Spatial spin nutation non-cooperative target safe approximation control method

Abstract

The invention relates to a space spinning nutation non-cooperative target safe approaching control method. The method comprises the following steps: establishing dynamics and kinematics models of the relative attitude error and the relative orbit error of the double spacecrafts, and compacting the relative attitude error and relative orbit error model into a six-degree-of-freedom form; the method comprises the following steps: defining constraint functions and constraint auxiliary variables of safety and motion boundaries of a service spacecraft, and constructing a spacecraft auxiliary system which is used for rendezvous and docking and takes safety constraints into consideration; designing a shortest trace direction sliding mode variable for the spacecraft auxiliary system, wherein the shortest trace direction sliding mode variable enables the attitude and the relative orbit of the service spacecraft to maneuver to an expected attitude orbit required by a task from an initial state in a shortest path; a non-singular auxiliary switching function is designed, and the singular phenomenon is avoided when a time-related derivative is solved by a shortest trace direction sliding mode variable; and constructing a security approximation controller considering security constraints for the spatial spin nutation non-cooperative target.

Description

Technical Field

[0001] The present invention relates to a method for safely approaching a non-cooperative space spin-nutation target. This method is primarily used to support spacecraft safe close-range rendezvous and approach missions with spin-nutation targets, or spin-nutation space debris, and implements short-range autonomous closed-loop control of the spacecraft's attitude and orbit coupling. This invention belongs to the field of spacecraft control technology. Background Art

[0002] Spacecraft development is costly and time-consuming. The on-orbit benefits of a spacecraft are directly correlated with its on-orbit service life and on-orbit health. Failures in spacecraft already in orbit directly impact the spacecraft's service capabilities and economic benefits. To support on-orbit repair and maintenance, on-orbit servicing services and related technologies are urgently needed. During on-orbit servicing missions, rendezvous and docking with the target spacecraft are crucial components and prerequisites for effective servicing. This includes long-range and mid-range approaches to the faulty spacecraft, close-range rendezvous and approach, autonomous control to achieve relative orbit (position) and attitude prior to docking, and successful docking to enable on-orbit servicing. The rendezvous and docking mission during the final close-range phase is one of the most complex current space missions, requiring the highest levels of system integration and the most demanding control tasks and performance. Attitude and relative orbit control during the rendezvous and approach phase requires high precision, reliability, and strong describability.

[0003] For target spacecraft with spin-nutation motion, the rendezvous process should have safety constraints on the range of motion, a relatively clear tracking trajectory design, and strong autonomous computation and tracking capabilities. Current rendezvous and docking control problems, when using more traditional control methods, are often accompanied by problems such as undescribable paths or trajectories during the control process, insufficient safety constraints before docking, and poor autonomous computation. Although prefabricated paths and tracking control can initially address these issues, for high-precision autonomous control tasks against spin-nutation targets, we prefer rendezvous approach control technology with safety constraints and a relatively describable trajectory. These safety constraints and short-distance trajectories can be autonomously calculated based on the changes in the target spacecraft.

[0004] To address the precise control issues associated with rendezvous and docking, patent document CN109507892A discloses an adaptive sliding mode attitude stabilization control method for flexible spacecraft, which improves the convergence speed and adaptability of the attitude system. Patent document CN111812981A discloses a finite-time stable sliding mode control method for spacecraft attitude tracking, which improves the temporal descriptiveness and robustness of attitude control. Patent document CN113697131A discloses an anti-unwinding sliding mode attitude tracking control method and system for rigid spacecraft, which addresses the perturbation issues in attitude tracking. However, these methods fail to improve the safety constraints and trajectory descriptiveness of the spacecraft system or attitude. To address the precise guidance and control of relative motion during rendezvous and docking, patent CN112000006A discloses a finite-time fast non-singular terminal sliding mode autonomous control method, which improves the convergence speed of rendezvous and docking. Patent CN109189091A discloses a multi-spacecraft collaborative control method based on integral sliding mode and model predictive control, which simultaneously addresses the relative motion of multiple spacecraft. However, these methods have not been able to improve the safety constraints and trajectory description of spacecraft systems and relative motions, and it is also difficult to solve the problem of safe tracking of the target spacecraft's spin nutation.

[0005] Combined with the mission requirements and the above analysis, the safe approach control method for non-cooperative targets of space spin-nutation has become one of the key directions in the current spacecraft rendezvous and docking mission. Research on autonomous computing safe approach control methods in spacecraft rendezvous and docking has important theoretical research and engineering exploration significance for the fields of spacecraft rendezvous and docking, on-orbit servicing and manipulation, attitude and relative orbit control, etc. Summary of the Invention

[0006] The technical problem solved by the present invention is: to overcome the deficiencies of the existing technology in solving the safety and describability of dynamic target satellite rendezvous and docking, and to propose a safe approach control method for space spin-nutation non-cooperative targets, so as to realize short-range autonomous closed-loop control of spacecraft attitude and orbit coupling for non-cooperative spacecraft targets or spin-nutation space debris in space with rotation and nutation.

[0007] The solution to the technical problem provided by the present invention is: a method for safe approach control of non-cooperative target of space spin nutation, the method comprising the following steps:

[0008] S1. Use unit quaternions to describe the motion attitude of the service spacecraft, use error quaternions to describe the relative attitude error between the service spacecraft and the target spacecraft, use the coordinates of the service spacecraft in the LVLH coordinate system of the target spacecraft to describe the relative position error between the two spacecraft, establish the dynamics and kinematics models of the relative attitude error and relative orbit error of the two spacecraft, and compact the relative attitude error and relative orbit error models into a six-degree-of-freedom form;

[0009] S2. Construct a spacecraft auxiliary system for rendezvous and docking that takes safety constraints into account by defining constraint functions and constraint auxiliary variables that serve the spacecraft's safety and motion boundaries.

[0010] S3. Designing shortest-path sliding mode variables for the spacecraft auxiliary system, wherein the shortest-path sliding mode variables enable the attitude and relative orbit of the service spacecraft to maneuver from the initial state to the desired attitude and orbit required for the mission via the shortest path;

[0011] S4. Design a non-singular auxiliary switching function to avoid singular phenomena when the shortest trace is used to calculate the time derivative of the sliding mode variable;

[0012] S5. Based on the six-degree-of-freedom relative attitude error and relative orbit error model, the spacecraft auxiliary system, the shortest track sliding mode variable, and the non-singular auxiliary switching function, a safe approach controller considering safety constraints is constructed for the non-cooperative target of space spin nutation. The established safe approach controller is applied to the attitude tracking and relative orbit control during the rendezvous and approach of the spacecraft, so as to achieve the mission goal of converging the attitude and relative orbit of the spacecraft during rendezvous and docking along the shortest track within the safety constraints within a limited and specified time.

[0013] Preferably, the dynamics and kinematics models of the relative attitude error of the two spacecraft are:

[0014]

[0015] in,

[0016]

[0017] Among them, the intermediate variable M a =P T J s P is the nonlinear matrix of the system, and the intermediate variable P=H -1 , intermediate variables I3 is a 3×3 identity matrix with all diagonal elements set to 1, C a , G a , Q a are all nonlinear matrices of the system, ω d is the expected angular velocity of the service spacecraft relative to the target spacecraft, R e is the error rotation matrix, defined as q e0 ,q ev They are respectively the fixed coordinate systems of the service spacecraft body Rotate to the target spacecraft body fixed coordinate system The three-dimensional Euler axis e on which it depends s and the Euler angle θ s The corresponding function value is: J s represents the spacecraft 3×3 moment of inertia matrix with positive constant, τ a It is the input of the attitude control torque of the service spacecraft, in N·m.

[0018] Preferably, the dynamics and kinematics model of the relative orbit error of the two spacecraft is:

[0019]

[0020] in, τ pl =Q p τ p

[0021] , is the transformation matrix considering the attitude-orbit coupling of spacecraft guidance, R lI and R bI M is the transformation matrix from the Earth-centered inertial coordinate system to the target spacecraft LVLH coordinate system and from the inertial system to the service spacecraft's own system; p =diag(m s ,m s ,m s ), m s represents the quality of the service spacecraft, represents the service spacecraft guidance input, C p is the linear coefficient matrix, G pl is the residual function term, is the desired relative position, q pe is the error between the current position and the expected relative position, τ p It is the force input for the spacecraft position control, unit: Newton.

[0022] Preferably, the six-degree-of-freedom compact form of the dual-spacecraft attitude relative error dynamics and kinematics model and the relative orbit dynamics and kinematics model is:

[0023]

[0024] Among them, q 6d =[q ev ,q pe ] T , M 6d =diag(M a ,M p ), C 6d =diag(C a ,C p ), G 6d =[G a ,G p ] T , τ6d =[τ a ,τ p ] T , Q 6d =diag(Q a ,Q p ).

[0025] Preferably, the constraint function is defined as follows:

[0026]

[0027] Among them, ρ i (t) is the one-dimensional boundary constraint function of the i-th degree of freedom in the six-degree-of-freedom model of relative attitude error and relative orbit error, ρ 0i is the initial value of the boundary function corresponding to ρi(t), ρ ti =ρ i (t ps ) is the predefined upper bound of the steady-state error corresponding to ρi(t), ε ρi is ρ i (t) corresponds to a small positive constant, which is used to adjust the asymptotic boundary position, t ps is the expected error convergence time, and t is time.

[0028] Preferably, the constraint auxiliary variable as follows:

[0029]

[0030] Among them, δ i ∈(0,1] is the constraint constant of the i-th degree of freedom that limits the attitude and orbit overshoot of the service spacecraft relative to the target spacecraft, q 6di (t) is the state variable q in the six-degree-of-freedom model of relative attitude error and relative orbit error 6d The element of the i-th degree of freedom.

[0031] Preferably, the auxiliary system model is as follows:

[0032]

[0033] where σ = [σ1, ..., σ6] T , A=[α1,...,α6] T , B=diag(β1,...,β6)

[0034]

[0035] σ i is the i-th degree of freedom variable of the auxiliary system;

[0036]

[0037] Preferably, the sliding mode variable ζ is:

[0038]

[0039] Among them, p1 is the power index related to the finite time convergence property, and its value range is between 0 and 1, sig NN (σ) and sign NN (σ) is the modulus normalized sign function about σ, Sign NN (σ) is in the power exponential form, and κ1 is a positive constant parameter.

[0040]

[0041] Preferably, the non-singular auxiliary switching function is as follows:

[0042]

[0043] Where φ is the non-singular auxiliary switching function, ι is the auxiliary constant coefficient, is the non-zero threshold of ||σ||, I6 is the unit matrix, κ1 is the positive constant gain of the first normalized sign function term about ξ, and its value can be freely adjusted according to the control effect, p1 is the positive power exponent of the first normalized sign function term about ξ,

[0044] Preferably, the safety approximation controller considering safety constraints for the non-cooperative target of spatial spin nutation is:

[0045]

[0046] Where κ2 is the positive constant gain of the second normalized sign function term with respect to ζ, and p2∈(0,1) is the positive power exponent of the second normalized sign function term with respect to ζ.

[0047] The beneficial effects of the present invention compared with the prior art are:

[0048] (1) The present invention transforms the spacecraft attitude tracking error model and position tracking error model into a Lagrangian system form, fully considers the coupling function terms of attitude-orbit coupling motion, and compacts it into a six-degree-of-freedom spacecraft attitude-orbit coupling model, which can facilitate the integrated tracking control of the attitude and relative position of the relative target spacecraft;

[0049] (2) The present invention can achieve time-varying motion range constraints and protection for a spacecraft during rendezvous and docking with a target by defining constraint functions for safety and motion boundaries, designing constraint auxiliary variables and system auxiliary variables, and constructing a spacecraft auxiliary system for rendezvous and docking that takes safety constraints into account;

[0050] (3) The present invention designs the shortest path sliding mode variable by normalizing the modulus value sign function and introduces it into the spacecraft control system, which can realize the attitude tracking during rendezvous and the shortest path of the relative position trajectory approximating a straight line in the three-dimensional Euclidean space;

[0051] (4) The present invention proposes a safety approximation controller for non-cooperative targets of spatial spin nutation based on the shortest trajectory sliding mode variable and non-singular auxiliary switching function, which takes safety constraints into consideration. The controller can achieve a trajectory approximation to a straight line, the system convergence time can be specified in advance, and the energy consumption can be reduced.

[0052] (5) The control method of the present invention has the characteristics of attitude and relative trajectory safety constraints, strong describability, high control accuracy, low energy consumption, and strong robustness. It is suitable for attitude orbit safety approximation and describable path specified time control in spacecraft rendezvous and docking missions, and is also suitable for general spacecraft rendezvous and docking control missions. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 A schematic flow chart of a non-cooperative target safe approach control method for space spin nutation provided by the present invention;

[0054] Figure 2 Schematic diagram of the coordinate system used in the present invention;

[0055] Figure 3 The following are the simulation results of the attitude error motion trajectory using the control method of the present invention (algorithm A), and a schematic comparison of the shortest trajectory and docking safety with the traditional algorithms (algorithms B and C). The subscripts of the variables in the figure represent the elements of the corresponding vector. The following figures are the same. Compared with the traditional method, the trajectory of this method is approximately a straight line and converges faster.

[0056] Figure 4 The simulation results of the relative position error motion trajectory using the control method of the present invention (algorithm A) are shown, and a schematic comparison of the shortest track trajectory and docking safety is made with the traditional algorithms (algorithms B and C). Compared with the traditional methods, using this method, the trajectory is approximately a straight line and converges faster;

[0057] Figure 5This is the partial convergence result of the attitude error quaternion vector using the control method of the present invention. It can be seen that the attitude motion is always within the safety boundary range specified by the constraint function, with the safety of attitude motion under rendezvous and docking, and the three-axis errors converge almost synchronously, and the steady-state error is within the safety boundary range;

[0058] Figure 6 This is the partial convergence result of the attitude error quaternion vector using the traditional comparative control algorithm B. Compared with the algorithm of the present invention, algorithm B does not use the normalized sign function, but only uses the conventional sign function. It can be seen that the three axes converge asynchronously. Therefore, the convergence trajectory curve is not an approximate shortest straight line.

[0059] Figure 7 This is the partial convergence result of the attitude error quaternion vector using the traditional comparative control algorithm C. Compared with the algorithm of the present invention, algorithm C only uses the conventional constraint function and does not use the normalization function. It can be seen that the three axes converge asynchronously. Therefore, the convergence curve does not approximate the shortest straight line.

[0060] Figure 8 The relative position tracking error convergence results of the control method of the present invention show that the relative position motion is always within the safety boundary range specified by the constraint function, with the safety of relative position motion under rendezvous and docking, and the three-axis errors converge almost synchronously, and the steady-state error is within the safety boundary range;

[0061] Figure 9 The relative position tracking error convergence result of the traditional comparative control algorithm B is shown. Compared with the algorithm of the present invention, the three-axis convergence of algorithm B is asynchronous, so the convergence curve does not approximate the shortest straight line.

[0062] Figure 10 This is the relative position tracking error convergence result of the traditional comparative control algorithm C. Compared with the algorithm of the present invention, algorithm C does not use a normalization function, and the three axes converge asynchronously. Therefore, the convergence curve does not approximate the shortest straight line.

[0063] Figure 11 The control input simulation result of the posture tracking control using the control method of the present invention;

[0064] Figure 12 The control input simulation results of the relative position tracking control using the control method of the present invention are as follows;

[0065] Figure 13 is the spacecraft attitude tracking error index, which is defined as I a =||q ev ||+||ω e ||;

[0066] Figure 14 is the spacecraft relative position tracking error index, which is defined as

[0067] Figure 15 The energy consumption of the attitude tracking control method of the present invention is compared with the traditional comparison algorithm (the solid line is the energy consumption of the present invention method), where the energy consumption is defined as

[0068] Figure 16 The energy consumption results of the relative position tracking control using the control method of the present invention are compared with the traditional comparison algorithm (the solid line is the energy consumption of the method of the present invention), where the energy consumption is defined as

[0069] Figure 17 is the attitude disturbance parameter, which is set much larger than the actual space environment in the simulation to verify the robustness of the algorithm of the present invention;

[0070] Figure 18 is the relative orbit perturbation parameter. In the simulation, this parameter is set much larger than the actual space environment to verify the robustness of the algorithm of the present invention. DETAILED DESCRIPTION

[0071] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only for illustration and are not intended to limit the present invention.

[0072] This invention provides a method for safely approaching a non-cooperative target with spin-nutation in space. First, it is clarified that the research scenario of this invention is the rendezvous and approach scenario of an on-orbit servicing mission of a spacecraft. In this scenario, the target spacecraft has spin and nutation characteristics. The research object is the rendezvous and approach behavior of the on-orbit servicing spacecraft toward the spin-nutation target spacecraft. The research problem is the tracking control of the relative attitude and relative orbit (position) of the servicing spacecraft to the target spacecraft. In detail: 1) Spin-nutation non-cooperative target refers to the target spacecraft spinning at a certain angular velocity of a single axis or multiple axes, accompanied by nutation, and the target spacecraft is a non-cooperative target, that is, the motion information of the service spacecraft to the target spacecraft comes from relative measurement. The present invention takes control into consideration, so it is assumed that the motion information of the target spacecraft can be obtained through the relevant measurement units on the spacecraft; 2) Tracking control target refers to tracking and control to the state before docking. At this time, the mechanical coordinate systems of the service spacecraft and the target spacecraft are relatively stationary, and the relative orbital positions converge, that is, the two coordinate systems are aligned with a certain desired fixed posture and position. In order to simplify the design, the coordinates of the two spacecraft are considered to coincide. This assumption does not affect the actual docking constant design. In engineering applications, it is only necessary to increase a certain fixed offset; 3) Safe approach refers to the situation where the target spacecraft rotates, and the service spacecraft is relatively stationary. The spacecraft cannot touch the target spacecraft body and the deployed components, that is, it is necessary to ensure that the two spacecraft do not collide. This goal is constrained by the constraint function in the present invention for safety, and the constraint function changes in real time with the position change and motion state of the target spacecraft. Therefore, satisfying the constraint conditions means that the service spacecraft is always in the collision avoidance safety area for non-cooperative and unstable target spacecraft; 4) Control method. On the basis of safety constraints, the present invention adopts a normalized function to optimize the actual trajectory of the rendezvous approximation, so that the rendezvous trajectory is approximately a straight line in the relative coordinate system and approaches a spiral line in the orbital coordinate system, and the system convergence time can be artificially specified in advance, that is, the service spacecraft will approach the docking position within a limited and specified time with a path that is approximately a straight line in the three-dimensional vector space under the premise of time-varying safety constraints, and has a reasonable docking posture. The algorithm flow is as follows Figure 1 As shown, the following steps are included:

[0073] Step S1: Use unit quaternions to describe the motion attitude of the service spacecraft, use error quaternions to describe the relative attitude error between the service spacecraft and the target spacecraft, use the coordinates of the service spacecraft in the LVLH coordinate system of the target spacecraft to describe the relative position error between the two spacecraft, establish the dynamic and kinematic models of the relative attitude error and relative orbit error of the two spacecraft, and compact the relative attitude error and relative orbit error models into a six-degree-of-freedom form;

[0074] For the rendezvous and docking dual spacecraft, the body-fixed coordinate system, the geocentric inertial coordinate system and the target spacecraft LVLH relative orbital coordinate system are established, and the relative attitude dynamics and kinematics model of the dual spacecraft is established with the body-fixed coordinate system and the geocentric inertial coordinate system as reference systems; the relative orbital dynamics and kinematics model of the dual spacecraft (the service spacecraft relative to the target spacecraft) is established with the body-fixed coordinate system, the target spacecraft LVLH (local vertical / local horizontal) coordinate system and the geocentric inertial coordinate system as reference systems.

[0075] Among them, the reference coordinate system is defined as the geocentric inertial coordinate system (the Earth-Centered Inertial frame, ECI), the origin of this coordinate system is at the center of the earth, x I The axis points to the Earth's vernal equinox γ,z I The axis points to the north of the earth's axis, y I Axis and x I axis and z I The axes are perpendicular to each other and form a right-handed coordinate system. To serve the spacecraft body fixed coordinate system, It is the fixed coordinate system of the target spacecraft body, the origin of the coordinate system is fixed at the center of mass of the corresponding spacecraft, and the coordinate axis is the principal inertia axis of the corresponding spacecraft. is the target spacecraft LVLH coordinate system (local vertical / local horizontal coordinate system), the origin of which is located at the center of mass of the target spacecraft, x l The axis points to the orbital radial direction (the center of the earth points to the center of mass of the target spacecraft), z l The axis points in the direction of orbital angular momentum, y l Axis and x l Axis and z l The axes form a right-handed coordinate system. The relative position between the spacecraft is defined as the vector q p , the above coordinate system is defined as Figure 2 shown.

[0076] In the present invention, unit quaternions are used to describe the motion attitude of the service spacecraft, error quaternions are used to describe the relative attitude error between the service spacecraft and the target spacecraft, and the coordinates of the service spacecraft in the LVLH coordinate system of the target spacecraft are used to describe the relative position error between the two spacecraft.

[0077] Considering the attitude kinematics of a rigid spacecraft whose body coordinate system is fixed to the center of mass, the service spacecraft body fixed coordinate system Relative to the Earth's inertial coordinate system The rotation of the service spacecraft in the inertial system is used to describe the attitude motion of the service spacecraft. According to the Euler rotation theorem, in three-dimensional Euclidean space, the rotation of an object can be described by the three-dimensional unit direction vector e of a fixed axis (arbitrary Euler rotation axis) passing through a fixed point (spacecraft center of mass) and an arbitrary rotation angle (Euler angle) θ. For the application scenario of the present invention, it means the geocentric inertial coordinate system Along a certain three-dimensional unit direction vector e in space, rotate an arbitrary rotation angle (Euler angle) θ to obtain the fixed coordinate system of the service spacecraft body This rotation process can be further described by unit quaternion. Considering the fixed point as the origin of the service spacecraft system coordinate, the service spacecraft system is defined relative to the geocentric inertial coordinate system. The unit quaternion associated with the rotation of is in where q v is a three-dimensional vector that satisfies The service spacecraft is represented in the Earth-centered inertial coordinate system The posture motion in can be described by the unit quaternion In the equation and in the following statements, for any vector x, the symbol and are the first and second derivatives of vector x with respect to time, respectively, and the symbol (·) × is a 3×3 skew-symmetric matrix corresponding to a three-dimensional vector. a Represents the fixed coordinate system of the service spacecraft body Relative to the center of inertia coordinate system The expression in the service spacecraft body fixed coordinate system The spacecraft attitude angular velocity in .

[0078] The same way as the service spacecraft is defined in the center inertial coordinate system, the relative motion of the service spacecraft and the target spacecraft can be determined by the service spacecraft body fixed coordinate system and the target spacecraft body fixed coordinate system The relative rotation of . Definition is the error quaternion of the desired attitude of the service spacecraft relative to the target spacecraft, q e0 ,q ev =[q ev1 ,q ev2 ,q ev3 ] T To serve the spacecraft body fixed coordinate system Rotate to the target spacecraft body fixed coordinate system The three-dimensional Euler axis e on which it depends s and the Euler angle θ s The corresponding function value And the unit error quaternion satisfies the constraint

[0079] The rigid body attitude dynamics of the servicing spacecraft can be described as

[0080]

[0081] Among them, J s represents the spacecraft 3×3 moment of inertia matrix with positive constant, τ a Represents the spacecraft attitude control input torque, in N·m, ω a The definition is the same as before, representing the fixed coordinate system of the service spacecraft body Relative to the inertial system The expression in the service spacecraft body fixed coordinate system The spacecraft attitude angular velocity in .

[0082] Considering that the general Eulerian Lagrangian system form is convenient for controller design, and it is also convenient to transfer the control algorithm of the present invention to the relative orbit controller design and robot control design with the same Eulerian Lagrangian model form, the present invention transforms the above-mentioned spacecraft attitude kinematics and dynamics into a general Eulerian Lagrangian system and provides a general control algorithm that conforms to the general model form. Considering that the unit error quaternion satisfies the constraint condition Therefore, only the three-dimensional vector part q of the error quaternion needs to be considered in the system. ev Then the general Eulerian Lagrangian model of the dynamics and kinematics of the relative attitude error of the two spacecraft is:

[0083]

[0084] in,

[0085]

[0086] Among them, the intermediate variable M a =P T J s P is the nonlinear matrix of the system, and the intermediate variable P = T -1 , intermediate variables I3 is a 3×3 identity matrix with diagonal elements of 1, and the intermediate variable C a , G a , Q a The nonlinear matrix of the system is defined as above, ω d is the expected angular velocity of the service spacecraft relative to the target spacecraft, R e is the error rotation matrix, defined as The control task of the present invention is to design the controller τ so that the relative attitude error between the service spacecraft and the target spacecraft converges to 0, and the attitude motion trajectory formed by the transient process of convergence is a straight line in the three-dimensional vector space, that is, the shortest distance path. The relative attitude error converges to 0, which means that no matter what attitude angular velocity and nutation angle the target spacecraft rotates at, the service spacecraft body coordinate system Through control, they can be rotated to the coordinate system of the target spacecraft Overlapping means that the service spacecraft can track and control the target spacecraft's arbitrary posture motion.

[0087] The dynamic and kinematic models of the relative orbit of the two spacecraft are:

[0088]

[0089] Among them, q p =[q px q py q pz ] T represents the position vector of the service spacecraft relative to the target spacecraft, expressed in the target spacecraft LVLH coordinate system. When the spacecraft is simplified as a point mass model, the origin is the target spacecraft center of mass, v p =[v px v py v pz ] T represents the velocity vector of the service spacecraft relative to the target spacecraft, expressed in the LVLH coordinate system of the target spacecraft, M p =diag(m s ,m s ,m s ), m s represents the quality of the service spacecraft, represents the service spacecraft guidance input, C p The linear coefficient matrix and G pl is the residual function term, defined as follows

[0090]

[0091]

[0092] Among them, r et and r es denote the distance from the center of the Earth to the target spacecraft and the service spacecraft, θ pt is the true anomaly angle of the target spacecraft, a pt and e pt represent the semi-major axis and orbital eccentricity of the target spacecraft's elliptical orbit, μ p represents the Earth's gravitational constant.

[0093] definition is the desired relative position, the relative orbit error dynamics and kinematics model between the two spacecraft can be obtained as follows:

[0094]

[0095] in, τ pl =Q p τ p , is the transformation matrix considering the attitude-orbit coupling of spacecraft guidance, R lI and R bI is the transformation matrix from the Earth-centered inertial coordinate system to the target spacecraft LVLH coordinate system and from the inertial system to the service spacecraft body coordinate system.

[0096] In order to realize the six-degree-of-freedom coupled control of the service spacecraft, the above model is written into a six-degree-of-freedom compact form as follows:

[0097]

[0098] Among them, q 6d =[q ev ,q pe ] T , M 6d =diag(M a ,M p ), C 6d =diag(C a ,C p ), G 6d =[G a ,G p ] T , τ 6d =[τ a ,τ p ] T , Q 6d =diag(Q a ,Q p ). τ a is the attitude control torque input for the service spacecraft, in Newton-meters (N·m), τ p It is the force input for the position control of the service spacecraft, in Newton (N).

[0099] Step S2: By defining the constraint functions and constraint auxiliary variables of the service spacecraft safety and motion boundaries, a spacecraft auxiliary system for rendezvous and docking that takes safety constraints into consideration is constructed;

[0100] The boundary constraint function is defined as follows:

[0101]

[0102] Among them, ρ i (t) is the one-dimensional boundary constraint function of the i-th degree of freedom in the six-degree-of-freedom model of relative attitude error and relative orbit error, ρ 0i is ρ i (t) corresponds to the initial value of the boundary function, ρ ti =ρ i (t ps ) is ρ i (t) corresponds to the predefined steady-state error safety upper bound, ε ρi is ρ i (t) corresponds to a small positive constant, which is used to adjust the asymptotic boundary position, t ps is the expected error convergence time, and t is time.

[0103] According to the inequality -δ i ρ i (t)<q 6di (t)<ρ i (t),q 6di (0)≥0 and -ρ i (t)<q 6di (t)<δ i ρ i (t),q 6di (0)<0, subscript i=1,...,6 represents the i-th degree of freedom in the six-degree-of-freedom model of relative attitude error and relative trajectory error, and the constraint auxiliary variables are defined as follows:

[0104]

[0105] Among them, δ i ∈(0,1] is the constraint constant of the i-th degree of freedom that limits the attitude and orbit overshoot of the service spacecraft relative to the target spacecraft, which can be set according to the mission requirements. i When it is close to 0, the system has almost no overshoot, q 6di (t) is the state variable q in the six-degree-of-freedom model of relative attitude error and relative orbit error 6d The element of the i-th degree of freedom.

[0106] Pick where σ i is the i-th degree of freedom variable of the auxiliary system;

[0107] but

[0108]

[0109] σ i Finding the derivative with respect to time, we can get,

[0110]

[0111] in,

[0112]

[0113]

[0114] By writing the above equation in a compact form, we can obtain the auxiliary system in which the spacecraft attitude orbit tracking error satisfies the boundary constraints as follows:

[0115]

[0116] where σ = [σ1, ..., σ6] T , A=[α1,...,α6] T , B=diag(β1,...,β6).

[0117] According to the constraint function design, the constraint function constrains the tracking error of the service spacecraft with respect to the target spacecraft. Therefore, the constraint relationship of the constraint function itself to the motion state of the target spacecraft remains unchanged. When the motion state of the target spacecraft changes, the constraint area of ​​safe motion in the inertial system changes accordingly. The service spacecraft is always constrained within the time-varying safety area, realizing safety constraint guarantee for the entire process of close rendezvous and docking.

[0118] Step S3: Designing the shortest-path sliding mode variables for the spacecraft auxiliary system, wherein the shortest-path sliding mode variables enable the attitude and relative orbit of the service spacecraft to maneuver from the initial state to the desired attitude and orbit required for the mission via the shortest path;

[0119] An approximate shortest-path sliding mode variable is designed for a spacecraft auxiliary system with safety constraints during rendezvous and docking. This sliding mode variable enables the service spacecraft to converge the tracking error of the target spacecraft with a more optimal path that is approximately a straight line. The general form of the sliding mode variable is as follows:

[0120]

[0121] Where ξ represents the universal sliding mode variable, κ j is the positive constant gain of the jth normalized sign function term with respect to ξ, is the positive constant gain of the first-order term of the universal sliding mode variable, which can be any positive constant, m is the number of sliding mode function terms, n≥1, p j is the positive power exponent of the jth term with respect to the normalized sign function, p j The value range is usually 0 to 1, sig NN (ξ) is the modulus-normalized sign function with respect to ξ. Positive exponents of the normalized sign function are associated with finite-time convergence properties.

[0122] Based on the above sliding mode variable design form, combined with the spacecraft tracking model in step 1 and the safety boundary constraint auxiliary system in step 2, the variable ξ in the above formula is defined as the independent variable σ of the safety boundary constraint auxiliary system in step 2 = [σ1,...,σ6] T , take the number of sliding mode function terms m as 1, The sliding mode variable ζ is designed for the constraint model of the spacecraft attitude orbit during rendezvous and docking as follows.

[0123]

[0124] Among them, κ1 is the positive constant gain of the first normalized sign function term about ξ, and its value can be freely adjusted according to the control effect. p1 is the positive power exponent of the first normalized sign function term about ξ, and its value range is between 0 and 1. NN (σ) and sign NN (σ) is the modulus normalized sign function about σ, Sign NN The power exponential form of (σ) is defined as follows,

[0125]

[0126] In this invention, the convergence curve of the variable σ from the initial error point to the origin approximates a straight line. This physically manifests itself as the service spacecraft attitude and the target spacecraft's relative orbit maneuvering from the initial state to the desired attitude orbit relative to the target spacecraft along a relatively short path, with significant uncertainty, while the range of motion always remains within the safety margin.

[0127] The time derivative of the sliding mode variable ζ is as follows:

[0128]

[0129] in,

[0130]

[0131] Step S4: design a non-singular auxiliary switching function to avoid the occurrence of singular phenomena when the shortest trace is used to calculate the time derivative of the sliding mode variable;

[0132] Considering the sliding surface design in step 3, when the time derivative of the sliding variable is taken, the following will appear: and The function term indicates a singular problem. In order to overcome the singular problem of the variable, a non-singular auxiliary switching function is designed as follows:

[0133]

[0134] Among them, ι is the auxiliary constant coefficient, is the non-zero threshold of ||σ||, which is a small positive constant used to prevent system singularity, and is usually 0.001.

[0135] Step S5: Based on the six-degree-of-freedom relative attitude error and relative orbit error model, the spacecraft auxiliary system, the shortest track sliding mode variable, and the non-singular auxiliary switching function, a safety approach controller considering safety constraints is constructed for the non-cooperative target of space spin nutation. The established safety approach controller is applied to the attitude tracking and relative orbit control during the rendezvous and approach of the spacecraft, so as to achieve the mission goal of converging the attitude and relative orbit of the spacecraft during rendezvous and docking along the shortest track within the safety constraint range within a limited and specified time.

[0136] Based on M 6d ,q 6d 、C 6d , G 6d , Q 6d ,ζ,φ,sig NN (·) Design a safe approximation controller for non-cooperative spatial spin nutation targets with safety constraints

[0137]

[0138] Among them, κ2 is the positive constant gain of the second normalized sign function term with respect to ζ, and its value range can be designed accordingly according to the control effect of the closed-loop system. p2∈(0,1) is the positive power exponent of the second normalized sign function term with respect to ζ.

[0139] The five steps described above have a progressive logical relationship, as explained below: Step S1 provides the spacecraft system model and relevant parameter definitions required for controller design and subsequent control system steps. Building on Step 1, model-based controller and closed-loop system design is performed. Considering the target spacecraft's spinning and nutating motion characteristics, to ensure safer rendezvous and docking, the present invention innovatively proposes a time-varying motion constraint function and auxiliary system in Step S2. This method applies motion constraints to each dimension of the target spacecraft's attitude and orbit characteristics based on the target spacecraft's real-time motion state, including constraints on system convergence time, overshoot, and steady-state error. This constraint ensures that the service spacecraft can maintain safe rendezvous and docking within its constraints. Even if the target spacecraft has complex attitudes or orbital motion, safe constraints and safe rendezvous approaches can still be achieved through real-time solution in the relative coordinate system. To enhance the describability of the closed-loop system's trajectory, Step S3 proposes a design method for an approximate shortest-path sliding surface within the relative coordinate system. Different vectors, constant gains, power exponents, and the number of sub-sliding surfaces can be defined to construct different sliding surfaces for different application scenarios. In response to the problem of spacecraft time-varying attitude and orbit coupling tracking control, step S3 designs a sliding surface for spacecraft attitude control based on the spacecraft state vector. Taking into account the existence of singularity problems in the derivative of the sliding surface designed in step S3, a non-singular control auxiliary switching function is designed in step S4 to avoid singularity and applied to the controller. Based on the design of steps S1 to S4, step S5 proposes a space spin-nutation non-cooperative target safety approach controller. The closed-loop system can be obtained by bringing the controller into the system of step 1. This controller can be directly applied to spacecraft attitude and relative orbit control or spacecraft relative attitude and orbit control during rendezvous approach, achieving multiple control objectives such as time-varying safety constraint guarantee, approximate straight line trajectory description, and definable convergence time. At this point, the entire control system design of the present invention is completed.

[0140] The method of the present invention can be demonstrated as follows.

[0141] The Lyapunov function V1 about ζ and the Lyapunov function V2 about σ are selected as follows

[0142]

[0143] Taking the time derivative of the above Lyapunov function, we can get

[0144]

[0145] According to the finite time stability theory, it can be seen that the dual spacecraft attitude tracking system has a finite time T m≤T1+T2 converges to the origin, that is, the attitude of the service spacecraft is in a finite time T m Converges to the desired posture. The subscript 0 indicates the initial value of the corresponding variable.

[0146] Through theoretical analysis, the space spin-nutation non-cooperative target safety approach control task, under the control method proposed in the present invention, can realize the time-varying spin-nutation target spacecraft safety motion constraint, constraint autonomous calculation, tracking trajectory description, finite time and specified time convergence, high-precision and strong robust attitude and orbit integrated rendezvous and tracking control.

[0147] The innovations and advantages of the present invention compared with the existing technology are:

[0148] (1) Compared with the traditional rendezvous control method, the proposed method can be effectively applied to the rendezvous approach tracking control mission of non-cooperative target spacecraft with spin-nutation motion characteristics.

[0149] (2) Compared with the traditional rendezvous control method, this method uses the time-varying constraint function of the sub-dimension to achieve the time-varying description of the rendezvous safety area of ​​the spin-nutation motion target.

[0150] (3) Based on the time-varying constraint function, the control method of the present invention can be applied to achieve safe rendezvous and approach to the spin-nutating target spacecraft. The service spacecraft always moves within the time-varying region described by the motion characteristics and constraint conditions of the target spacecraft, avoiding collision between the two spacecraft during the rendezvous and approach process.

[0151] (4) Based on the shortest-path sliding surface, the shortest-path trajectory control can be achieved within the safe motion constraint range, that is, in the tracking error coordinate system, the tracking trajectory is approximately a straight line, with strong trajectory descriptibility, good convergence characteristics, good control performance and less energy consumption.

[0152] (5) Due to the existence of the constraint function and the finite time convergence characteristic of the control algorithm, the control method of the present invention can achieve the convergence of the closed-loop system within a finite time and a specified time, so that the designer can prepare the flight program and rendezvous approach plan within the specified time according to the specific mission.

[0153] Based on the above implementation method, a space spin nutation non-cooperative target safe approach control method simulation results can be obtained as follows: Figure 3-18During the simulation process, in order to illustrate the advantages and characteristics of the algorithm of the present invention, similar traditional algorithms were selected for comparative simulation. The algorithm of the present invention is denoted as Algorithm A, and the traditional algorithms are denoted as Algorithms B and C. Compared with the algorithm of the present invention, Algorithm B does not use the normalized sign function but only uses the conventional sign function, and Algorithm C only uses the conventional constraint function but does not use the normalization function. Figure 3 The following figure shows the simulation results of the attitude error motion trajectory using the control method of the present invention (algorithm A), and a schematic comparison of the shortest trajectory and docking safety with the traditional algorithms (algorithms B and C). As can be seen from this figure, compared with the traditional methods, this method has a shorter maneuvering path and more precise control effect in the relative coordinate system trajectory (attitude trajectory direction). Using this method, the trajectory is approximately a straight line and converges faster. Figure 4 The simulation results of the relative position error motion trajectory using the control method of the present invention (algorithm A) are shown, and a schematic comparison of the shortest track direction trajectory and docking safety is made with the traditional algorithms (algorithms B and C). Compared with the traditional method, it has a shorter maneuvering path and more precise control effect in the relative coordinate system track direction (relative position track direction). Using this method, the trajectory is approximately a straight line and converges faster; Figure 5 This is the partial convergence result of the attitude error quaternion vector using the control method of the present invention. It can be seen that the attitude motion is always within the safety boundary range specified by the constraint function, with the safety of attitude motion under rendezvous and docking, and the convergence time is less than the predefined convergence time, verifying the finite and specified time convergence. The three-axis errors converge almost synchronously, and the steady-state error is within the safety boundary range; Figure 6 This is the partial convergence result of the attitude error quaternion vector using the traditional comparative control algorithm B. Compared with the algorithm of the present invention, algorithm B does not use the normalized sign function, but only uses the conventional sign function. It can be seen that the three axes converge asynchronously. Therefore, the convergence trajectory curve is not an approximate shortest straight line and is not the optimal situation. Figure 7 This is the partial convergence result of the attitude error quaternion vector using the traditional comparative control algorithm C. Compared with the algorithm of the present invention, algorithm C only uses the conventional constraint function and does not use the normalization function. It can be seen that the three axes converge asynchronously. Therefore, the convergence curve does not approximate the shortest straight line. Figure 8 The results of the relative position tracking error convergence using the control method of the present invention show that the relative position motion is always within the safety boundary range specified by the constraint function, with the safety of relative position motion under rendezvous and docking, and the convergence time is less than the predefined convergence time, verifying the finite and specified time convergence. The three-axis errors converge almost synchronously, and the steady-state error is within the safety boundary range. Figure 9 The relative position tracking error convergence result of the traditional comparative control algorithm B is shown. Compared with the algorithm of the present invention, the three-axis convergence of algorithm B is asynchronous, so the convergence curve does not approximate the shortest straight line. Figure 10This is the relative position tracking error convergence result of the traditional comparative control algorithm C. Compared with the algorithm of the present invention, algorithm C does not use a normalization function, and the three axes converge asynchronously. Therefore, the convergence curve does not approximate the shortest straight line. Figure 11 The control input simulation results of the attitude tracking control using the control method of the present invention are presented, which verifies the feasibility of the method of the present invention. Figure 12 The control input simulation results of the relative position tracking control using the control method of the present invention are shown to verify the feasibility of the method of the present invention. During the simulation, relatively extreme simulation conditions were selected. Figure 11 and Figure 12 The control input in is large. In actual application, the conditions such as the desired attitude and relative position setting, convergence speed, and convergence time will be greatly relaxed. The obtained control input will adapt to the actual actuator. The simulation verification of this invention adopts relatively strict working conditions to illustrate the wide applicability of this algorithm. Figure 13 is the spacecraft attitude tracking error index, which is defined as I a =||q ev ||+||ω e ||,I a is the spacecraft attitude tracking error, ω e To serve the spacecraft's attitude angular velocity tracking error, it can be seen that under the three algorithms, the errors can converge, and the relevant parameter adjustments make the transient and steady-state performances similar. Therefore, based on similar performance, characteristic performance comparisons can be made, such as the linear convergence characteristics and the characteristics of less energy consumption; Figure 14 is the spacecraft relative position tracking error index, which is defined as I p The spacecraft relative position tracking error index provides a comparison benchmark. That is, under the three algorithms, the transient and steady-state performance are similar, so the characteristic performance, such as the straight line convergence characteristic and the low energy consumption characteristic, can be compared. Figure 15 The energy consumption of the attitude tracking control method of the present invention is compared with the traditional comparison algorithm (the solid line is the energy consumption of the present invention method), where the energy consumption is defined as It can be seen that the energy consumption is lower when the algorithm of the present invention is adopted; τ 6di (t) is time tτ 6d The value of the i-th degree of freedom is, Figure 16 The energy consumption results of the relative position tracking control using the control method of the present invention are compared with the traditional comparison algorithm (the solid line is the energy consumption of the method of the present invention), where the energy consumption is defined as It can be seen that the algorithm of the present invention can consume similar energy for the relative position control situation and obtain more stringent rendezvous and docking conditions such as approximate straight lines; Figure 17 and Figure 18is the attitude and relative orbit perturbation parameter. In the simulation, this parameter was set much higher than the actual space environment, verifying the strong robustness of the proposed algorithm and its ability to cope with complex environmental disturbances. Using the proposed integrated attitude-orbit coupling control method, combined with the convergence simulation results of attitude and relative position (orbit) tracking errors, the algorithm's effectiveness, safety constraints, trajectory describability, and time-constrained convergence for the attitude-orbit coupling six-degree-of-freedom control of a service spacecraft targeting a spin-nutation target were verified.

[0154] The above simulation results fully demonstrate that the space spin-nutation non-cooperative target safety approach control task, under the control method proposed in the present invention, can realize the time-varying spin-nutation target spacecraft safety motion constraint, constraint autonomous calculation, trajectory description, finite time and specified time convergence, high-precision and strong robust attitude and orbit integrated rendezvous approach control.

[0155] Although the present invention has been disclosed above in terms of preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solutions of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the scope of protection of the technical solutions of the present invention.

Claims

1. A non-cooperative target safe approach control method for space spin nutation, characterized in that The steps include: S1. Use unit quaternions to describe the motion attitude of the service spacecraft, use error quaternions to describe the relative attitude error between the service spacecraft and the target spacecraft, use the coordinates of the service spacecraft in the LVLH coordinate system of the target spacecraft to describe the relative position error between the two spacecraft, establish the dynamics and kinematics models of the relative attitude error and relative orbit error of the two spacecraft, and compact the relative attitude error and relative orbit error models into a six-degree-of-freedom form; S2. Construct a spacecraft auxiliary system for rendezvous and docking that takes safety constraints into account by defining constraint functions and constraint auxiliary variables that serve the spacecraft's safety and motion boundaries. S3. Designing shortest-path sliding mode variables for the spacecraft auxiliary system, wherein the shortest-path sliding mode variables enable the attitude and relative orbit of the service spacecraft to maneuver from the initial state to the desired attitude and orbit required for the mission via the shortest path; S4. Design a non-singular auxiliary switching function to avoid singular phenomena when the shortest trace is used to calculate the time derivative of the sliding mode variable; S5. Based on the six-degree-of-freedom relative attitude error and relative orbit error model, the spacecraft auxiliary system, the shortest track sliding mode variable, and the non-singular auxiliary switching function, a safe approach controller considering safety constraints is constructed for the non-cooperative target of space spin nutation. The established safe approach controller is applied to the attitude tracking and relative orbit control during the rendezvous and approach of the spacecraft, so as to achieve the mission goal of converging the attitude and relative orbit of the spacecraft during rendezvous and docking along the shortest track within the safety constraints within a limited and specified time.

2. A space spin nutation non-cooperative target safe approach control method according to claim 1, characterized in that: The dynamic and kinematic models of the relative attitude error of the two spacecraft are: in, Among them, the intermediate variable M a =P T J s P is the nonlinear matrix of the system, and the intermediate variable P=H -1 , intermediate variables I3 is a 3×3 identity matrix with all diagonal elements set to 1, C a , G a , Q a are all nonlinear matrices of the system, ω d is the expected angular velocity of the service spacecraft relative to the target spacecraft, R e is the error rotation matrix, defined as q e0 ,q ev They are respectively the fixed coordinate systems of the service spacecraft body Rotate to the target spacecraft body fixed coordinate system The three-dimensional Euler axis e on which it depends s and the Euler angle θ s The corresponding function value is: J s represents the spacecraft 3×3 moment of inertia matrix with positive constant, τ a It is the input of the attitude control torque of the service spacecraft, in N·m.

3. A space spin nutation non-cooperative target safe approach control method according to claim 2, characterized in that: The dynamics and kinematics model of the relative orbit error of the two spacecraft is: in, τ pl =Q p τ p , is the transformation matrix considering the attitude-orbit coupling of spacecraft guidance, R lI and R bI M is the transformation matrix from the Earth-centered inertial coordinate system to the target spacecraft LVLH coordinate system and from the inertial system to the service spacecraft's own system; p =diag(m s ,m s ,m s ), m s represents the quality of the service spacecraft, represents the service spacecraft guidance input, C p is the linear coefficient matrix, G pl is the residual function term, is the desired relative position, q pe is the error between the current position and the expected relative position, τ p It is the force input for the spacecraft position control, unit: Newton.

4. A method for safe approaching control of non-cooperative target of space spin nutation according to claim 3, characterized in that: The six-degree-of-freedom compact forms of the dual-spacecraft attitude relative error dynamics and kinematics model and the relative orbit dynamics and kinematics model are: where q 6d = [q ev , q pe T , M 6d = diag(M a , M p ), C 6d = diag(C a , C p ), G 6d = [G a , G p T , τ 6d = [τ a , τ p T , Q 6d = diag(Q a , Q p ).​​​ 5. The method for safe approaching control of non-cooperative target of space spin nutation according to claim 3, characterized in that: The constraint function is defined as follows: Among them, ρ i (t) is the one-dimensional boundary constraint function of the i-th degree of freedom in the six-degree-of-freedom model of relative attitude error and relative orbit error, ρ 0i is ρ i (t) corresponds to the initial value of the boundary function, ρ ti =ρ i (t ps ) is ρ i (t) corresponds to the predefined steady-state error safety upper bound, ε ρi is ρ i (t) corresponds to a small positive constant, which is used to adjust the asymptotic boundary position, t ps is the expected error convergence time, and t is time.

6. A method for safe approaching control of non-cooperative target of space spin nutation according to claim 5, characterized in that: The constrained auxiliary variable θ i as follows: Among them, δ i ∈(0,1] is the constraint constant of the i-th degree of freedom that limits the attitude and orbit overshoot of the service spacecraft relative to the target spacecraft, q 6di (t) is the state variable q in the six-degree-of-freedom model of relative attitude error and relative orbit error 6d The element of the i-th degree of freedom.

7. A space spin nutation non-cooperative target safe approach control method according to claim 6, characterized in that: The auxiliary system model is as follows: Where, σ=[σ1,...,σ6] T ,A=[α1,...,α6] T ,B=diag(β1,...,β6) σ i is the i-th degree of freedom variable of the auxiliary system; 8. The method for safe approaching control of non-cooperative target of space spin nutation according to claim 1, characterized in that: The sliding mode variable ζ is: Among them, p1 is the power index related to the finite time convergence property, and its value range is between 0 and 1, sig NN (σ) and sign NN (σ) is the modulus normalized sign function about σ, Sign NN (σ) is in the power exponential form, and κ1 is a positive constant parameter.

9. A space spin nutation non-cooperative target safe approach control method according to claim 8, characterized in that: The non-singular auxiliary switching function is as follows: Where φ is the non-singular auxiliary switching function, ι is the auxiliary constant coefficient, is the non-zero threshold of ‖σ||, I6 is the unit matrix, κ1 is the positive constant gain of the first normalized sign function term with respect to ξ, and its value can be freely adjusted according to the control effect, and p1 is the positive power exponent of the first normalized sign function term with respect to ξ.

10. A space spin nutation non-cooperative target safe approach control method according to claim 1, characterized in that The safety approximation controller considering safety constraints for the non-cooperative target of spatial spin nutation is: Where κ2 is the positive constant gain of the second normalized sign function term with respect to ζ, and p2∈(0,1) is the positive power exponent of the second normalized sign function term with respect to ζ.

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