Relative pose tracking control method for failed satellite removal

Abstract

The application discloses a relative position tracking control method for failed satellite removal, solves the problems of navigation measurement uncertainty, limited model precision and complex external disturbance, and is difficult to identify in the existing relative position tracking control algorithm for failed satellite removal, and belongs to the technical field of on-orbit service. The application comprises the following steps: according to the difference between a control tracking star and a target star, a linear relative position tracking controller and a nonlinear attitude synchronous controller are designed; according to the relative motion state of the tracking star and the target star, an expected trajectory for approaching the target star is obtained; based on the expected trajectory and the component of the relative position vector in the orbit coordinate system at the current time, the linear relative position tracking controller is used to control the tracking star to track the expected trajectory under complex disturbance; and based on the relative attitude quaternion, the nonlinear attitude synchronous controller is used to control the tracking star to track the attitude of the target star under complex disturbance. The application has the characteristics of low calculation complexity, good disturbance suppression effect and strong engineering applicability.

Description

Technical Field

[0001] The present 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] 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 servoing control algorithm.

[0003] The core idea of ​​the sliding mode control-based posture tracking control algorithm is to design a sliding surface based on the error between the current state and the desired state. By driving the system state to reach the sliding surface within a finite time and sliding along it to an equilibrium point, the spacecraft can track the desired position and attitude. In addition to traditional sliding mode control algorithms, researchers have applied improved sliding mode control algorithms such as sliding mode control with sliding mode estimators, dual sliding surface control, and optimal sliding mode control to spacecraft tracking of the desired posture. These algorithms effectively demonstrate the robustness advantages of sliding mode algorithms. However, there are still some shortcomings: First, the control law design that comprehensively considers the effects of measurement uncertainty and external disturbances is complex, and the output switches frequently, causing chattering, which makes it less suitable for engineering applications. Second, mathematical simulations do not accurately incorporate these interference factors, resulting in a poor match between the simulation results and the actual conditions.

[0004] Optimal control-based pose tracking algorithms address the problem of achieving optimal control of pose tracking while fully accounting for the complex constraints, strong time-variation, and diverse sources of uncertainty inherent in the pose tracking process, while also addressing the control requirements of fuel optimization and tracking time optimization. Typical approaches include linear quadratic regulation (LQR), H² and H∞ control based on linear matrix inequalities, and model predictive control (MPC) based on rolling optimization. All of these algorithms can achieve fuel- and time-optimal tracking of a desired pose under certain constraints. However, these optimal control-based pose tracking algorithms suffer from high computational complexity and poor timeliness, making real-time tracking of the desired pose difficult and limiting their engineering application value. Furthermore, for practical on-orbit capture missions, the fuel consumption of pose tracking control at close range (hundreds of meters) is not prohibitive for spacecraft, and the process is typically short (approximately 3-5 minutes). Therefore, fuel- and time-optimization is not a pressing engineering requirement. Instead, the focus remains on mitigating strong time-variation, high 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 a relative measurement device as an information source. Conventional visual servo control is position-based, that is, it relies on the relative position information obtained by relative navigation measurement, and the tracking control is achieved by the control law. Based on this, relevant scholars have proposed image-based visual servo control, that is, using the image features captured by the relative navigation measurement device as the control input, which can effectively suppress the impact 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 existing technology, when tracking and controlling the desired position calculated by the guidance solution in the process of approaching a failed 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 response to the problems of navigation measurement uncertainty, limited model accuracy, complex external disturbances and difficulty in 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 satellite and the target satellite, a desired trajectory approaching the target satellite 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 satellite 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 component ρ| of the relative position vector between 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 state of 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 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;

[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 track the trajectory of the target star.

[0016] As an optimization, 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] Where 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 preference, the binary star relative position dynamics model is:

[0023]

[0024] Where, 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 Relative to the expected attitude quaternion q d , we can 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 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, and a and δ are filter constants.

