Relative pose tracking control method for failure satellite clearing

Abstract

The invention discloses a relative pose tracking control method for failure satellite removal, solves the problems of navigation measurement uncertainty, limited model precision, complex external disturbance, difficulty in identification and the like of the existing pose tracking control algorithm for failure satellite removal, and belongs to the technical field of in-orbit service. The method comprises the following steps: designing a linear relative position tracking controller and a nonlinear attitude synchronization controller according to the difference between a tracking star and a target star, and obtaining an expected trajectory close to the target star according to the relative motion state of the tracking star and the target star; based on the expected trajectory and the component of the relative position vector under the orbital coordinate system at the current moment, using a linear relative position tracking controller to control the tracking star to track the expected trajectory under complex disturbance; and based on the relative attitude quaternion, using a nonlinear attitude synchronization controller to control the tracking star to track the attitude of the target star under complex disturbance. The method has the characteristics of low calculation complexity, good disturbance suppression effect and high engineering applicability.

Description

Technical Field

[0001] The invention relates to a relative posture tracking control method for removing a failed satellite, belonging to the technical field of on-orbit services. Background Art

[0002] The existing posture tracking control algorithms for failed satellite removal include: posture tracking control algorithm based on sliding mode control, posture tracking control algorithm based on optimal control and visual servo control algorithm.

[0003] The core idea of ​​the posture tracking control algorithm based on sliding mode control is to design a sliding surface according to the error between the current state and the desired state, drive the system state to reach the sliding surface within a limited time, and slide along it to the equilibrium point, so as to achieve the tracking control of the spacecraft to the desired position and attitude. In addition to the traditional sliding mode control algorithm, relevant scholars have applied improved sliding mode control algorithms such as sliding mode control with sliding mode estimator, dual sliding surface control and optimal sliding mode control to the tracking control of the spacecraft to the desired posture, which effectively reflects the robustness advantage of the sliding mode algorithm. However, there are still some shortcomings: first, the control law design that comprehensively considers the influence of measurement uncertainty and external disturbances is complex, and the output switches at high frequency, causing jitter, which makes the engineering applicability poor; second, the above interference factors are not accurately introduced in the mathematical simulation, so that the simulation results do not match the actual situation.

[0004] The problem solved by the posture tracking control algorithm based on optimal control is: on the basis of fully considering the complex constraints, strong time variation and various sources of uncertainty in the posture tracking process, considering the control requirements of optimal fuel and optimal tracking time in the posture tracking process, to achieve optimal control of posture tracking. Typical methods include linear quadratic regulation control (LQR), H2 and H∞ control based on linear matrix inequality, and model predictive control (MPC) based on rolling optimization. The above algorithms can achieve fuel-optimal / time-optimal tracking control of the desired posture under certain constraints. However, the above posture tracking control algorithms based on optimal control have high solution complexity and poor timeliness, making it difficult to achieve real-time tracking of the desired posture, and the engineering application value is low. In addition, for actual on-orbit capture missions, the fuel consumption of posture tracking control at close range (hundreds of meters) is not unaffordable for spacecraft, and the time of this process is usually short (about 3min-5min), so fuel / time optimization is not an urgent need in engineering. The actual focus is still on the suppression of strong time variation, strong uncertainty and complex interference.

[0005] The visual servo control algorithm aims to achieve synchronous tracking of the 6-DOF attitude and orbit of the target spacecraft by using the relative measurement device as the information source. Conventional visual servo control is position-based servo control, that is, the tracking control is achieved by the control law based on the relative attitude information obtained by relative navigation measurement. On this basis, relevant scholars proposed image-based visual servo control, that is, the image features taken by the relative navigation measurement device are used as the control input, which can effectively suppress the influence of measurement uncertainty. However, the above-mentioned related algorithms are all based on the assumption that the tracking satellite platform and the target satellite basically maintain relative stillness, which is obviously not suitable for the mission scenario of capturing and docking a failed slow-rotating spacecraft.

[0006] In summary, in the prior art, when tracking and controlling the desired position calculated by the guidance solution in the process of approaching failure of a slowly rotating spacecraft, there are problems such as uncertain navigation measurement, limited model accuracy, and complex and difficult to identify external disturbances. Summary of the invention

[0007] In view of the problems of navigation measurement uncertainty, limited model accuracy, complex external disturbances and difficult identification in existing posture tracking control algorithms for failed satellite removal, the present invention provides a relative posture tracking control method for failed satellite removal.

[0008] A relative posture tracking control method for removing a failed satellite according to the present invention comprises:

[0009] According to the relative motion state of the tracking star and the target star, a desired trajectory approaching the target star is obtained, and based on the desired trajectory and the components of the relative position vector in the orbital coordinate system at the current moment, a linear relative position tracking controller is used to control the tracking star to track the desired trajectory under complex disturbances;

[0010] Based on the relative attitude quaternion, a nonlinear attitude synchronization controller is used to control the attitude of the tracking star to track the target star under complex disturbances.

[0011] Preferably, the linear relative position tracking controller includes a linear error feedback control law, a binary satellite relative position dynamics model and a linear extended state observer;

[0012] The linear error feedback control law is used to calculate the relative position vector component ρ of the tracking star and the target star in the orbital coordinate system at the current moment according to the desired trajectory. ot , the observer state quantities z1, z2, z3 obtain the control signal u, and send it to the linear expansion state observer and the binary star relative position dynamics model at the same time; z1 represents ρ| ot Estimate of z2 The estimate of , z3 is the disturbance estimate;

[0013] A linear extended state observer is used to calculate the control signal u and the component ρ| ot , for the observer state z = [z1 z2 z3] T Observe and send it to the linear error feedback control law, which will;

[0014] The binary satellite relative position dynamics model is used to obtain the component ρ| of the relative position vector of the tracking star and the target star in the orbital coordinate system at the next moment according to the control signal u. ot , and sent to the linear error feedback control law and the linear extended state observer at the same time;

[0015] According to the component ρ of the relative position vector between the tracking star and the target star in the orbital coordinate system at the next moment | ot The thrust of the tracking star is controlled to achieve trajectory tracking of the target star.

[0016] Preferably, the linear extended state observer is:

[0017]

[0018] Where L is the gain matrix, C=[I 3×3 0 3×3 0 3×3 ],0 3×3 is a three-dimensional zero matrix, I 3×3 is the third-order identity matrix, u c =[uρ| ot ] T For combined input, y c is the output.

[0019] As a preference, the linear error feedback control law is:

[0020]

[0021] In the formula, k p , k d is the proportional gain coefficient and the differential gain coefficient, x ref is the desired trajectory of the target star, and u0 is the control signal of the undisturbed compensation.

[0022] As a preferred embodiment, the binary star relative position dynamics model is:

[0023]

[0024] Among them, ρ| ot =[ρ x ρ y ρ z ] T Denotes the component ρ| otThe three-axis components in the orbital coordinate system, a c | ot =[a cx a cy a cz ] T Indicates the controlled acceleration a of the tracking star c | ot The three-axis components in the orbital coordinate system, ΔJ = [ΔJ x ΔJ y ΔJ z ] T represents the three-axis components of the spatial disturbance acceleration ΔJ in the orbital coordinate system, is the orbital angular velocity of the target star, is the orbital angular acceleration of the target star, r t is the relative distance between the target star and the center of the earth, and μ is the gravitational constant of the earth.

[0025] Preferably, the nonlinear attitude synchronization controller includes a nonlinear angular position regulation law, a nonlinear error feedback control law, a nonlinear extended state observer, relative attitude kinematics and relative attitude dynamics;

[0026] The nonlinear angular position adjustment law is used to adjust the relative attitude quaternion q at the current moment. e The relative attitude quaternion q d , we get the expected change law of relative angular velocity ω d , and sent to the nonlinear error feedback control law;

[0027] The nonlinear error feedback control law is used to d -z1 and disturbance estimate z2, and obtain the control torque T c , and sent to relative attitude kinematics and relative attitude dynamics at the same time; z1 is the estimate of relative angular velocity;

[0028] The nonlinear extended state observer is used to calculate the relative angular velocity ω at the current moment. e , observe the state variables z1 and z2, and send them to the nonlinear error feedback control law;

[0029] Relative attitude kinematics and relative attitude dynamics are used to calculate the relative attitude kinematics and relative attitude dynamics according to the control torque T c , get the relative attitude quaternion q at the next moment e , and sent to the nonlinear angular position regulation law.

