A method and system for controlling the shortest path of attitude in spacecraft rendezvous and docking

Abstract

A method and system for controlling the shortest path of attitude in spacecraft rendezvous and docking, including: establishing a quaternion dynamics and kinematics model of the attitude of dual spacecrafts in rendezvous and docking with the system and the geocentric inertial coordinate system as reference systems; designing a shortest path sliding surface; designing an approximate shortest path sliding surface for the attitude model of the spacecraft in rendezvous and docking; designing a non-singular control auxiliary switching function; designing a shortest path controller for attitude in spacecraft rendezvous and docking; and the attitude of the spacecraft during rendezvous and docking converges along the shortest path within a finite time. The control method of the present invention has the characteristics of strong descriptiveness of attitude trajectory, high control accuracy, low energy consumption, strong robustness, etc., and is suitable for attitude shortest path control in spacecraft rendezvous and docking missions, and is also suitable for general spacecraft attitude control missions.

Description

Technical Field

[0001] The present invention relates to the field of spacecraft control technology, and in particular to a method and system for controlling the shortest path attitude of a spacecraft during rendezvous and docking. The method and system are mainly used for attitude control during the process of spacecraft rendezvous and docking, and attitude control during on-orbit operation of a spacecraft, and can also be used for attitude control of general spacecraft. Technical Background

[0002] The spacecraft rendezvous and docking mission is one of the most complex space missions in the current space missions, with the highest system integration, control mission requirements and control performance requirements. The attitude control for the rendezvous and docking process needs to have high precision, high reliability, strong describability and other characteristics. The current rendezvous and docking attitude control problem, when using more traditional control methods, is often accompanied by indescribable paths or trajectories in the control process. Although this problem can be initially solved through prefabricated paths and tracking control, for high-precision control tasks, we hope to describe the control trajectory in spacecraft rendezvous and docking theoretically.

[0003] In order to solve the problem of precise control of 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 spacecraft attitude tracking sliding mode control method, which improves the time description and robustness of attitude control. Patent document CN113697131A discloses an anti-unwinding sliding mode attitude tracking control method and system for rigid spacecraft, which solves the perturbation problem in attitude tracking. However, these methods have not been able to improve the trajectory description of the spacecraft system or attitude, nor have they been able to theoretically prove the linearity or shortest nature of the trajectory.

[0004] Combined with the mission requirements and the above analysis, the attitude shortest path control method has become one of the key directions in the current spacecraft rendezvous and docking mission. Research on the attitude shortest path control method in spacecraft rendezvous and docking has important theoretical research and engineering exploration significance for the fields of spacecraft rendezvous and docking, on-orbit service and manipulation, and attitude control. Summary of the invention

[0005] The technical problem solved by the present invention is: in order to solve the problem of relative attitude tracking control between a service spacecraft and a target spacecraft during rendezvous and docking, the present invention proposes a method and system for attitude shortest path control in spacecraft rendezvous and docking.

[0006] The technical solution of the present invention is:

[0007] A method for controlling the shortest path of attitude in spacecraft rendezvous and docking includes: Step 1: Based on the attitude tracking error q of the service spacecraft relative to the target spacecraft ev Establish the quaternion dynamics and kinematics model of the dual spacecraft attitude; Step 2: According to the attitude tracking error q of the service spacecraft relative to the target spacecraft ev Design the shortest track sliding surface to achieve the finite time tracking control of the shortest track of the spacecraft; Step 3: Based on the sliding surface, according to the attitude tracking error q of the service spacecraft relative to the target spacecraft ev , design the shortest track sliding mode variable s for the rendezvous and docking spacecraft; Step 4: Based on the attitude tracking error q of the service spacecraft relative to the target spacecraft ev , design a non-singular control auxiliary switching function φ to eliminate the singularity of the shortest track sliding mode variable s; Step 5: Based on the dual spacecraft attitude quaternion dynamics and kinematics model, the attitude tracking error q of the service spacecraft relative to the target spacecraft ev , the shortest-track sliding mode variable s, and the non-singular control auxiliary switching function φ are used to design the attitude shortest path controller τ in the rendezvous and docking of the service spacecraft and the target spacecraft, so that the attitude tracking error of the service spacecraft to the target spacecraft can converge within a finite time and the attitude tracking trajectory is the shortest.

[0008] Furthermore, the dual-spacecraft attitude quaternion dynamics and kinematics model described in step 1 is: Its general Euler Lagrangian form is:

[0009]

[0010]

[0011]

[0012]

[0013] 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 variable I3 is a 3×3 identity matrix with diagonal elements of 1, and the intermediate parameter C a , G a , Q a is the nonlinear matrix 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, q ev It is the attitude tracking error of the serving spacecraft relative to the target spacecraft.

[0014] Furthermore, the shortest sliding surface in step 2 is:

[0015]

[0016] Among them, ξ represents an arbitrary vector, α i and β are positive constant gains, is an arbitrary positive constant, n is the number of sub-sliding surfaces, p i is a positive power exponent, p i The value range is 0 to 1, sig NN (ξ) is the modulus normalized sign function about ξ, and the variable ξ is taken as the attitude tracking error q of the service spacecraft relative to the target spacecraft. ev .

[0017] Furthermore, the shortest-trace sliding mode variable s in step 3 includes:

[0018] The number of sub-sliding surfaces n is set to 1, Among them, κ1, κ3 are positive constant gains, p1 is the power index related to the finite time convergence property, and its value range is between 0 and 1, sign NN (q ev ) is about q ev The modulus normalization sign function of is defined as follows:

[0019]

[0020]

[0021] Furthermore, the non-singular control auxiliary switching function φ in step 4 is specifically:

[0022]

[0023] Among them, ι and It is an auxiliary coefficient, and its value is a normal number to prevent system singularity, usually 0.001.

[0024] Furthermore, the attitude shortest path controller τ in the rendezvous and docking between the service spacecraft and the target spacecraft in step 5 is:

[0025]

[0026] Among them, κ2 and κ4 are positive definite constant gains, and p2∈(0,1) is a positive definite constant power exponent.

[0027] A shortest path control system for attitude in spacecraft rendezvous and docking, comprising: a motion model building module, a sliding surface building module, a sliding variable determination module, an auxiliary switching module, and a controller building module; wherein the motion model building module: based on the attitude tracking error q of the service spacecraft relative to the target spacecraft ev Establish the quaternion dynamics and kinematics model of the dual spacecraft attitude; Sliding surface construction module: According to the attitude tracking error q of the service spacecraft relative to the target spacecraft ev Design the shortest track sliding surface to realize the finite time tracking control of the shortest track of the spacecraft; Sliding mode variable determination module: Based on the sliding surface, according to the attitude tracking error q of the service spacecraft relative to the target spacecraft ev , design the shortest track sliding mode variable s for the rendezvous and docking spacecraft; auxiliary switching module: according to the attitude tracking error q of the service spacecraft relative to the target spacecraft ev , design a non-singular control auxiliary switching function φ to eliminate the singularity of the shortest path sliding mode variable s; controller building module: based on the dual spacecraft attitude quaternion dynamics and kinematics model, the attitude tracking error q of the service spacecraft relative to the target spacecraft ev , the shortest-track sliding mode variable s, and the non-singular control auxiliary switching function φ are used to design the attitude shortest path controller τ in the rendezvous and docking of the service spacecraft and the target spacecraft, so that the attitude tracking error of the service spacecraft to the target spacecraft can converge within a finite time and the attitude tracking trajectory is the shortest.

[0028] Furthermore, the motion model building module establishes the dual-spacecraft attitude quaternion dynamics and kinematics model in the general Euler Lagrangian form as follows:

[0029]

[0030]

[0031]

[0032]

[0033] 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 variable I3 is a 3×3 identity matrix with diagonal elements of 1, and the intermediate parameter C a , G a , Q a is the nonlinear matrix 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, q ev It is the attitude tracking error of the serving spacecraft relative to the target spacecraft.

[0034] Furthermore, the sliding mode variable determination module designs the shortest-track sliding mode variable s by: taking the number of sub-sliding mode surfaces n as 1, Among them, κ1, κ3 are positive constant gains, p1 is the power index related to the finite time convergence property, and its value range is between 0 and 1, sign NN (q ev ) is about q ev The modulus normalization sign function of is defined as follows:

[0035]

[0036]

[0037] Furthermore, the controller building module designs the attitude shortest path controller τ in the rendezvous and docking between the service spacecraft and the target spacecraft as follows:

[0038]

[0039] Among them, κ2 and κ4 are positive definite constant gains, and p2∈(0,1) is a positive definite constant power exponent.

[0040] The advantages of the present invention compared with the prior art are:

[0041] (1) Compared with the traditional attitude control method, the shortest-path sliding mode surface of the present invention can provide the shortest-path control characteristics for the attitude control of the spacecraft.

[0042] (2) Since the construction of the straight-line trajectory / approximate shortest-trace sliding mode variable is based on the finite-time theory, it has a faster convergence rate.

[0043] (3) Compared with the control method based on the traditional sign function, the control energy consumption of the present invention is significantly reduced, which can effectively improve the control performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 A schematic flow chart of a method for controlling the shortest path of attitude in a spacecraft rendezvous and docking provided by the present invention;

[0045] Figure 2 A schematic diagram of a coordinate system used in the present invention;

[0046] Figure 3The simulation results of the attitude error motion trajectory using the control method of the present invention are shown, and a schematic comparison of the straight line / shortest trajectory with the traditional finite time algorithm is made. The subscripts of the variables in the figure represent the elements of the corresponding vector, and the latter figure is the same;

[0047] Figure 4 This is the partial simulation result of the error quaternion vector using the control method of the present invention;

[0048] Figure 5 The control input simulation result of the control method of the present invention is adopted;

[0049] Figure 6 The energy consumption results of the control method of the present invention are compared with the traditional algorithm, where the energy consumption is defined as DETAILED DESCRIPTION

[0050] The technical solutions in the embodiments of the present invention will be clearly and completely described below 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.

[0051] The present invention provides a method and system for the shortest path control of attitude in spacecraft rendezvous and docking. First, it is clear that the research scenario of the invention is the rendezvous and docking scenario of the spacecraft on-orbit service mission, the research objects are the on-orbit service spacecraft and the target spacecraft, the research problem is the relative attitude tracking control of the service spacecraft to the target spacecraft, and the control goal to be achieved is that the service spacecraft achieves attitude tracking error convergence with the target spacecraft within a limited time, and the attitude tracking trajectory is the shortest path or its approximation. The algorithm flow is as follows: Figure 1 shown.

[0052] The present invention provides a method for controlling the shortest path of attitude in spacecraft rendezvous and docking, comprising:

[0053] Step 1: Based on the attitude tracking error q of the service spacecraft relative to the target spacecraft ev Establish the quaternion dynamics and kinematics model of dual spacecraft attitude.

[0054] Step 2: Based on the attitude tracking error q of the service spacecraft relative to the target spacecraft ev The shortest-track sliding surface is designed to realize the finite-time tracking control of the spacecraft in the shortest track.

[0055] Step 3: Based on the sliding surface, according to the attitude tracking error q of the service spacecraft relative to the target spacecraft ev , design a straight line trajectory / approximate shortest track sliding mode variable s for the rendezvous and docking spacecraft.

[0056] Step 4: Based on the attitude tracking error q of the service spacecraft relative to the target spacecraft ev , a non-singular control auxiliary switching function φ is designed to eliminate the singularity of the shortest trace sliding mode variable s.

[0057] Step 5: Based on the dual-spacecraft attitude quaternion dynamics and kinematics model, the attitude tracking error q of the service spacecraft relative to the target spacecraft ev , the shortest-path sliding mode variable s, and the non-singular control auxiliary switching function φ are used to design the attitude shortest path controller for the rendezvous and docking of the service spacecraft and the target spacecraft, so that the attitude tracking error of the service spacecraft to the target spacecraft can converge within a finite time, and the attitude tracking trajectory is a straight line trajectory / approximate shortest trajectory.

[0058] The specific steps of this method are as follows:

[0059] Step 1 (S1): Establish a body-fixed coordinate system, a geocentric inertial coordinate system and an orbital coordinate system for the dual spacecraft for rendezvous and docking, and establish a dual spacecraft attitude quaternion dynamics and kinematics model with the body-fixed coordinate system and the geocentric inertial coordinate system as reference systems.

[0060] The reference coordinate system is defined as is the Earth-centered inertial coordinate system (ECI), the origin of which 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 fixed coordinate system of the spacecraft body, 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 orbital coordinate system, the origin of which is located at the target spacecraft mass center, x l The axis points to the orbital radial direction (the center of the earth points to the center of mass of the 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.

[0061] In the present invention, unit quaternions are used to describe the motion attitude of the service spacecraft, and error quaternions are used to describe the attitude error between the service spacecraft and the target spacecraft.

[0062] Considering the attitude kinematics of a rigid spacecraft whose body coordinate system is fixed to the center of mass, Relative to inertial frame 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 a three-dimensional Euclidean space, the rotation of an object can be described by a three-dimensional unit direction vector e of a fixed axis (arbitrary Euler rotation axis) passing through a fixed point (the center of mass of the spacecraft) and an arbitrary rotation angle (Euler angle) θ. For the application scenario of the present invention, this means that the inertial system Along a certain three-dimensional unit direction vector e in space. Rotate any rotation angle (Euler angle) θ to obtain this system This rotation process can be further described by unit quaternion. Considering the fixed point as the origin of the service spacecraft's own coordinate system, relative to the inertial system The unit quaternion associated with the service spacecraft rotation is defined as where q v is a three-dimensional vector that satisfies The service spacecraft is represented in the inertial frame 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 inertial frame The expression in The spacecraft attitude angular velocity in .

[0063] The relative motion of the service spacecraft and the target spacecraft can be defined by and 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 For the coordinate system Rotate to 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

[0064] The rigid body attitude dynamics of the servicing spacecraft can be described as

[0065]

[0066] Among them, J s represents the spacecraft 3×3 moment of inertia matrix with positive constant value, τ is expressed in where ω represents the input torque of the spacecraft attitude control in N·m. a The definition is the same as before, representing the fixed coordinate system of the service spacecraft body Relative to inertial frame The expression in The spacecraft attitude angular velocity in .

[0067] