Space safety approaching control method for spin wobbling non-cooperative target

Abstract

The present application relates to a kind of space spin wobble non-cooperative target safety approach control method.The method includes the following steps: establishing the dynamics and kinematics model of double spacecraft relative attitude error and relative orbit error, and compacting relative attitude error and relative orbit error model into six degrees of freedom form;By defining the constraint function of service spacecraft safety and motion boundary, constraint auxiliary variable, construct spacecraft auxiliary system for rendezvous and docking and consider safety constraints;Design shortest trajectory sliding mode variable for spacecraft auxiliary system, the shortest trajectory sliding mode variable makes service spacecraft attitude and relative orbit from initial state to the desired attitude orbit required by task with the shortest path maneuver;Design nonsingular auxiliary switching function, avoid singular phenomenon when the derivative of shortest trajectory sliding mode variable is solved about time;Build safety approach controller for space spin wobble non-cooperative target considering safety constraints.

Description

Technical Field

[0001] This invention relates to a safe approach control method for non-cooperative spacecraft targets exhibiting spin and nutation in space, or space debris exhibiting spin and nutation. It is primarily applied to short-range safe rendezvous and approach missions of service spacecraft to these spin-nutation targets, achieving coupled short-range autonomous closed-loop control of the spacecraft's attitude and orbit. This invention belongs to the field of spacecraft control technology. Background Technology

[0002] Spacecraft development is costly and time-consuming. On-orbit benefits are directly and positively correlated with on-orbit service life and on-orbit health. For spacecraft already in orbit, malfunctions directly impact their service capabilities and economic efficiency. Therefore, on-orbit servicing operations and related technologies urgently need development to address on-orbit maintenance and repair objectives. In on-orbit servicing missions, rendezvous and docking with the target spacecraft is a crucial link and prerequisite for effective servicing. This includes: long-range and medium-range approach of the servicing spacecraft to the malfunctioning spacecraft; short-range rendezvous and approach of the servicing spacecraft to the malfunctioning spacecraft; autonomous control of the servicing spacecraft to achieve relative orbit (position) and attitude before docking; and successful docking to commence on-orbit servicing. Among these, the final short-range rendezvous and docking mission is one of the most complex, highly integrated, and demanding space missions in terms of control requirements and performance. Attitude and relative orbit control during the rendezvous and approach process requires high precision, high reliability, and strong describability, among other characteristics.

[0003] For target spacecraft with spin nutation, rendezvous should involve safety constraints on the range of motion, a well-defined tracking trajectory, and strong autonomous computational tracking capabilities. Current rendezvous and docking control methods, when employing more traditional approaches, often suffer from problems such as indescribable paths or trajectories during the control process, insufficient pre-docking safety constraints, and poor autonomous computation. While pre-designed paths and tracking control can initially address these issues, for high-precision autonomous control missions targeting spin nutation targets, we prefer rendezvous approximation control techniques with safety constraints and a degree of describability, where these safety constraints and short-distance trajectories can be autonomously calculated based on changes in the target spacecraft.

[0004] To address the precise control problem in rendezvous and docking, patent document CN109507892A discloses an adaptive sliding mode attitude stabilization control method for flexible spacecraft, improving the convergence speed and adaptability of the attitude system. Patent document CN111812981A discloses a finite-time stable spacecraft attitude tracking sliding mode control method, improving the temporal descriptiveness and robustness of attitude control. Patent document CN113697131A discloses an anti-retreat sliding mode attitude tracking control method and system for rigid spacecraft, solving the disturbance problem in attitude tracking. However, these methods have not improved the safety constraints and trajectory descriptiveness of the spacecraft system or attitude. To address the precise guidance and control of relative motion in rendezvous and docking, patent CN112000006A discloses a fast non-singular terminal sliding mode autonomous control method based on finite time, improving the convergence speed of rendezvous and docking. Patent CN109189091A discloses a multi-spacecraft cooperative control method based on integral sliding mode and model predictive control, simultaneously handling the relative motion problem of multiple spacecraft. However, these methods have not improved the safety constraints and trajectory description of spacecraft systems and relative motion, and are also less effective in solving the problem of safe tracking of the target spacecraft's spin nutation.

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

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

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

[0008] S1. 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. Dynamic and kinematic models of the relative attitude error and relative orbital error of the two spacecraft are established, and the relative attitude error and relative orbital error models are compacted into a six-degree-of-freedom form.

[0009] S2. By defining constraint functions and constraint auxiliary variables for the safety and motion boundaries of the service spacecraft, construct a spacecraft auxiliary system that takes into account safety constraints for rendezvous and docking.

[0010] S3. Design the shortest trajectory sliding mode variable for the spacecraft auxiliary system, wherein the shortest trajectory sliding mode variable enables the service spacecraft's attitude and relative orbit to maneuver from the initial state to the desired attitude and orbit required by the mission via the shortest path.

[0011] S4. Design a non-singular auxiliary switching function to avoid singular phenomena when taking the derivative of the shortest path sliding mode variable with respect to time;

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

[0013] Preferably, the dynamic and kinematic model of the relative attitude error between the two spacecraft is as follows:

[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 diagonal elements of 1, C a G a Q a Both are nonlinear matrices of the system, ω d To serve the desired angular velocity of the spacecraft relative to the target spacecraft, R e Let the error rotation matrix be defined as follows: q e0 ,q ev These are the fixed coordinate systems for the service spacecraft body. Rotate to the target spacecraft's fixed coordinate system The three-dimensional Euler axis on which it depends s and Euler angle θ s Corresponding function value: J s τ represents the 3×3 moment of inertia matrix of a spacecraft with positive definite values. a The torque input is used to serve the attitude control of spacecraft, and the unit is Newton-meter.

[0018] Preferably, the dynamics and kinematics model of the relative orbital error between the two spacecraft is as follows:

[0019]

[0020] in, τ pl =Q p τ p

[0021] , To account for the attitude-orbit coupling case of spacecraft guidance, R lI and R bI M represents the transformation matrix from the geocentric inertial coordinate system to the target spacecraft's LVLH coordinate system and from the inertial frame to the service spacecraft's intrinsic frame; p =diag(m s ,m s ,m s ), m s Indicates the quality of serviced spacecraft. Indicates the guidance input for service spacecraft, C p G is the coefficient matrix of the first-order terms. pl For residual function terms, For the desired relative position, q pe τ is the error between the current position and the desired relative position. p Force input for 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 orbital dynamics and kinematics model is as follows:

[0023]

[0024] 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 , τ6d =[τ a ,τ p ] T Q 6d =diag(Q a Q p ).

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

[0026]

[0027] Where, 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 ρi(t) is the initial value of the boundary function corresponding to ρi(t), ρ ti =ρ i (t ps ) is the predefined upper bound for the steady-state error safety of ρi(t), ε ρi For ρ i The positive definite small constant corresponding to (t) is used to adjust the position of the asymptotic boundary, t ps Let t be the expected error convergence time.

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

[0029]

[0030] Where, δ i ∈(0,1] is the constraint constant for the i-th degree of freedom that restricts the attitude and orbital overshoot of the service spacecraft relative to the target spacecraft, q 6di (t) represents 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 Let i be the variable with the i-th degree of freedom in the auxiliary system;

[0036]

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

[0038]

[0039] Where p1 is the power exponent related to the finite-time convergence property, and its value ranges from 0 to 1, sig NN (σ) and sign NN (σ) is the modulus-normalized sign function with respect to σ. for sign NN The power-law form of (σ), where κ1 is a positive definite 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, and ι is the auxiliary constant coefficient. Let ||σ|| be the non-zero threshold, I6 be the identity matrix, κ1 be the positive definite constant gain of the first normalized sign function term with respect to ξ (its value can be freely adjusted according to the control effect), and p1 be the positive power exponent of the first normalized sign function term with respect to ξ.

[0044] Preferably, the safety approximation controller considering safety constraints for non-cooperative targets with space spin nutation is:

[0045]

[0046] Where κ2 is the positive definite 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 advantages of this invention compared to the prior art are:

[0048] (1) This 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 coupled motion, and compacts it into a six-degree-of-freedom spacecraft attitude-orbit coupled model, which can facilitate the integrated tracking control of attitude and relative position of the target spacecraft.

[0049] (2) 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, this invention can realize the constraint and protection of the spacecraft's time-varying motion range safety range during rendezvous and docking with the target.

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

[0051] (4) This invention proposes a safety approximation controller based on the shortest trajectory sliding mode variable and non-singular auxiliary switching function for non-cooperative targets of spatial spin nutation, which takes into account safety constraints. It can achieve a trajectory approximation of a straight line, the system convergence time can be predetermined, and control objectives such as reducing energy consumption can be achieved.

[0052] (5) The control method of the present invention has the characteristics of attitude and relative trajectory safety constraints, strong descriptibility, high control accuracy, low energy consumption and strong robustness. It is suitable for attitude and orbit safety approximation descriptible path specified time control in spacecraft rendezvous and docking missions, and is also suitable for general spacecraft rendezvous and docking control missions. Attached Figure Description

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

[0054] Figure 2 This is a schematic diagram of the coordinate system used in this invention;

[0055] Figure 3 The simulation results of the attitude error motion trajectory using the control method (algorithm A) of this invention are presented, and a schematic comparison of the shortest trajectory and docking safety is made with the traditional algorithms (algorithms B and C). In the figure, the subscript of the variable represents the element of the corresponding vector. The same applies to the following figures. 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 (algorithm A) of this invention are presented, and a schematic comparison of the shortest trajectory and docking safety is made with the traditional algorithms (algorithms B and C). Compared with the traditional methods, the trajectory of this method is approximately a straight line and converges faster.

[0057] Figure 5The results of the partial convergence of the attitude error quaternion vector using the control method of this invention show that the attitude motion is always within the safety boundary range specified by the constraint function, which has the safety of attitude motion under rendezvous and docking, and the three-axis errors converge almost synchronously, with the steady-state error within the safety boundary range.

[0058] Figure 6 The attitude error quaternion vector partial convergence result is obtained by using the traditional contrast control algorithm B. Compared with the algorithm of this invention, algorithm B does not use a normalized sign function, but only a conventional sign function. It can be seen that the three-axis convergence is asynchronous. Therefore, the convergence trajectory curve is not the shortest straight line.

[0059] Figure 7 The attitude error quaternion vector partial convergence result is obtained by using the traditional contrast control algorithm C. Compared with the algorithm of this invention, algorithm C only uses conventional constraint functions and does not use normalization functions. It can be seen that the three-axis convergence is asynchronous. Therefore, the convergence curve does not approximate the shortest straight line.

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

[0061] Figure 9 To assess the convergence result of the relative position tracking error using the traditional contrast control algorithm B, compared to the algorithm of this invention, the three-axis convergence of algorithm B is asynchronous, therefore, the convergence curve does not approximate the shortest straight line;

[0062] Figure 10 To assess the convergence result of the relative position tracking error using the traditional contrast control algorithm C, compared to the algorithm of this invention, algorithm C does not use a normalization function, and the three-axis convergence is asynchronous. Therefore, the convergence curve does not approximate the shortest straight line.

[0063] Figure 11 Simulation results of the control input for attitude tracking control using the control method of this invention;

[0064] Figure 12 The simulation results show the control input for relative position tracking control using the control method of this invention.

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

[0066] Figure 14 The spacecraft relative position tracking error index is defined as follows:

[0067] Figure 15 The energy consumption results of attitude tracking control using the control method of this invention are shown, and compared with traditional comparison algorithms (the solid line represents the energy consumption of the method of this invention), where energy consumption is defined as...

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

[0069] Figure 17 The attitude perturbation parameter is set much larger than the actual space environment in the simulation to verify the robustness of the algorithm of this invention.

[0070] Figure 18 The relative orbital perturbation parameter is set much larger than the actual space environment in the simulation to verify the robustness of the algorithm of this invention. Detailed Implementation

[0071] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are merely illustrative and are not intended to limit the present invention.

[0072] This invention provides a safe approach control method for a space-spin-nutating non-cooperative target. First, the research scenario of this invention is defined as a rendezvous and approach scenario during an on-orbit servicing mission of a spacecraft. In this scenario, the target spacecraft exhibits spin and nutation characteristics. The research object is the rendezvous and approach behavior of the on-orbit servicing spacecraft towards the spin-nutating target spacecraft, and the research problem is the relative attitude and relative orbit (position) tracking control of the servicing spacecraft towards the target spacecraft. In detail: 1) Spin-nutation non-cooperative target: This refers to a target spacecraft that spins at a certain angular velocity along one or more axes, accompanied by nutation. The target spacecraft is non-cooperative, meaning the service spacecraft's motion information about the target spacecraft comes from relative measurements. This invention considers control, therefore assuming the target spacecraft's motion information can be obtained through relevant measurement units on the spacecraft; 2) Tracking-control target: This refers to the state before docking, where the mechanical coordinate systems of the service spacecraft and the target spacecraft are relatively stationary, and their relative orbital positions converge. That is, the two coordinate systems are aligned with a desired fixed attitude and position. 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, only a fixed offset needs to be added; 3) Safe approach: This refers to the service spacecraft approaching the target spacecraft while it is rotating. The spacecraft must not touch the target spacecraft body or deployment components, ensuring no collision between the two spacecraft. In this invention, the target is constrained by a constraint function, which changes in real time with the target spacecraft's position and motion. Therefore, satisfying the constraint conditions means the serving spacecraft is always within the collision avoidance safety zone for the non-cooperative, unstable target spacecraft. 4) Control method: Based on the safety constraints, this invention uses a normalized function to optimize the rendezvous trajectory, making the rendezvous trajectory approximately a straight line in the relative coordinate system and a spiral approach in the orbital coordinate system. The system convergence time can be pre-defined, meaning the serving spacecraft, under time-varying safety constraints, will approach the docking position within a finite and predetermined time using an approximately straight path in three-dimensional vector space, with a reasonable docking attitude. The algorithm flow is as follows: Figure 1 As shown, it includes the following steps:

[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 dynamic and kinematic models of the relative attitude error and relative orbital error of the two spacecraft, and compact the relative attitude error and relative orbital error models into a six-degree-of-freedom form;

[0074] To establish a fixed coordinate system for the two spacecraft during rendezvous and docking, a geocentric inertial coordinate system and a target spacecraft LVLH relative orbital coordinate system are established. A relative attitude dynamics and kinematic model of the two spacecraft with the fixed coordinate system and the geocentric inertial coordinate system as reference frames is established. A relative orbital dynamics and kinematic model of the two spacecraft (service spacecraft relative to target spacecraft) with the fixed coordinate system, the target spacecraft LVLH (local vertical / local horizontal) coordinate system and the geocentric inertial coordinate system as reference frames is established.

[0075] The reference coordinate system is defined as the geocentric inertial coordinate system. (The Earth-Centered Inertial Frame, ECI), the origin of which is located at the Earth's center, x I The axis points to the Earth's vernal equinox γ,z I The axis points 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's fixed coordinate system, The coordinate system is a fixed coordinate system for the target spacecraft body, with the origin of the coordinate system fixed at the center of mass of the corresponding spacecraft, and the coordinate axes are the principal inertia axes of the corresponding spacecraft. Let x be the target spacecraft's LVLH coordinate system (local vertical / local horizontal coordinate system), with its origin located at the target spacecraft's center of mass. l The axis points radially to the orbit (from the Earth's center to the target spacecraft's center of mass), z l The axis points in the direction of the orbital angular momentum, y l axis and x l axis and z l The axes form a right-handed coordinate system. The relative positions between spacecraft are defined by the vector q. p The coordinate system above is defined as follows: Figure 2 As shown.

[0076] In this 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 body spacecraft with its body coordinate system fixed to the center of mass, the kinematics is obtained by serving the spacecraft's body fixed coordinate system. Relative to the geocentric inertial coordinate system The rotation is used to describe the attitude motion of a service spacecraft in an inertial frame. According to Euler's rotation theorem, in three-dimensional Euclidean space, the rotation of an object can be described by a three-dimensional unit direction vector e passing through a fixed axis (an arbitrary Euler rotation axis) at a fixed point (the spacecraft's center of mass) and an arbitrary rotation angle (Euler angle) θ. For the application of this invention, this means a geocentric inertial coordinate system. By rotating the spacecraft along a three-dimensional unit direction vector e in space by an arbitrary rotation angle (Euler angle) θ, we obtain the fixed coordinate system of the service spacecraft. This rotation process can be further described using unit quaternions. Considering the fixed point as the origin of the service spacecraft's intrinsic coordinate system, the service spacecraft's intrinsic coordinate system is defined relative to the geocentric inertial coordinate system. The rotation-related unit quaternion is in Where q v It is a three-dimensional vector, and satisfies The service spacecraft is represented in the geocentric inertial coordinate system. The posture motion in the image can be described by a unit quaternion. In the equation and subsequent statements, for any vector x, the sign and Let be the first and second derivatives of vector x with respect to time, respectively, denoted by (·). × Let ω be a 3×3 skew-symmetric matrix corresponding to the three-dimensional vector. a Represents the fixed coordinate system of the spacecraft body. Relative to the inertial coordinate system The expression in the fixed coordinate system of the service spacecraft body The attitude angular velocity of the spacecraft.

[0078] The relative attitude motion of the servicing spacecraft and the target spacecraft can be determined by the fixed coordinate system of the servicing spacecraft, which is defined in the same way as the servicing spacecraft in the central inertial coordinate system. Fixed coordinate system with the target spacecraft body Relative rotation is represented by [the property]. Definition To serve as the quaternion for the error in the desired attitude of the spacecraft relative to the target spacecraft, q e0 ,q ev =[q ev1 ,q ev2 ,q ev3 ] T To serve the spacecraft's fixed coordinate system Rotate to the target spacecraft's fixed coordinate system The three-dimensional Euler axis on which it depends s and Euler angle θ s Corresponding function value And the unit error quaternion satisfies the constraints.

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

[0080]

[0081] Among them, J s τ represents the 3×3 moment of inertia matrix of a spacecraft with positive definite values. a Represents the input torque for spacecraft attitude control, measured in N·m, ω a As defined above, it represents the fixed coordinate system of the service spacecraft. Relative to inertial frame The expression in the fixed coordinate system of the service spacecraft body The attitude angular velocity of the spacecraft.

[0082] Considering that the generalized Eulerian-Lagrange system form facilitates controller design and also makes it easier to transfer the control algorithm of this invention to relative orbit controller design and robot control design with the same Eulerian-Lagrange model form, this invention transforms the aforementioned spacecraft attitude kinematics and dynamics into a generalized Eulerian-Lagrange system, providing a generalized control algorithm conforming to the generalized model form. This is based on the assumption that the unit error quaternion satisfies the constraints. Therefore, the system only needs to consider the three-dimensional vector part q of the error quaternion. ev That's it. The general Euclidean-Lagrangian model of the dynamics and kinematics of the relative attitude error between the two spacecraft is then:

[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 is... a G a Q a The nonlinear matrix of the system is defined as shown in the above equation, ω d To serve the desired angular velocity of the spacecraft relative to the target spacecraft, R e Let the error rotation matrix be defined as follows: The control task of this invention is to design a controller τ such that the relative attitude error between the service spacecraft and the target spacecraft converges to zero, and the attitude trajectory formed by the transient process of convergence is a straight line in the three-dimensional vector space, i.e., the shortest path. The convergence of the relative attitude error to zero also means that regardless of the target spacecraft's attitude angular velocity and nutation angle, the coordinate system of the service spacecraft remains constant. Through control, they can all be rotated to the coordinate system of the target spacecraft. Overlap means achieving tracking and control of the target spacecraft's arbitrary attitude and motion by the service spacecraft.

[0087] The dynamic and kinematic model of the relative orbits of the two spacecraft is as follows:

[0088]

[0089] Where, q p =[q px q py q pz ] T The v vector represents the position vector of the service spacecraft relative to the target spacecraft, where v is the center of mass of the target spacecraft in the LVLH coordinate system, with the origin being the center of mass of the target spacecraft when the spacecraft is simplified to a point mass model. p =[v px v py v pz ] T Let M represent the velocity vector of the service spacecraft relative to the target spacecraft, and let M represent the velocity vector of the service spacecraft relative to the target spacecraft in the LVLH coordinate system. p =diag(m s ,m s ,m s ), m s Indicates the quality of serviced spacecraft. Indicates the guidance input for service spacecraft, C p The coefficient matrix of the first term and G pl The residual function term is defined as follows:

[0090]

[0091]

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

[0093] definition Given the desired relative positions, the dynamics and kinematics model of the relative orbital error between the two spacecraft can be obtained as follows:

[0094]

[0095] in, τ pl =Q p τ p , To account for the attitude-orbit coupling case of spacecraft guidance, R lI and R bI This represents the transformation matrix from the geocentric inertial coordinate system to the target spacecraft's LVLH coordinate system and from the inertial frame to the service spacecraft's body coordinate system.

[0096] To achieve six-degree-of-freedom coupled control of the servicing spacecraft, the above model is written in a compact six-degree-of-freedom form as follows:

[0097]

[0098] 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 ). τ a The torque input for spacecraft attitude control is expressed in Newton-meters (N·m), τ. p The unit for force input to serve spacecraft position control is Newton (N).

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

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

[0101]

[0102] Where, 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 It is ρ i The initial value of the boundary function corresponding to (t), ρ ti =ρ i (t ps ) is ρ i The predefined upper bound for steady-state error safety corresponding to (t), ε ρi For ρ i The positive definite small constant corresponding to (t) is used to adjust the position of the asymptotic boundary, t ps Let t be the expected error convergence 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, where subscripts i = 1, ..., 6 represent the i-th degree of freedom in the six-degree-of-freedom model of relative attitude error and relative orbit error. The constraint auxiliary variables are defined as follows:

[0104]

[0105] Where, δ i ∈(0,1] is a constraint constant for the i-th degree of freedom that restricts the attitude and orbital overshoot of the service spacecraft relative to the target spacecraft. It can be set according to mission requirements. When δ i When the value is close to 0, the system has almost no overshoot, q 6di (t) represents 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 Let i be the variable with the i-th degree of freedom in the auxiliary system;

[0107] ,but

[0108]

[0109] For σ i Taking the derivative with respect to time, we get:

[0110]

[0111] in,

[0112]

[0113]

[0114] Rewriting the above equation in a compact form, we obtain the following auxiliary system that satisfies the boundary constraints for spacecraft attitude and orbit tracking errors:

[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 to the target spacecraft. Therefore, the constraint relationship of the constraint function itself on the motion state of the target spacecraft remains unchanged. When the motion state of the target spacecraft changes, the constraint region for safe motion in the inertial frame changes accordingly. The service spacecraft is always constrained within the time-varying safe region, thus achieving safety constraint guarantee for the entire process of close rendezvous and docking.

[0118] Step S3: Design the shortest trajectory sliding mode variable for the spacecraft auxiliary system, which enables the service spacecraft's attitude and relative orbit to maneuver from the initial state to the desired attitude and orbit required by the mission via the shortest path;

[0119] For spacecraft auxiliary systems considering safety constraints during rendezvous and docking, an approximate shortest path sliding mode variable is designed. This sliding mode variable enables the servicing spacecraft to converge its tracking error to the target spacecraft along a better, approximately straight path. The general form of the sliding mode variable is as follows:

[0120]

[0121] Where ξ represents the general sliding mode variable, κ j Let be the positive definite constant gain of the j-th normalized sign function term with respect to ξ. The gain is a positive definite constant of the first-order term of the general sliding mode variable, which can be any positive definite constant, where m is the number of sliding mode function terms, n≥1, and p j p is the positive power exponent of the j-th term with respect to the normalized sign function. j The value range is usually from 0 to 1, sig NN (ξ) is the normalized sign function with respect to the modulus of ξ. The positive power exponent of the normalized sign function is related to the finite-time convergence property.

[0122] Based on the sliding mode variable design described above, and combining 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 = [σ1,...,σ6] of the safety boundary constraint auxiliary system in step 2. T Let the number of sliding mode function terms m be 1. The sliding mode variable ζ is designed as follows for the constraint model of the spacecraft's attitude and orbit during rendezvous and docking.

[0123]

[0124] Where κ1 is the positive definite 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; p1 is the positive power exponent of the first normalized sign function term with respect to ξ, and its value ranges from 0 to 1; sig NN (σ) and sign NN (σ) is the modulus-normalized sign function with respect to σ. for sign NN The power form of (σ) is defined as follows:

[0125]

[0126] In this invention, the convergence curve of variable σ from the initial error point to the origin is approximately a straight line. Physically, this means that when the attitude of the service spacecraft and the relative orbit of the target spacecraft maneuver from their initial state to their desired attitude orbit relative to the target spacecraft via a shorter path, and when there is significant uncertainty, the range of motion remains within the safety boundary.

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

[0128]

[0129] in,

[0130]

[0131] Step S4: Design a non-singular auxiliary switching function to avoid singular phenomena when calculating the derivative of the shortest path sliding mode variable with respect to time;

[0132] Considering the sliding surface design in step 3, when taking the derivative of the sliding variable with respect to time, the following will occur: and The function term exhibits a singularity problem. To overcome this problem, a non-singular auxiliary switching function is designed as follows:

[0133]

[0134] Where ι is the auxiliary constant coefficient, The threshold for ||σ|| is a non-zero value, which is a small positive constant used to prevent system singularities, and is usually 0.001.

[0135] Step S5: Based on the six-degree-of-freedom relative attitude error and relative orbit error model, spacecraft auxiliary system, shortest path sliding mode variable, and non-singular auxiliary switching function, construct a safety approach controller considering safety constraints for space spin nutation non-cooperative targets. Apply the established safety approach controller to attitude tracking and relative orbit control during spacecraft rendezvous and approach, and achieve the mission objective of convergence of the attitude and relative orbit of spacecraft during rendezvous and docking within the safety constraints along the shortest path in a finite and specified time.

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

[0137]

[0138] Where κ2 is the positive definite constant gain of the second normalized sign function term with respect to ζ, and its value range can be designed 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 above five steps have a progressive logical relationship, as explained below: Step S1 provides the spacecraft system model and related parameter definitions required for the control system design and subsequent steps. Based on Step 1, model-based controller and closed-loop system design are performed. Considering the spin and nutation motion characteristics of the target spacecraft, in order to make rendezvous and docking safer, this invention originally proposes a time-varying motion constraint function and auxiliary system in Step S2. Through this method, motion constraints can be applied to each dimension of attitude and orbit characteristics based on the real-time motion state of the target spacecraft, including constraints on system convergence time, overshoot, and steady-state error. Through this constraint, the motion of the service spacecraft relative to the target spacecraft can be achieved within the safe constraint range. Even if the target spacecraft has complex attitude or orbital motion, safety constraints and safe rendezvous approximation can still be achieved through real-time calculation of the relative coordinate system. To make the trajectory of the closed-loop system more describable, Step S3 proposes a design method for the approximate shortest path sliding surface in the relative coordinate system. For different application scenarios, different vectors, constant gains, power exponents, and the number of sub-sliding surfaces can be defined to construct different sliding surfaces. To address the time-varying attitude-orbit coupled tracking control problem of spacecraft, step S3 designs a sliding mode surface for spacecraft attitude control based on the spacecraft's state vector. Considering the singularity problem in the derivative of the sliding mode surface designed in step S3, step S4 designs a non-singular control auxiliary switching function to avoid singularities, which will be applied to the controller. Based on the designs in steps S1 to S4, step S5 proposes a space spin-nutation non-cooperative target safety approximation controller. Substituting this controller into the system of step 1 yields the closed-loop system. This controller can be directly applied to spacecraft attitude and relative orbit control or spacecraft relative attitude and orbit control during rendezvous and approximation, achieving multiple control objectives such as time-varying safety constraint guarantees, describable approximately linear trajectories, and definable convergence times. This completes the design of the entire control system of this invention.

[0140] The method in this invention can be demonstrated in the following ways.

[0141] The Lyapunov functions V1 and V2 with respect to ζ are selected as follows:

[0142]

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

[0144]

[0145] According to the finite-time stability theory, the attitude tracking system of two spacecraft can achieve stability within a finite time T. mThe spacecraft converges to the origin within ≤T1+T2, meaning it serves the spacecraft's attitude within a finite time T. m It converges inward 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 safe approach control mission, under the control method proposed in this invention, can achieve integrated attitude and orbit rendezvous and approach tracking control with safe motion constraints on time-varying spin nutation target spacecraft, autonomous constraint calculation, describable tracking trajectory, finite time and specified time convergence, and high precision and strong robustness.

[0147] The innovations and advantages of this invention compared to existing technologies are as follows:

[0148] (1) Compared with traditional rendezvous control methods, this method can be effectively applied to rendezvous, approach and tracking control tasks of non-cooperative target spacecraft with spin nutation characteristics.

[0149] (2) Compared with the traditional rendezvous control method, this method uses a multidimensional time-varying constraint function to realize the time-varying description of the safe rendezvous 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 used to achieve safe rendezvous and approximation of the spin nutation target spacecraft, and the service spacecraft always moves within the time-varying region described by the motion characteristics and constraint conditions of the target spacecraft, thus avoiding collisions between the two spacecraft during the rendezvous and approximation process.

[0151] (4) Based on the shortest trajectory sliding surface, the relatively shortest trajectory control can be achieved within the safe motion constraint range. That is, within the tracking error coordinate system, the tracking trajectory is approximately a straight line, which has strong trajectory describability, good convergence characteristics, good control performance and less energy consumption.

[0152] (5) Due to the existence of constraint functions and the finite-time convergence characteristics 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 within a specified time, so that designers can formulate flight procedures and rendezvous and approximation plans within a specified time according to specific tasks.

[0153] Based on the above implementation method, a simulation result of a space spin nutation non-cooperative target safe approximation control method can be obtained, as shown below. Figure 3-18As shown. During the simulation, 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 Algorithm B and Algorithm C. Compared with the algorithm of the present invention, Algorithm B did not use a normalized sign function, but only a conventional sign function, while Algorithm C only used a conventional constraint function and did not use a normalized function. Figure 3 The simulation results of the attitude error motion trajectory using the control method (algorithm A) of this invention are presented, and a schematic comparison of the shortest trajectory and docking safety with traditional algorithms (algorithms B and C) is made. As can be seen from the figure, compared with the traditional method, this method has a shorter maneuver 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 (algorithm A) of this invention are presented, and a schematic comparison of the shortest trajectory and docking safety is made with the traditional algorithms (algorithms B and C). Compared with the traditional methods, this method has a shorter maneuver path and more precise control effect in the relative coordinate system trajectory (relative position trajectory direction). Using this method, the trajectory is approximately a straight line and converges faster. Figure 5 The results of the attitude error quaternion vector partial convergence using the control method of this invention show that the attitude motion is always within the safety boundary range specified by the constraint function, which has the safety of attitude motion under rendezvous and docking. Moreover, the convergence time is less than the predefined convergence time, which verifies the convergence of finite and specified time. The three-axis errors converge almost synchronously, and the steady-state error is within the safety boundary range. Figure 6 The attitude error quaternion vector partial convergence result is obtained by using the traditional contrast control algorithm B. Compared with the algorithm of this invention, algorithm B does not use a normalized sign function, but only a conventional sign function. It can be seen that the three-axis convergence is asynchronous. Therefore, the convergence trajectory curve is not the shortest straight line, which is not the optimal case. Figure 7 The attitude error quaternion vector partial convergence result is obtained by using the traditional contrast control algorithm C. Compared with the algorithm of this invention, algorithm C only uses conventional constraint functions and does not use normalization functions. It can be seen that the three-axis convergence is asynchronous. Therefore, the convergence curve does not approximate the shortest straight line. Figure 8 The convergence result of the relative position tracking error using the control method of this invention shows that the relative position motion is always within the safety boundary range specified by the constraint function, which has the safety of the relative position motion under rendezvous and docking. Moreover, the convergence time is less than the predefined convergence time, which verifies the convergence of finite and specified time. The three-axis errors converge almost synchronously, and the steady-state error is within the safety boundary range. Figure 9 To assess the convergence result of the relative position tracking error using the traditional contrast control algorithm B, compared to the algorithm of this invention, the three-axis convergence of algorithm B is asynchronous, therefore, the convergence curve does not approximate the shortest straight line; Figure 10To assess the convergence result of the relative position tracking error using the traditional contrast control algorithm C, compared to the algorithm of this invention, algorithm C does not use a normalization function, and the three-axis convergence is asynchronous. Therefore, the convergence curve does not approximate the shortest straight line. Figure 11 The simulation results of the control input for attitude tracking control using the control method of the present invention verify the usability of the method of the present invention; Figure 12 Simulation results of the control input for relative position tracking control using the control method of this invention were used to verify the applicability of the method. During the simulation, relatively extreme simulation conditions were selected. Figure 11 and Figure 12 The control input is relatively large. In practical applications, the conditions such as desired attitude and relative position settings, convergence speed, and convergence time will be greatly relaxed, and the obtained control input will be adapted 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 The spacecraft attitude tracking error index is defined as I. a =||q ev ||+||ω e ||,I a Let ω be the spacecraft attitude tracking error. e To address the attitude and angular velocity tracking errors of spacecraft, it can be seen that the errors can converge under all three algorithms, and the relevant parameter adjustments make the transient and steady-state performance similar. Therefore, characteristic performances such as linear convergence and low energy consumption can be compared based on similar performance. Figure 14 The spacecraft relative position tracking error index is defined as follows: I p The spacecraft relative position tracking error index provides a benchmark for comparison. That is, if the transient and steady-state performances are similar under the three algorithms, then characteristic performances such as linear convergence characteristics and low energy consumption characteristics can be compared. Figure 15 The energy consumption results of attitude tracking control using the control method of this invention are shown, and compared with traditional comparison algorithms (the solid line represents the energy consumption of the method of this invention), where energy consumption is defined as... It is evident that the algorithm of this invention consumes less energy; τ 6di (t) represents τ at time t. 6d The value of the i-th degree of freedom, Figure 16 The energy consumption results of relative position tracking control using the control method of this invention are shown, and compared with traditional comparison algorithms (the solid line represents the energy consumption of the method of this invention), where energy consumption is defined as... It is evident that by employing the algorithm of this invention, in the case of relative position control, more stringent rendezvous and docking conditions, such as approximate straight lines, can be obtained by consuming similar energy; Figure 17 and Figure 18The parameters for attitude and relative orbital perturbations are set much larger than those in the actual space environment during simulation, verifying the strong robustness of the algorithm of this invention. The algorithm can cope with complex environmental disturbances. Using the attitude-orbit coupled integrated control method of this invention, and integrating the convergence simulation results of attitude and relative position (orbit) tracking errors, the effectiveness, safety constraints, trajectory descriptibility, and specified-time convergence of the algorithm for the attitude-orbit coupled six-degree-of-freedom control of a servicing spacecraft targeting a spin nutation target are verified.

[0154] The simulation results above fully demonstrate that, under the control method proposed in this invention, the space spin nutation non-cooperative target safe approach control task can achieve integrated attitude and orbit rendezvous and approximation control with safe motion constraints, autonomous constraint calculation, describable trajectory, finite time and specified time convergence, and high precision and strong robustness for time-varying spin nutation target spacecraft.

[0155] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations 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 protection scope of the technical solutions of the present invention.

Claims

1. A method for safe approximation control of a space spin-nutation non-cooperative target, characterized in that... Includes the following steps: S1. 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. Dynamic and kinematic models of the relative attitude error and relative orbital error of the two spacecraft are established, and the relative attitude error and relative orbital error models are compacted into a six-degree-of-freedom form. S2. By defining constraint functions and constraint auxiliary variables for the safety and motion boundaries of the service spacecraft, construct a spacecraft auxiliary system that takes into account safety constraints for rendezvous and docking. S3. Design the shortest trajectory sliding mode variable for the spacecraft auxiliary system, wherein the shortest trajectory sliding mode variable enables the service spacecraft's attitude and relative orbit to maneuver from the initial state to the desired attitude and orbit required by the mission via the shortest path. S4. Design a non-singular auxiliary switching function to avoid singular phenomena when taking the derivative of the shortest path sliding mode variable with respect to time; S5. Based on the six-degree-of-freedom relative attitude error and relative orbit error model, spacecraft auxiliary system, shortest path sliding mode variable, and non-singular auxiliary switching function, a safe approach controller considering safety constraints is constructed for space spin nutation non-cooperative targets. The established safe approach controller is applied to attitude tracking and relative orbit control during spacecraft rendezvous and approach, so as to achieve the mission objective of the spacecraft rendezvous and docking attitude and relative orbit converging along the shortest path within a finite and specified time within the safety constraints. The dynamic and kinematic model of the relative attitude error between the two spacecraft is as follows: in, Among them, intermediate variables The system's nonlinear matrix, intermediate variables intermediate variables , For diagonal elements that are 1 identity matrix , , All are nonlinear matrices of the system. To serve the desired angular velocity of the spacecraft relative to the target spacecraft, Let the error rotation matrix be defined as follows: , These are the fixed coordinate systems for the service spacecraft body. Rotate to the target spacecraft's fixed coordinate system The three-dimensional Euler axis on which it depends Euler angles Corresponding function value: , , Spacecraft representing positive constant values Matrix of inertia The torque input is used to serve the attitude control of spacecraft, and the unit is Newton-meter (N·m). The sliding mode variable for: in, The power exponent is related to the finite-time convergence property, and its value ranges from 0 to 1. and For about The modulus normalization sign function, for The power form, These are positive definite constant parameters; The non-singular auxiliary switching function is as follows: in, It is a non-singular auxiliary switching function. For auxiliary constant coefficients, for Non-zero threshold, It is the identity matrix. For about The The positive definite constant gain of the normalized sign function term can be freely adjusted according to the control effect. For about The The positive power exponent of a normalized sign function term.

2. The method for safe approximation control of a space spin-nutation non-cooperative target according to claim 1, characterized in that, The dynamics and kinematics model of the relative orbital error between the two spacecraft is as follows: in, , , To account for the attitude-orbit coupling situation in spacecraft guidance, the transformation matrix is... and This represents the transformation matrix from the geocentric inertial coordinate system to the target spacecraft's LVLH coordinate system and from the inertial frame to the service spacecraft's intrinsic frame; , Indicates the quality of serviced spacecraft. Indicates the guidance input for the service spacecraft. The coefficient matrix of the first-order terms. For residual function terms, For the desired relative position, This represents the error between the current position and the desired relative position. Force input for spacecraft position control, unit: Newton.

3. The method for safe approximation control of a space spin-nutation non-cooperative target according to claim 2, characterized in that, The six-degree-of-freedom compact form of the dynamics and kinematics model of the relative attitude error of the two spacecraft and the dynamics and kinematics model of the relative orbit is as follows: in, , , , , , .

4. The method for safe approximation control of a space spin-nutation non-cooperative target according to claim 3, characterized in that, The constraint function is defined as follows: in, In the six-degree-of-freedom model of relative attitude error and relative orbital error, the first... One-dimensional boundary constraint function for degrees of freedom yes The corresponding initial values ​​of the boundary functions, yes The corresponding predefined upper bound for steady-state error safety, for The corresponding positive definite small constant is used to adjust the position of the asymptotic boundary. Let the expected error convergence time be... For time.

5. The method for safe approximation control of a space spin-nutation non-cooperative target according to claim 4, characterized in that, The constraint auxiliary variable as follows: in, To limit the attitude and orbital overshoot of the service spacecraft relative to the target spacecraft. Constraint constants for each degree of freedom State variables in a six-degree-of-freedom model of relative attitude error and relative orbit error No. An element with one degree of freedom.

6. The method for safe approximation control of a space spin-nutation non-cooperative target according to claim 5, characterized in that, The auxiliary system model is as follows: in, , , ， For auxiliary system One degree of freedom variable; 。 7. A method for safe approximation control of a space spin-nutation non-cooperative target according to claim 6, characterized in that... The safety approximation controller considering safety constraints for non-cooperative targets with space spin nutation is as follows: in, For about The positive definite constant gain of the second normalized sign function term, For about The positive power exponent of the second normalized sign function term.

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