of step S3 are as follows:

[0076] Step S31, physical domain quantization:

[0077] Fuzzy logic is used to fuzzify the distance to adjust the parameters of the model predictive controller for the tracking spacecraft and the target spacecraft at different distances. Therefore, the physical domain is the distance h between the tracking spacecraft and the target spacecraft j , as shown in the following formula:

[0078]

[0079] x0, y0, and z0 are the positions of the target spacecraft in three directions, x1, y1, and z1 are the positions of the tracking spacecraft in three directions, and h1 is the distance between the two spacecraft; the object to be fuzzified in this step is h j , and the ultimate goal to be achieved is to make h j be 0;

[0080] Step S32: Establish fuzzy sets:

[0081] After quantifying the physical domain, it is necessary to determine the membership degrees of the elements in each fuzzy set. When the tracking spacecraft and the target spacecraft are far apart, that is, greater than a threshold value, the weight of energy conservation is emphasized rather than the weights of position and velocity. When the tracking spacecraft and the target spacecraft are close to each other, that is, less than another threshold value, the velocities and positions are emphasized to ensure precise docking rather than energy conservation. This is the linguistic description of the membership degrees of the elements in each fuzzy set, which is converted into a mathematical description

[0082] Compared with the prior art, the present invention has the following beneficial effects:

[0083] The present invention studies the problem of achieving the control objectives of two stages with a single controller for spacecraft during long-distance pursuit and short-distance rendezvous, and discloses an integrated control method for long-distance pursuit and short-distance rendezvous of small spacecraft

[0084] (1) An integrated control method for long-distance pursuit and short-distance rendezvous of spacecraft based on model predictive control proposed by the present invention expands the traditional controller into a controller with trajectory prediction ability. The model predictive controller and the predicted trajectory feedback calculated by it help the tracking spacecraft to be able to predict the next state in advance during the tracking process and finally generate a reference of the state quantity at the next sampling moment. Such a reference can better guide the model predictive controller to obtain better control performance. The predictive behavior control overcomes the problem of improper switching timing of the task priorities of the existing behavior control, thereby significantly improving the safety of the spacecraft

[0085] (2) By means of the fuzzy logic concept, when the two spacecraft are far apart, the present invention attaches importance to energy conservation rather than the weights of position and velocity. When the two spacecraft are close to each other, the present invention attaches importance to velocity and position to ensure precise docking and pays less attention to energy conservation. Therefore, the relative distance between the two spacecraft is fuzzified, and different weight matrices are used in different distance intervals to automatically adjust the weights of position, velocity, and control quantity at the fuzzy concept of far and near, so as to obtain a better control effect and greatly reduce the fuel consumption of the spacecraft. Brief Description of the Drawings

[0086] The drawings forming a part of this application are used to provide a further understanding of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0087] Figure 1 is the integrated architecture diagram of model predictive control plus fuzzy logic parameter tuning control in the background technology of the present invention;

[0088] Figure 2 is the cumulative energy consumption comparison chart of the tracking spacecraft using the MPC controller and the MPC plus fuzzy logic parameter tuning controller in the embodiment of the present invention;

[0089] Figure 3 is the thrust diagram of each direction of the tracking spacecraft using the MPC controller in the embodiment of the present invention;

[0090] Figure 4 is the position and velocity diagram of each direction of the tracking spacecraft using the MPC controller in the embodiment of the present invention;

[0091] Figure 5 is the relative position and velocity diagram of each direction of the tracking spacecraft using the MPC controller in the embodiment of the present invention;

[0092] Figure 6 is the three-dimensional trajectory diagram of long-distance pursuit and short-distance rendezvous of the spacecraft using the MPC controller in the embodiment of the present invention;

[0093] Figure 7 is the thrust diagram of each direction of the tracking spacecraft using the MPC plus fuzzy logic parameter tuning controller in the embodiment of the present invention;

[0094] Figure 8 is the position and velocity diagram of each direction of the tracking spacecraft using the MPC plus fuzzy logic parameter tuning controller in the embodiment of the present invention;

[0095] Figure 9 is the relative position and velocity diagram of each direction of the tracking spacecraft using the MPC plus fuzzy logic parameter tuning controller in the embodiment of the present invention;

[0096] Figure 10 It is a three-dimensional trajectory diagram of a spacecraft's long-distance pursuit and close-range rendezvous using an MPC plus fuzzy logic tuning parameter controller in an embodiment of the present invention. Specific Embodiments

[0097] The technical solution of the present invention will be specifically described below in conjunction with the accompanying drawings.

[0098] It should be noted that the following detailed description is illustrative and is intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used in the present invention have the same meaning as commonly understood by those of ordinary skill in the technical field to which this application belongs.

[0099] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0100] As Figure 1 shown; this embodiment provides an integrated control method for a small spacecraft's long-distance pursuit and close-range rendezvous, including the following steps:

[0101] Step 1: Design a nine-state variable tracking spacecraft dynamics model based on position, velocity, and thrust, and establish the operating trajectory of the target spacecraft.

[0102] Step S11: Tracking spacecraft dynamics modeling:

[0103] A) Tracking spacecraft characteristics

[0104] Since the spacecraft designed in the present invention is a small spacecraft, there are some serious limitations in the design space. The present invention simplifies the problem by assuming that the mass is evenly distributed inside the spacecraft and adopts the main axis, which greatly simplifies the rotational dynamics. Therefore, the moment of inertia of each main axis of the spacecraft can be expressed as:

[0105]

[0106]

[0107]

[0108] Where m is the mass of the small spacecraft in kilograms, Z represents the moment of inertia, and a, b, and c are the dimensions of the small spacecraft in meters. Given that the mass of the spacecraft is 4 kg and the dimensions are [0.1, 0.3, 0.1] m, substituting these values into equations (1), (2), and (3) in the present invention yields the approximate values of the moments of inertia in each direction in the simulation system, with the unit of kg / m 2 .

[0109] B) Dynamics of the Tracking Spacecraft System

[0110] Since the entire system motion studied in the present invention is carried out around the Earth, to establish an accurate model, it is necessary to carefully observe the Earth's gravitational field.

[0111] First, the present invention assumes that the Earth is a perfect sphere, and then the acceleration of the spacecraft is as follows:

[0112]

[0113] μ is the gravitational parameter of the Earth, and its value is 398,600 km³, is the position vector of the object in the Earth's inertial coordinate system, with the unit of km, r is the radius of the Earth;

[0114] However, in fact, the Earth is an ellipsoid, so its gravitational field is asymmetric. The present invention can simulate the oblateness of the Earth by superimposing additional harmonic terms, thereby giving a more accurate simulation approximation. The mathematical form of the acceleration at this time can be obtained as follows:

[0115]

[0116]

[0117]

[0118] B is a constant representing the oblateness of the Earth, and its value is 1082.63×10 -6 . μ is the gravitational parameter of the Earth. R is the equatorial radius of the Earth, and its value is 6378 km. x, y, and z are used to describe the position of the spacecraft on the x, y, and z axes of the geocentric equatorial inertial coordinate system. Other harmonic effects are not included in the model because their importance is much lower.

[0119] C) Modeling of the Dynamics of the Tracking Spacecraft System

[0120] With the theoretical research above in this section, the present invention can establish the model of the tracking spacecraft system to be studied. Since the present invention only studies the dynamics of the position, there are 9 state variables, which are as follows:

[0121] There are three position state variables (x, y, z) in the geocentric equatorial inertial coordinate system;

[0122] There are three velocity state variables (v x , v y , v z ) in the geocentric equatorial inertial coordinate system;

[0123] There are three control state variables (T x , T y , T z ) in the geocentric equatorial inertial coordinate system;

[0124] In MATMPC, the spacecraft dynamics are defined by writing the derivative equations for each state. All nine are written below. It can be seen that the acceleration of the spacecraft only considers the gravitational force from the Earth and the force from the thrusters.

[0125]

[0126]

[0127]

[0128]

[0129]

[0130]

[0131]

[0132]

[0133]

[0134] represents the derivatives of x, y, z, represents the derivatives of v x , v y , v z , and T x,ECI represents the thrust in the x - direction in the geocentric equatorial inertial coordinate system (ECI), represents the derivatives of the thrust in the x, y, z directions of the tracking spacecraft, and c1, c2, c3 represent the control quantities in the x, y, z directions of the tracking spacecraft.

[0135] Step S12, Trajectory planning of the target spacecraft:

[0136] In the present invention, the simulation trajectory of the target spacecraft also needs to be designed in order to achieve the result of enabling the tracking spacecraft to track. The initial position and velocity of the target spacecraft are set as: [6678; 0; 0; 0; 6.69; 3.862], and its trajectory is set to rotate once around the side of the earth, which is a special case of the target spacecraft trajectory designed in the present invention. The trajectory expression is as follows:

[0137] v a = 7.7247 (20)

[0138]

[0139] x m = x0 * cos(w * (t + T * n)) (22)

[0140]

[0141]

[0142]

[0143]

[0144]

[0145] Among them, v a represents the total velocity of the target spacecraft. The three position quantities of the target spacecraft are x m , y m , z m , and the three velocity quantities are v xm , v ym , v zm . x0 is the initial x-direction position of the target spacecraft, y0 is the initial y-direction position of the target spacecraft, z0 is the initial z-direction position of the target spacecraft, w represents the angular velocity of the target spacecraft, t is the current time, T is the simulation sampling time, n is the current step number, and the step size N = 100; the dynamic model of the target spacecraft is established by the above equations.

[0146] Step 2: Identify the controller to be designed for the integrated control of long-distance pursuit and close-range rendezvous of the spacecraft, and design the MPC controller according to the model predictive control method.

[0147] Step S21: Design the MATMPC toolbox based on "An Integrated Control Method for Long-Distance Pursuit and Close-Range Rendezvous of Small Spacecraft":

[0148] MATMPC is a collection of MATLAB functions, including standard functions and MEX functions. MATMPC is open-source software written in MATLAB and MATLAB CAPI. It consists of many algorithm modules that can be easily replaced or extended. MATMPC aims to build fast and flexible algorithm prototypes and have competitive running performance.

[0149] The main content of MATMPC is divided into two parts: the model generation part and the simulation part.

[0150] (1) The model generation part

[0151] The model generation function uses a user-defined dynamic model and, using automatic differentiation (AD) in CasADi, generates C code for the model analytical function and its derivatives.

[0152] Note that MATMPC only generates code from the model dynamics, taking the model and optimization parameters as parameters that can be changed online.

[0153] (2) The simulation part

[0154] The simulation function is used to run closed-loop NMPC simulations in MATLAB. It starts from initializing the controller options, data, and memory defined in the MATLAB structure format. The NMPC controller in MATMPC is a MATLAB function that calls multiple modules. They include qp generation for performing multiple shoots, compression for performing (partial) compression routines, qp solver for calling the qp solver, solution information for calculating constraint residuals and optimal solution information such as Karush-Kuhn-Tucker (KKT) values, and online search for performing globalization. These modules are MEX functions that share the same data and memory structure created during initialization without the need to allocate any memory online. In addition, since the data storage structure is globally accessible in MATLAB, the simulation can be paused and intermediate data can be checked, just like debugging a standard MATLAB function.

[0155] In MATMPC, there are two sources of external dependencies. First is CasADi, which is used to perform AD and generate C code for the model function and its derivatives. CasADi is open-source software and pre-compiled MATLAB binary files are ready for use. The second source comes from QP solvers, which are carefully selected from open-source software libraries for NMPC applications.

[0156] Step S22, MPC controller design:

[0157] Assume the current state is \(x(t)\), and the optimal control problem to be solved at time \(t\) is expressed as

[0158]

[0159]

[0160] 0 = x k+1 −φ k (x k , u k ), k = 0, 1,......, N - 1, (30)

[0161] r 1k ≤ r k (x k , u k ) ≤ r 2k , k = 0, 1,......, N - 1, (31)

[0162] r 1N ≤ r N (x N ) ≤ r 2N , (32)

[0163] where, is the measured value of the current state, \(x_0\) is the given value of the current state, \(W\) represents the constraint of the optimal control problem of the chaser spacecraft, \(W N represents the constraint of the optimal control problem of the target spacecraft, Equation (31) is the constraint on the operation path of the chaser spacecraft, \(r k represents the operation radius of the chaser spacecraft, \(r 1k and \(r 2k are the upper and lower limits of \(r k respectively, Equation (32) is the operation path constraint of the target spacecraft, and the parameter meanings are the same as those in Equation (31). When \(k = 0, 1,......, N\), the system state \(x k is defined at the discrete point \(t k ), and when \(k = 0, 1,......, N - 1\), the control input \(u k is a piecewise constant; \(h k (x k , u k ) represents the position of the chaser spacecraft, \(h N (x N ) represents the position of the target spacecraft; Equation (30) represents a continuity constraint, where \(\varphi k (x k , u k ) is a numerical integration operator;

[0164] The control action should allow for a trade - off between the speed, position of performing the rendezvous mission, and minimizing the associated fuel consumption. The W - matrix is the matrix that weighs these three factors. By simply adjusting the corresponding parameters in the W - matrix, the weights of the three can be adjusted to achieve a good control effect.

[0165] The optimal control problem is formulated by applying multiple - shooting to the optimal control problem over the prediction horizon \(T = [t_0,t f \), where \(t_0\) and \(t f are the upper and lower bounds of the model - predictive control prediction horizon. Divide \(N\) into \([t_0,t_1,\cdots,t N \), and \(t N represents the time at the \(N\)th moment.

[0166] Step 3: Use the MATMPC toolbox to implement the integrated control of MPC for the long - distance pursuit and close - range rendezvous of the spacecraft, and then use fuzzy logic to tune the parameters to obtain an optimized controller.

[0167] Step S31: Physical domain quantization:

[0168] The fuzzy logic of the present invention is used to fuzzify the far and near distances to adjust the parameters of the model - predictive controller for the two spacecraft at different distances. Therefore, the physical domain of the present invention is the distance \(h\) between the two spacecraft j , as follows:

[0169]

[0170] \(x_0,y_0,z_0\) are the positions of the target spacecraft in three directions, \(x_1,y_1,z_1\) are the positions of the tracking spacecraft in three directions, and \(h_1\) is the distance between the two spacecraft. The object to be fuzzified in this step is \(h j , and the ultimate goal of the present invention is to make \(h j equal to 0.

[0171] Step S32: Establish fuzzy sets:

[0172] As known from the previous subsection, the input object of the fuzzy logic is the distance \(h\) between the two spacecraft j . We formulated the fuzzy rules in Table 1 according to the ultimate goal of this design.

[0173] Table 1

[0174]

[0175]

[0176] After quantifying the physical domain, it is necessary to determine the membership degrees of the elements in each fuzzy set. From the above analysis, it can be seen that when the two spacecraft are far apart, the present invention attaches importance to energy conservation rather than the weights of position and velocity. When the two spacecraft are close to each other, the present invention attaches importance to velocity and position to ensure precise docking and pays less attention to energy conservation issues. This is the linguistic description of the membership degrees of the elements in each fuzzy set. Now, it is converted into a mathematical description as shown in Table 2. Thus, the purpose of automatically adjusting the model predictive control weight matrix parameters through fuzzy logic can be achieved, and better control effects can be obtained.

[0177] Table 2

[0178]

[0179] Step 4: Simulation comparison and analysis

[0180] The present invention sets the prediction range T = 5000 and the prediction step N = 100. The approximate values of the moments of inertia in each direction in the simulation system are in kg / m 2 , and the data is as follows:

[0181] Z x = 0.0333 (4)

[0182] Z y = 0.0067 (5)

[0183] Z z = 0.0333 (6)

[0184] In the tracking mission, the initial position and velocity of the target spacecraft are set as: [6678; 0; 0; 0; 6.69; 3.862], and the initial position and velocity of the tracking spacecraft are set as: [7000; -1004; -579; 1.341; 6.589; 3.804]. The initial value of the weight matrix W is [1000; 1000; 10; 1; 1; 1; 0.01; 0.01; 0.01].

[0185] In the given simulation cases, two methods are carried out respectively: the MPC control method and the MPC plus fuzzy logic parameter tuning control method. It can be seen from Figure 2 that the energy consumption mass of the tracking spacecraft after using fuzzy logic parameter tuning is significantly reduced, indicating that the control method of fuzzifying the distance between the two spacecraft to control the weights among position, velocity and thrust plays an energy-saving role and makes the tracking effect of the spacecraft better. Figure 3 Figure is the thrust diagram of each direction of the tracking spacecraft using the MPC controller in the embodiment of the present invention; Figure 4 Figure is the position and velocity diagram of each direction of the tracking spacecraft using the MPC controller; Figure 5 Figure is the relative position and velocity diagram of each direction of the tracking spacecraft using the MPC controller;Figure 6 It is a three-dimensional trajectory diagram of a spacecraft's long-distance pursuit and close-range rendezvous using an MPC controller; Table 1 shows the fuzzy rule settings of the embodiments of the present invention; Table 2 shows the fuzzy set display of the embodiments of the present invention; after fuzzification, there is a simulation diagram of the MPC plus fuzzy logic tuning parameter controller adjustment, Figure 7 It is a thrust diagram of each direction of the tracking spacecraft using the MPC plus fuzzy logic tuning parameter controller in the embodiments of the present invention; Figure 8 It is a position and velocity diagram of each direction of the tracking spacecraft using the MPC plus fuzzy logic tuning parameter controller in the embodiments of the present invention; Figure 9 It is a relative position and velocity diagram of each direction of the tracking spacecraft using the MPC plus fuzzy logic tuning parameter controller in the embodiments of the present invention; Figure 10 It is a three-dimensional trajectory diagram of a spacecraft's long-distance pursuit and close-range rendezvous using the MPC plus fuzzy logic tuning parameter controller in the embodiments of the present invention; Table 3 shows the relative distance h between two spacecrafts under the adjustment of two different controllers in the embodiments of the present invention j Real-time simulation data comparison table.

[0186] Table 3

[0187]

[0188]

[0189] The above are only the preferred embodiments of the present invention. The present invention is not limited to the above embodiments. Any local modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. An integrated control method for long-distance pursuit and close-range rendezvous of a small spacecraft, characterized in that, It includes the following steps: Step S1: Design a nine-state variable tracking spacecraft dynamics model based on position, velocity, and thrust, establish the operating trajectory of the target spacecraft, and establish the target spacecraft dynamics model; Step S2: Identify the controller to be designed for the integrated control of long-distance pursuit and close-range rendezvous of the spacecraft, design the MPC controller according to the model predictive control method, and conduct a simulation to observe the simulation diagram of the cumulative fuel consumption; Step S3: Use the MATMPC toolbox to implement the integrated control of long-distance pursuit and close-range rendezvous of the spacecraft by the MPC controller, then use fuzzy logic to tune the parameters to obtain an optimized MPC controller, and conduct a simulation to observe the simulation diagram of the cumulative fuel consumption; The specific implementation steps of step S2 are as follows: Step S21: Design the MATMPC toolbox: MATMPC is a collection of MATLAB functions, including standard functions and MEX functions; MATMPC is divided into two parts: the model generation part and the simulation part; (1) Model generation part The model generation function uses a user-defined dynamic model and uses automatic differentiation in CasADi to generate the C code of the model analytical function and its derivative; (2) Simulation part The simulation function is used to run the closed-loop NMPC simulation in MATLAB; It starts from initializing the controller options, data, and memory defined in the MATLAB structure format; the NMPC controller in MATMPC is a MATLAB function that calls multiple modules, which are MEX functions, and they share the same data and memory structure created during initialization; Step S22: Design the MPC controller: Assume the current state is x(t), and the optimal control problem to be solved at time t is expressed as 0 = x k+1 -φ k (x k , u k ), k = 0, 1,......, N - 1, (30) r 1k ≤ r k (x k , u k ) ≤ r 2k , k = 0, 1,......, N - 1, (31) r 1N ≤r N (x N )≤r 2N , (32) Among them, is the measured value of the current state, x0 is the given value of the current state, W represents the constraint of the optimal control problem of the tracking spacecraft, and W N represents the constraint of the optimal control problem of the target spacecraft. Equation (31) is the constraint on the operating path of the tracking spacecraft, and r k represents the operating radius of the tracking spacecraft, and r 1k and r 2k are the upper and lower limits of r k respectively. Equation (32) is the operating path constraint of the target spacecraft, and the parameter meanings are the same as those in Equation (31). When k = 0, 1,......, N, the system state x k is defined at the discrete point t k . When k = 0, 1,......, N - 1, the control input u k is a piecewise constant; h k (x k , u k ) represents the position of the tracking spacecraft, and h N (x N ) represents the position of the target spacecraft; Equation (30) represents a continuity constraint, where φ k (x k , u k ) is a numerical integration operator; The control action should allow for a trade-off between the velocity, position of the rendezvous mission, and minimizing the associated fuel consumption, and the W matrix is the matrix that weighs these three factors. By simply adjusting the corresponding parameters in the W matrix, the weights of the three factors can be adjusted to achieve a good control effect; The optimal control problem is formulated by applying multiple shooting to the optimal control problem over the prediction horizon T = [t0, t f , where t0 and t f are the lower and upper bounds of the model predictive control prediction horizon, and N is divided into [t0, t1,......, t N , t N denotes the time at the Nth moment; The specific implementation steps of step S3 are as follows: Step S31: Physical domain quantization: Fuzzy logic is used to fuzzify the distance to adjust the parameters of the model predictive controller for the tracking spacecraft and the target spacecraft at different distances. Therefore, the physical domain is the distance h between the tracking spacecraft and the target spacecraft j , as shown in the following equation: x0, y0, and z0 are the positions of the target spacecraft in three directions, x1, y1, and z1 are the positions of the chasing spacecraft in three directions, and h1 is the distance between the two spacecrafts; the object to be fuzzified in this step is h j , and the ultimate goal to be achieved is to make h j equal to 0; Step S32: Establish fuzzy sets: After quantifying the physical domain, it is necessary to determine the membership degrees of the elements in each fuzzy set. When the tracking spacecraft and the target spacecraft are far apart, i.e., greater than a threshold, energy conservation is emphasized rather than the weights of position and velocity. When the tracking spacecraft and the target spacecraft are close, i.e., less than another threshold, velocity and position are emphasized to ensure precise docking rather than energy conservation. This is the linguistic description of the membership degrees of the elements in each fuzzy set, which is converted into a mathematical description.

2. The integrated control method for long-distance pursuit and close-range rendezvous of a small spacecraft according to claim 1, wherein The specific content of step S1 includes: defining the state variables and control variables of the tracking spacecraft model, establishing the dynamic equation and control equation of the tracking spacecraft, and establishing the target spacecraft dynamics model according to the designed target spacecraft trajectory.

3. A method for integrated control of long-distance pursuit and close-range rendezvous of a small spacecraft according to claim 1, characterized in that, The specific content of step S2 includes: using the tracking spacecraft dynamics model, target spacecraft dynamics model, and MATMPC toolbox established in step S1, combining the difference between the predicted future state and the reference trajectory and the control quantity into the cost function of the optimization problem, and realizing the trajectory tracking of the target spacecraft through receding horizon optimization.

4. A method for integrated control of long-distance pursuit and close-range rendezvous of a small spacecraft according to claim 1, characterized in that The specific content of step S3 includes: using the tracking spacecraft dynamics model, target spacecraft dynamics model, and MATMPC toolbox established in step S1, combining the difference between the predicted future state and the reference trajectory and the control quantity into the cost function of the optimization problem, and through receding horizon optimization, adding fuzzy logic, adjusting the weight matrix parameters of the MPC controller by fuzzifying the relative distance between the tracking spacecraft and the target spacecraft, and realizing the trajectory tracking of the target spacecraft.

5. A method for integrated control of long-distance pursuit and close-range rendezvous of a small spacecraft according to claim 1, characterized in that, The specific implementation steps of step S1 are as follows: Step S11, Tracking spacecraft dynamics modeling: A) Tracking spacecraft characteristics The tracking spacecraft is a small spacecraft, and the moments of inertia of each main axis of the tracking spacecraft are expressed as: where m is the mass of the small spacecraft, Z represents the moment of inertia, and a, b, c are the dimensions of the small spacecraft; B) Tracking spacecraft system dynamics Assuming that the Earth is a perfect sphere, the acceleration of the tracking spacecraft is as follows: μ is the gravitational parameter of the Earth, is the position vector of the object in the Earth inertial coordinate system, and r is the radius of the Earth; In fact, the Earth is an ellipsoid, so its gravitational field is asymmetric. By superimposing additional harmonic terms to simulate the oblateness of the Earth, a more accurate simulation approximation is given. The mathematical form of the acceleration at this time is as follows: B is a constant representing the oblateness of the Earth, R is the equatorial radius of the Earth, and x, y, z are used to describe the position of the spacecraft on the x, y, z axes of the geocentric equatorial inertial coordinate system; C) Tracking spacecraft system dynamics modeling Establish a tracking spacecraft system model, only studying the dynamics of the position, so there are 9 state variables, which are as follows: There are 3 position state variables (x, y, z) in the geocentric equatorial inertial coordinate system; There are three velocity state variables (v x , v y , v z ) in the geocentric equatorial inertial coordinate system; There are three control state variables (T x , T y , T z ) in the geocentric equatorial inertial coordinate system; In the MATMPC toolbox, the tracking spacecraft dynamics are defined by writing the derivative equations of each state; the acceleration of the tracking spacecraft only considers the gravity from the Earth and the force from the thruster; Denote the derivatives of x, y, and z, Denote v x , v y , v z 's derivative, T x,ECI Denote the thrust in the x direction in the Earth-centered equatorial inertial coordinate system ECI, Denote the thrust derivatives of the tracking spacecraft in the x, y, and z directions, and c1, c2, and c3 denote the control quantities of the tracking spacecraft in the x, y, and z directions; Step S12, Target spacecraft trajectory planning: Set the initial position and velocity of the target spacecraft as: [6678; 0; 0; 0; 6.69; 3.862], and set its trajectory to rotate around the Earth once. The trajectory expression is as follows: v＝7.7247 (20) x m = x0 * cos(ω * (t + T * n)) (22) Among them, v a represents the total velocity of the target spacecraft. The three position quantities of the target spacecraft are x m , y m , z m respectively, and the three velocity quantities are v xm , v ym , v zm respectively. x0 is the initial x-direction position of the target spacecraft, y0 is the initial y-direction position of the target spacecraft, z0 is the initial z-direction position of the target spacecraft, w represents the angular velocity of the target spacecraft, t is the current moment, T is the simulation sampling time, n is the current step number, and the step size N = 100. The dynamic model of the target spacecraft is established by the above formulas.

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