[0035] As an optimization, the nonlinear extended state observer is:

[0036]

[0037] Among them, e1 is the observer's observation error of the relative angular velocity, and β1 and β2 are both 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 present invention has the beneficial effect of tracking the desired trajectory and attitude separately. Based on the differences between the tracking satellite and the target satellite, a linear relative position tracking controller and a nonlinear attitude synchronization controller are designed to achieve tracking of the desired trajectory and attitude, respectively. This system has the advantages of low computational complexity, excellent disturbance suppression, and strong engineering applicability.

[0047] Traditional control law design often includes differential terms of error state quantities, such as relative velocity or relative angular velocity. However, in actual engineering, these physical quantities often require differential or extended filtering of the original information to obtain. Differential processing is easily distorted by noise contamination, and extended filtering relies on partial 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 differential methods and extended filtering methods.

[0048] Compared to sliding-mode-based posture tracking control algorithms, the control method of this invention is simpler in design and has clearer physical implications. Compared to optimal control-based posture tracking control algorithms, the control method of this invention does not require iterative solutions, significantly reduces computational complexity, and focuses on suppressing complex disturbances, making it more adaptable to practical engineering applications.

[0049] The observer and control law design in this invention is based on a "model-free" approach, meaning that precise knowledge of the relative position and attitude motion between the two satellites is not required. Instead, constant matrices and precisely measurable information are often used in the design, essentially avoiding the impact of the unmodeled components of traditional posture tracking control algorithms on accuracy. Furthermore, the control algorithm in this invention does not distinguish between external disturbances such as measurement uncertainty, spatial interference torque, and perturbation acceleration, nor internal disturbances such as changes in the mass characteristics of the tracking star and center of mass shifts caused by fuel sloshing. Instead, it treats all complex disturbances uniformly, estimates them through an extended state observer, and actively compensates for disturbances during control law design. This significantly improves the algorithm's control accuracy and robustness compared to conventional posture tracking control algorithms. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0051] Figure 2 This is a schematic diagram of the principle of the nonlinear attitude synchronization controller;

[0052] Figure 3 This 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 of the relative velocity from the terminal velocity;

[0055] Figure 6 is the three-axis deviation of the guidance trajectory from the reference trajectory;

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

[0057] Figure 8 is the relative attitude quaternion variation;

[0058] Figure 9 is the relative angular velocity variation. DETAILED DESCRIPTION

[0059] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative labor fall within the protection scope of the present application.

[0060] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0061] The present application will be further described below with reference to the drawings and specific embodiments, but is not limited by the present application.

[0062] The relative pose tracking control method for removing the failed satellite in the embodiment is divided into tracking of the expected trajectory and tracking of the expected attitude; specifically, the method comprises:

[0063] According to the relative motion state of the tracking satellite and the target satellite, an expected trajectory approaching the target satellite is obtained, and a linear relative position tracking controller is used to control the tracking satellite to track the expected trajectory under complex disturbance based on the component of the relative position vector in the orbital coordinate system at the current time and the expected trajectory.

[0064] A nonlinear attitude synchronization controller is used to control the tracking satellite to track the attitude of the target satellite under complex disturbance based on the relative attitude quaternion.

[0065] The specific process comprises:

[0066] I. Establishing coordinate systems

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

[0068] (1) Geocentric inertial coordinate system: the origin is the geocenter 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, which 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 center of mass, 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 coordinate system. This coordinate system is used to describe the relative position motion between the tracking star and the target star.

[0070] (3) Tracking star coordinate system: The origin is located at the center of mass of the tracking star 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: 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, a method for controlling a tracking satellite to track the desired trajectory under complex disturbances using a linear relative position tracking controller based on the desired trajectory and the components of the relative position vector in the orbital coordinate system at the current moment includes:

[0073] Define 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. 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] Where, f p To represent the total position disturbance including the measurement uncertainty, the unmodeled part and the spatial interference force / torque, 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] Where, 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 identity 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] Establishing 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 extended state observer gain matrix L is properly designed, the linear extended state observer can achieve 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 components, 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 for 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 form 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, a method for controlling the attitude of a tracking star to track a target star under complex disturbances using a nonlinear attitude synchronization controller based on relative attitude quaternions 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 tracking star angular velocity as ω c , the target star angular velocity is ω t , then the relative angular velocity is:

[0093]

[0094] Where, is the coordinate transformation matrix from the target star's local system to the tracking star's local system.

[0095] Taking the tracking star system as the reference coordinate system, the dynamic and kinematic 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 interference 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 tends to a 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 by formula (9). Therefore, the process is as follows: First, the current relative attitude quaternion q e Relative to the expected attitude quaternion q d Design a nonlinear angular position adjustment process to obtain the expected change law of relative angular velocity ω dSecondly, a nonlinear extended state observer is constructed to perform extended observation on the state of the relative attitude dynamics system; finally, a nonlinear error feedback control law (NLESF) is designed based on 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 variable of relative attitude kinematics, the nonlinear angular position adjustment law is designed:

[0100]

[0101] Where 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 rate 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] Where 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 change law ω d tracking quality.

[0114] 4. Application scenarios of this implementation:

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

[0116] 2. On-orbit service and maintenance of spacecraft: This embodiment is suitable for on-orbit service and maintenance of spacecraft. It can control the tracking satellite 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 Spacecraft Orbit and Attitude Maneuvers: This implementation is applicable to conventional spacecraft attitude and orbit maneuvers. The proposal does not require specific reference trajectory signals for tracking and is fully scalable to conventional orbital maneuvers. The proposed attitude tracking control objective is to achieve attitude synchronization with the target satellite. Without changing the algorithm framework, by adjusting the navigation information source, this control objective can be transformed into attitude maneuvers to any feasible attitude.

[0118] This implementation method offers high control accuracy and robustness: by observing and actively suppressing disturbances, it is able to achieve high-precision tracking of the desired trajectory under conditions 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, significantly reduces on-board computing power consumption, significantly improves the computing rate, and can achieve real-time tracking of the desired posture.

[0120] This implementation method has strong engineering applicability: The sliding-mode-based posture tracking control algorithm involves complex mathematical models and parameter tuning in control law design, making it difficult to implement in engineering. It can also cause output oscillation, leading to actuator life loss, structural vibration, and reduced control accuracy. In contrast, the control law proposed in this solution boasts a simple structure and intuitive parameter tuning. By eliminating the high-frequency switching characteristics of the control signal, it effectively extends the life of the actuator while ensuring control accuracy. This significantly improves engineering applicability in complex space environments and better meets the control system reliability requirements of aerospace engineering missions.

[0121] 5. Simulation Verification

[0122] Table 1 Initial orbital parameters

[0123]

[0124]

[0125] Table 2 Initial posture parameters

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

[0127] Table 3 Binary mass characteristic parameters

[0128] Parameter Type Value Mass of the chaser (kg) 100 Moment of inertia of the chaser (kg-m2) diag([7.5, 4.5, 7]) Mass of the target (kg) 30 Moment of inertia of the target (kg-m2) 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 Value Observer feedback gain matrix L [[3I 3×3 9I 3×3 9I 3×3 ] T ]]> <![CDATA[LESF比例增益k p ]]> diag([0.08 0.08 0.1]) <![CDATA[LESF微分增益k d ]]> diag([0.25 0.25 0.3]) Simulation time 300s Simulation time step 1s Relative position measurement accuracy 1 cm

[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 in Figure 2, the following conclusions can be drawn based on trajectory tracking simulation:

[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 0 m / s, and the speed accuracy is about 5 cm / s.

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

[0141] The simulation results of relative attitude tracking control are as follows: Figure 8 and Figure 9 As shown in Figure 2, 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 Figure 9 It can be seen that the relative angular velocity between the tracking satellite and the target satellite can be maintained within ±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 illustrative of the principles and applications of the invention. It should be understood that many modifications may be made to the illustrative embodiments, and that other arrangements may be devised, without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in ways other than those described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be employed in conjunction with 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 satellite and the target satellite, a desired trajectory approaching the target satellite 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 satellite to track the desired trajectory under complex disturbances; Based on the relative attitude quaternion, a nonlinear attitude synchronization controller is used to control the tracking satellite to track the target satellite under complex disturbances. 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 determine the components of the relative position vectors of the tracking star and the target star in the orbital coordinate system at the current moment according to the desired trajectory. , observer state quantity 、 、 Get control signal , and is simultaneously sent to the linear expansion state observer and the binary star relative position dynamics model; express Estimates, express Estimates, is the disturbance estimate; A linear extended state observer is used to calculate the control signal and the components , for the observer state Observe and send it to the linear error feedback control law, which will; The binary star relative position dynamics model is used to calculate the control signal Get the components of the relative position vector of the tracking star and the target star in the orbital coordinate system at the next moment , and sent to the linear error feedback control law and the linear extended state observer at the same time; According to the components of the relative position vector of the tracking star and the target star in the orbital coordinate system at the next moment Control the thrust of the tracking star to track the target star's trajectory; The linear extended state observer is: in, is the gain matrix, , , , is a three-dimensional zero matrix, is the third-order identity matrix, For combined input, is the output; The linear error feedback control law is: Where, 、 are the proportional gain coefficient and the differential gain coefficient, is the expected trajectory of the target star, is the control signal for undisturbed compensation.

2. The relative posture tracking control method for failed satellite removal according to claim 1 is characterized in that: The dynamic model of the relative position of the binary stars is: in, Indicates quantity The three-axis components in the orbital coordinate system are: Indicates the controlled acceleration of the tracking star The three-axis components in the orbital coordinate system, represents the spatial disturbance acceleration The three-axis components in the orbital coordinate system, is the orbital angular velocity of the target star, is the orbital angular acceleration of the target star, is the relative distance between the target star and the center of the earth, is the Earth's gravitational constant.

3. The relative posture tracking control method for failed satellite removal according to claim 1, 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; Nonlinear angular position adjustment law is used to adjust the relative attitude quaternion at the current moment Quaternion relative to the expected attitude , and obtain the expected change law of relative angular velocity , and sent to the nonlinear error feedback control law; The nonlinear error feedback control law is used to and disturbance estimation , and the control torque is obtained , and sent to relative attitude kinematics and relative attitude dynamics at the same time; is the estimate of the relative angular velocity; Nonlinear extended state observer is used to calculate the relative angular velocity at the current moment , for state variables 、 Make observations and send them to the nonlinear error feedback control law; Relative attitude kinematics and relative attitude dynamics are used to calculate the relative attitude according to the control torque. , get the relative attitude quaternion at the next moment , and sent to the nonlinear angular position regulation law.

4. The relative posture tracking control method for removing a failed satellite according to claim 3, characterized in that: The nonlinear angular position regulation law is: in, 、 are the vector parts of the relative attitude quaternion and the expected relative attitude quaternion, is the antisymmetric matrix of the vector part of the quaternion is the tracking factor, is a nonlinear filter function, , is the input variable, 、 is the filter constant.

5. The relative posture tracking control method for removing a failed satellite according to claim 4, characterized in that: The nonlinear extended state observer is: in, is the observation error of the observer on the relative angular velocity, 、 are all observer gain matrices, is the nominal moment of inertia of the tracking star.

6. The relative posture tracking control method for failed satellite removal according to claim 5, characterized in that: The nonlinear error feedback control law is: in, is the controller gain matrix, , To track the angular velocity of the star.

7. The relative posture tracking control method for removing a failed satellite according to claim 6, characterized in that: The kinematic equation of relative attitude is: in, 、 are the moments of inertia of the tracking star and the target star, 、 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, 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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