[0030] Preferably, the nonlinear angular position adjustment law is:

[0031]

[0032] Among them, qev ,q dv are the vector parts of the relative attitude quaternion and the expected relative attitude quaternion, Q ev is the antisymmetric matrix of the quaternion vector part, α1 is the tracking factor, fal(·) is the nonlinear filter function,

[0033]

[0034] e is the input variable, a and δ are filter constants.

[0035] Preferably, the nonlinear extended state observer is:

[0036]

[0037] Among them, e1 is the observation error of the observer on the relative angular velocity, and β1 and β2 are the observer gain matrices.

[0038] As a preference, the nonlinear error feedback control law is:

[0039] T c =I0(α2fal(ω d -ω e ,a,δ)-z2)-I0g

[0040] Where α2 is the controller gain matrix, I0 is the nominal moment of inertia of the tracking star, ω c To track the angular velocity of the star.

[0041] As a preference, the relative attitude kinematic equation is:

[0042]

[0043] Among them, I c ,I t are the moments of inertia of the tracking star and the target star, T dc 、T dt are the interference torques on the tracking star and the target star respectively, is the coordinate transformation matrix from the target star system to the tracking star system, ω t is the target star angular velocity, (·) × Represents the operation of converting a vector into an antisymmetric matrix;

[0044] The relative attitude dynamics equation is:

[0045]

[0046] The beneficial effect of the present invention is that the present invention tracks the desired trajectory and the desired attitude respectively. According to the difference between the control tracking star and the target star, a linear relative position tracking controller and a nonlinear attitude synchronization controller are designed to respectively realize the tracking of the desired trajectory and the desired attitude. It has the characteristics of low computational complexity, good disturbance suppression effect and strong engineering applicability.

[0047] Traditional control law design often includes differential terms of error state quantities, such as physical quantities such as relative speed or relative angular velocity. However, in actual engineering, the above physical quantities often require differential or extended filtering of the original information to obtain. Differential processing is easily distorted by noise pollution, and extended filtering relies on part of the model information, which increases the complexity of the algorithm. The control method of this embodiment uses an extended state observer to observe the differential terms, and uses the observed values ​​to design the control law, avoiding the problems caused by the differential method and the extended filtering method.

[0048] Compared with the posture tracking control algorithm based on sliding mode, the control method in the present invention is simpler in design and has a clearer physical meaning. Compared with the posture tracking control algorithm based on optimal control, the control method in the present invention does not require iterative solution, the computational complexity is significantly reduced, and it focuses on suppressing complex disturbances, which is more adaptable to actual engineering.

[0049] The design of the observer and control law in the present invention is actually based on a "model-free" idea, that is, it is not required to accurately know the relative position and attitude motion law between the two stars. The constant matrix and information that can be accurately measured are often used in the design, which essentially avoids the influence of the unmodeled part of the traditional posture tracking control algorithm on the accuracy. In addition, the control algorithm in the present invention does not distinguish between external interferences such as measurement uncertainty, space interference torque and perturbation acceleration, and internal interferences such as changes in the mass characteristics of the tracking star body and the center of mass shift caused by fuel sloshing. All complex disturbances are uniformly processed, estimated through the extended state observer, and actively compensated for the disturbance when designing the control law, so that the control accuracy and robustness of the algorithm are significantly improved compared with the general posture tracking control algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is the principle diagram of the linear relative position tracking controller;

[0051] Figure 2 It is the principle diagram of nonlinear attitude synchronization controller;

[0052] Figure 3 It is the overall simulation block diagram;

[0053] Figure 4 for Figure 4 Three-axis deviation of the guidance trajectory and terminal position;

[0054] Figure 5 is the deviation between the relative velocity and the terminal velocity;

[0055] Figure 6 is the three-axis deviation between the guidance trajectory and the reference trajectory;

[0056] Figure 7 is the terminal position error scatter diagram;

[0057] Figure 8 is the change of relative attitude quaternion;

[0058] Fig. 9 is the change of relative angular velocity. DETAILED DESCRIPTION

[0059] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0060] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0061] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

[0062] The relative posture tracking control method for removing a failed satellite in this embodiment is divided into tracking of a desired trajectory and tracking of a desired posture; specifically, it includes:

[0063] According to the relative motion state of the tracking star and the target star, a desired trajectory approaching the target star is obtained, and based on the desired trajectory and the components of the relative position vector in the orbital coordinate system at the current moment, a linear relative position tracking controller is used to control the tracking star to track the desired trajectory under complex disturbances;

[0064] Based on the relative attitude quaternion, a nonlinear attitude synchronization controller is used to control the attitude of the tracking star to track the target star under complex disturbances.

[0065] The specific process includes:

[0066] 1. Establishing the coordinate system

[0067] The definitions of the geocentric inertial coordinate system, orbital coordinate system, and tracking star body coordinate system are given:

[0068] (1) Geocentric inertial coordinate system: The origin is the center of the earth O E , OE X E The axis is along the intersection of the Earth's equatorial plane and the ecliptic plane, pointing to the vernal equinox, O E Z E The axis points to the North Pole, O E Y E Axis and O E X E Axis, O E Z E The axes form a right-handed coordinate system. This coordinate system is used to describe the orbital state and absolute attitude of a spacecraft.

[0069] (2) Orbital coordinate system (LVLH): origin O t Located at the target star's mass center, O t X ot The axis points outward along the direction of the geocentric vector, O t Z ot The axis is along the direction of orbital angular momentum, O t Y ot Axis and O t X ot Axis, O t Z ot The axes form a right-handed system. This coordinate system is used to describe the relative position movement between the tracking star and the target star.

[0070] (3) Tracking star body coordinate system: The origin is located at the tracking star mass center O c , O c X c , O c Y c , O c Z c The axis is along the principal axis of inertia. This coordinate system is used as the reference coordinate system for relative attitude dynamics.

[0071] To clarify the meaning of each symbol in the formula, the following symbol convention is used here: For any vector R, its coordinate system S a The first-order derivative with respect to time is expressed as The second-order derivative is expressed as In the coordinate system S a The component form below is expressed as R| a =[R x R y R z ] T ;

[0072] 2. In this embodiment, based on the desired trajectory and the components of the relative position vector in the orbital coordinate system at the current moment, a method for controlling the tracking star to track the desired trajectory under complex disturbances using a linear relative position tracking controller includes:

[0073] Define the relative position vector ρ = Rc -R t , where R c , R t are the position vectors of the tracking star and the target star relative to the center of the earth, respectively. Taking the orbital coordinate system as the reference coordinate system, let the component ρ of the relative position vector in the orbital coordinate system be ot =[ρ x ρ y ρ z ] T , the controlled acceleration a of the tracking star in the orbital coordinate system c | ot =[a cx a cy a cz ] T , after derivation, the dynamic equation describing the relative position motion between the tracking star and the target star is:

[0074]

[0075] in is the orbital angular velocity of the target star, is the orbital angular acceleration of the target star, r t is the relative distance between the target star and the center of the earth, μ is the gravitational constant of the earth, ΔJ=[ΔJ x ΔJ y ΔJ z ] T is the spatial disturbance acceleration.

[0076] Formula (1) is used to describe the change of the relative position between the two stars, which can be written as the general form of a second-order system:

[0077]

[0078] In the formula, f p To include the total position disturbance including measurement uncertainty, unmodeled parts and spatial interference forces / torques, the state variable is selected: x1 = ρ| ot , x3=f p , then [x1 x2 x3] T is the expanded state including the disturbance. Convert equation (2) into a continuous expanded state space description:

[0079]

[0080] In the formula, C=[I 3×3 0 3×3 0 3×3 ],0 3×3 is a three-dimensional zero matrix, I 3×3is a third-order unit matrix, which is a constant matrix independent of the model. y is the output of the linear extended state observer, which should be the relative position vector ρ| in the orbital system. ot ; u is the control input of the linear extended state observer;

[0081] f p First derivative with respect to time;

[0082] Building a Linear Extended State Observer

[0083]

[0084] Where L is the linear extended state observer gain matrix, z = [z1 z2 z3] T is the state variable of the linear extended state observer, u c =[uy] T For combined input, y c is the output of the linear extended state observer. When the gain matrix L of the extended state observer is designed reasonably, the linear extended state observer can realize real-time tracking of the original system (3), that is, z→x. This means that the extended state observer described by equation (4) can observe disturbances including measurement uncertainty, unmodeled parts, and spatial interference forces / torques.

[0085] Based on the linear extended state observer, a linear error feedback control law is designed. Since the linear extended state observer can estimate and compensate the total disturbance in real time, the integrator used in the traditional PID to eliminate the static error under constant disturbance is no longer necessary. Therefore, the PD combination is simplified when designing the linear error feedback control law:

[0086]

[0087] Where k p , k d is the proportional gain coefficient and the differential gain coefficient, x ref is the desired trajectory, and u is the output control signal. The linear extended state observer and the linear error feedback control law together constitute the core of the linear relative position tracking controller.

[0088] 3. In this embodiment, the method of controlling the attitude of the tracking star to track the target star under complex disturbances by using a nonlinear attitude synchronization controller based on relative attitude quaternion includes:

[0089] The attitude quaternion is used to describe the spacecraft attitude, and the tracking star attitude quaternion is defined as q c , the target star attitude quaternion is q t , then the relative attitude quaternion of the tracking star relative to the target star is

[0090]

[0091] in, is the target star attitude quaternion q t The conjugate quaternion of .

[0092] Define the angular velocity of the tracking star as ω c , the target star angular velocity is ω t , then the relative angular velocity is:

[0093]

[0094] In the formula, It is the coordinate transformation matrix from the target star system to the tracking star system.

[0095] Taking the tracking star system as the reference coordinate system, the dynamics and kinematics equations describing the relative attitude motion between the binary stars are derived:

[0096]

[0097] Among them, I c ,I t are the moments of inertia of the tracking star and the target star, T dc , T dt are the disturbance torques on the tracking star and the target star, respectively, (·) × represents the operation of transforming a vector into an antisymmetric matrix, equation (8) is the relative attitude dynamics equation, and equation (9) is the relative attitude kinematics equation. The control target of the nonlinear attitude synchronization controller is the relative attitude quaternion q e The constant quaternion q d , relative angular velocity ω e Tends to 0.

[0098] Since the relative angular velocity output by the relative attitude dynamics is the input of the relative attitude kinematics, the two can be regarded as a cascade system. The internal disturbances caused by the unmodeled part and the parameter uncertainty and the unmeasurable external disturbances in space only act on equation (8). In other words, the above disturbances only affect the relative angular velocity ω. e has a direct impact on the relative attitude quaternion q e The influence is through ω e The nonlinear attitude synchronization controller is indirectly transferred through formula (9). Therefore, the process of the nonlinear attitude synchronization controller is as follows: First, the current relative attitude quaternion q e The relative attitude quaternion q d Design the nonlinear angular position adjustment process to obtain the expected change law of relative angular velocity ω d; Secondly, a nonlinear extended state observer is constructed to perform extended observation of the state in the relative attitude dynamics system; finally, a nonlinear error feedback control law (NLESF) is designed according to the observer state, and the control quantity is output so that the relative angular velocity ω e Tracking d , and then realize the relative attitude quaternion q e Track the desired relative pose quaternion q d ;

[0099] Taking the expected change law of relative angular velocity as the virtual control quantity of relative attitude kinematics, the nonlinear angular position adjustment law is designed:

[0100]

[0101] In the formula, q ev ,q dv are the vector parts of the current relative attitude quaternion and the expected relative attitude quaternion, Q ev For q ev =[q ev1 q ev2 q ev3 ] T The antisymmetric matrix of the constructed quaternion vector part is written in component form:

[0102]

[0103] α1 is the tracking factor, which determines q ev Converges to q dv The convergence speed of fal(·) is the nonlinear filter function, which is written as:

[0104]

[0105] When e is a vector, each component needs to be operated. a and δ are the constants of the filter to be designed. a determines the flatness of the function, and δ is the boundary between the linear region and the nonlinear region.

[0106] Taking the relative attitude dynamics equation (8) as the controlled object, it is written as the general form of a first-order system:

[0107]

[0108] Where f a is the total attitude disturbance including measurement uncertainty, unmodeled parts and external interference, is the deterministic term in the model, I0 is the nominal moment of inertia of the tracking star, T c is the control torque acting on the tracking star. Construct a nonlinear extended state observer:

[0109]

[0110] In the formula, z1 and z2 are the state variables of the nonlinear extended state observer, z1 is the estimate of the relative angular velocity, z2 is the disturbance estimate, e1 is the observation error of the nonlinear extended state observer on the relative angular velocity, β1 and β2 are the gain matrices of the nonlinear extended state observer, which determine the observation quality of the observer. When β1 and β2 are reasonably designed, the nonlinear extended state observer can realize real-time observation of the system (13), that is, z1→ω e , z2→f a ;

[0111] Based on the nonlinear extended state observer, a nonlinear error feedback control law is designed:

[0112] T c =I0(α2fal(ω d -ω e ,a,δ)-z2)-I0g (15)

[0113] Where α2 is the controller gain matrix, which determines the control relative angular velocity ω e Track the expected relative angular velocity variation law ω d tracking quality.

[0114] 4. Application scenarios of this implementation method:

[0115] 1. Active removal of failed satellites: This implementation is applicable to the active removal of failed satellites. It can control the tracking star to perform high-precision approach and attitude synchronization on a failed target star with slow-rotating dynamic characteristics, so that the tracking star has stable relative dynamic conditions to complete the capture of the target star.

[0116] 2. On-orbit service and maintenance of spacecraft: This implementation method is applicable to the on-orbit service and maintenance of spacecraft. The tracking satellite can be controlled to make a high-precision attitude synchronous approach to the target to be serviced, so that the maintenance equipment such as the robotic arm on the tracking satellite has good working conditions.

[0117] 3. Conventional orbit and attitude maneuvers of spacecraft: This implementation method is applicable to conventional attitude and orbit maneuvers of spacecraft. The proposal has no special requirements for the reference trajectory signal to be tracked, and it can be fully extended to conventional orbital maneuvering tasks. The control goal of attitude tracking in the proposal is to complete attitude synchronization with the target satellite. Without changing the algorithm framework, by adjusting the navigation information source, the control goal can be converted into attitude maneuvers for any feasible attitude.

[0118] This implementation has high control accuracy and strong robustness: by observing and actively suppressing disturbances, it is possible to achieve high-precision tracking of the desired trajectory under the circumstances of relative navigation measurement uncertainty, spatial perturbations, interference torques and changes in quality parameters. The trajectory tracking accuracy is better than ±5cm, and the terminal velocity error is less than 5cm / s; the attitude tracking accuracy is better than ±1°, and the angular velocity error is less than 0.5° / s.

[0119] This implementation has low computing resource consumption and strong real-time performance: compared with the posture tracking control algorithm based on optimal control, it does not require iterative calculations and solving optimization problems, which significantly reduces the on-board computing power consumption, significantly improves the calculation rate, and can achieve real-time tracking of the desired posture.

[0120] This implementation method has strong engineering applicability: the control law design of the sliding mode-based posture tracking control algorithm involves complex mathematical models and parameter setting processes, which is difficult to implement in engineering and may cause output oscillation, causing life loss of the actuator, structural vibration, and reduced control accuracy. In contrast, the control law proposed in this solution has the advantages of simple structure and intuitive parameter setting. By eliminating the high-frequency switching characteristics of the control signal, it effectively extends the service life of the actuator while ensuring control accuracy, significantly improving the engineering applicability in complex space environments, and more in line with the reliability requirements of aerospace engineering missions for control systems.

[0121] 5. Simulation Verification

[0122] Table 1 Initial orbit parameters

[0123]

[0124]

[0125] Table 2 Initial posture parameters

[0126] Parameter Type Numeric Tracking star initial attitude <![CDATA[[0.5477,0.6,-0.5,0.3] T ]]> Tracking star initial angular velocity / (° / s) <![CDATA[[0.5,0.5,0.5] T ]]> Target star initial attitude <![CDATA[[0.5862,0.2693,0.7539,-0.1243] T ]]> Initial angular velocity of target star / (° / s) <![CDATA[[-1,1,1] T ]]>

[0127] Table 3 Binary mass characteristic parameters

[0128] Parameter Type Numeric Tracking star mass / (kg) 100 Tracking star moment of inertia / (kg·㎡) diag([7.5,4.5,7]) Target star mass / (kg) 30 Target star moment of inertia / (kg·㎡) diag([1.5,3,1.5])

[0129] Table 4 Simulation related parameters

[0130]

[0131]

[0132] Table 5 Trajectory tracking control related parameters

[0133] Parameter Type Numeric Observer feedback gain matrix L <![CDATA[[3I 3×3 9I 3×3 9I 3×3 ] T ]]> <![CDATA[LESF proportional gain k p > diag([0.080.080.1]) <![CDATA[LESF differential gain k d > diag([0.250.250.3]) Simulation time 300s Simulation time step 1s Relative position measurement accuracy 1cm

[0134] Table 6 Attitude tracking control related parameters

[0135]

[0136]

[0137] The simulation results of relative position tracking control are as follows: Figures 4 to 7 As shown, according to the trajectory tracking simulation, the following conclusions can be drawn:

[0138] Depend on Figure 4 , Figure 6 It can be seen that under different initial positions and initial velocities, the tracking satellite can be controlled to approach the terminal position along the reference trajectory, and the tracking accuracy is better than ±5cm.

[0139] Depend on Figure 5 It can be seen that the relative speed between the tracking star and the target star can converge to near 0m / s, and the speed accuracy is about 5cm / s.

[0140] Depend on Figure 7 It can be seen that the error between the tracking star and the terminal position is scattered around 5 cm.

[0141] The simulation results of relative attitude tracking control are as follows: Figure 8 and Fig. 9 As shown in the figure, the following conclusions can be drawn based on the posture tracking simulation:

[0142] Depend on Figure 8 It can be seen that the tracking satellite can be controlled to achieve attitude synchronization with the target satellite, and the attitude pointing accuracy is better than 1°.

[0143] Depend on Fig. 9 It can be seen that the relative angular velocity between the tracking star and the target star can be maintained between ±0.5° after the relative attitude converges.

[0144] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. It should therefore be understood that many modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in a manner different from that described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be used in other described embodiments.

Claims

1. A relative posture tracking control method for removing failed satellites, characterized in that: include: According to the relative motion state of the tracking star and the target star, a desired trajectory approaching the target star is obtained, and based on the desired trajectory and the components of the relative position vector in the orbital coordinate system at the current moment, a linear relative position tracking controller is used to control the tracking star to track the desired trajectory under complex disturbances; Based on the relative attitude quaternion, a nonlinear attitude synchronization controller is used to control the attitude of the tracking star to track the target star under complex disturbances.

2. The relative posture tracking control method for removing failed satellites according to claim 1 is characterized in that: The linear relative position tracking controller includes a linear error feedback control law, a binary satellite relative position dynamics model and a linear extended state observer; The linear error feedback control law is used to calculate the relative position vector component ρ of the tracking star and the target star in the orbital coordinate system at the current moment according to the desired trajectory. ot , the observer state quantities z1, z2, z3 obtain the control signal u, and send it to the linear expansion state observer and the binary star relative position dynamics model at the same time; z1 represents ρ| ot Estimate of z2 The estimate of , z3 is the disturbance estimate; A linear extended state observer is used to calculate the control signal u and the component ρ| ot , for the observer state z = [z1 z2 z3] T Observe and send it to the linear error feedback control law, which will; The binary star relative position dynamics model is used to obtain the component ρ| of the relative position vector of the tracking star and the target star in the orbital coordinate system at the next moment according to the control signal u. ot , and sent to the linear error feedback control law and the linear extended state observer at the same time; According to the component ρ of the relative position vector between the tracking star and the target star in the orbital coordinate system at the next moment | ot The thrust of the tracking star is controlled to achieve trajectory tracking of the target star.

3. The relative posture tracking control method for removing failed satellites according to claim 2 is characterized in that: The linear extended state observer is: Where L is the gain matrix, C=[I 3×3 0 3×3 0 3×3 ],0 3×3 is a three-dimensional zero matrix, I 3×3 is the third-order identity matrix, u c =[uρ| ot ] T For combined input, y c is the output.

4. The relative posture tracking control method for removing failed satellites according to claim 3 is characterized in that: The linear error feedback control law is: In the formula, k p , k d is the proportional gain coefficient and the differential gain coefficient, x ref is the desired trajectory of the target star, and u0 is the control signal of the undisturbed compensation.

5. The relative posture tracking control method for failed satellite removal according to claim 2 is characterized in that: The dynamic model of the relative position of the binary star is: Among them, ρ| ot =[ρ x ρ y ρ z ] T Denotes the component ρ| ot The three-axis components in the orbital coordinate system, a c | ot =[a cx a cy a cz ] T Indicates the controlled acceleration a of the tracking star c | ot The three-axis components in the orbital coordinate system, ΔJ = [ΔJ x ΔJ y ΔJ z ] T represents the three-axis components of the spatial disturbance acceleration ΔJ in the orbital coordinate system, is the orbital angular velocity of the target star, is the orbital angular acceleration of the target star, r t is the relative distance between the target star and the center of the earth, and μ is the gravitational constant of the earth.

6. The relative posture tracking control method for failed satellite removal according to claim 1 is characterized in that: The nonlinear attitude synchronization controller includes a nonlinear angular position regulation law, a nonlinear error feedback control law, a nonlinear extended state observer, relative attitude kinematics and relative attitude dynamics; The nonlinear angular position adjustment law is used to adjust the relative attitude quaternion q at the current moment. e The relative attitude quaternion q d , we get the expected change law of relative angular velocity ω d , and sent to the nonlinear error feedback control law; The nonlinear error feedback control law is used to d -z1 and disturbance estimate z2, and obtain the control torque T c , and sent to relative attitude kinematics and relative attitude dynamics at the same time; z1 is the estimate of relative angular velocity; The nonlinear extended state observer is used to calculate the relative angular velocity ω at the current moment. e , observe the state variables z1 and z2, and send them to the nonlinear error feedback control law; Relative attitude kinematics and relative attitude dynamics are used to calculate the relative attitude kinematics and relative attitude dynamics according to the control torque T c , get the relative attitude quaternion q at the next moment e , and sent to the nonlinear angular position regulation law.

7. The relative posture tracking control method for removing failed satellites according to claim 6 is characterized in that: The nonlinear angular position regulation law is: Among them, q ev ,q dv are the vector parts of the relative attitude quaternion and the expected relative attitude quaternion, Q ev is the antisymmetric matrix of the quaternion vector part, α1 is the tracking factor, fal(·) is the nonlinear filter function, e is the input variable, a and δ are filter constants.

8. The relative posture tracking control method for removing failed satellites according to claim 7 is characterized in that: The nonlinear extended state observer is: Among them, e1 is the observation error of the observer on the relative angular velocity, and β1 and β2 are the observer gain matrices.

9. The relative posture tracking control method for removing failed satellites according to claim 8, characterized in that: The nonlinear error feedback control law is: T c =I0(α2fal(ω d -oh e ,a,δ)-z2)-I0g Where α2 is the controller gain matrix, I0 is the nominal moment of inertia of the tracking star, ω c To track the angular velocity of the star.

10. The relative posture tracking control method for removing failed satellites according to claim 9, characterized in that: The relative attitude kinematic equation is: Among them, I c ,I t are the moments of inertia of the tracking star and the target star, T dc , T dt are the interference torques on the tracking star and the target star respectively, is the coordinate transformation matrix from the target star system to the tracking star system, ω t is the target star angular velocity, (·) × Represents the operation of converting a vector into an antisymmetric matrix; The relative attitude dynamics equation is:

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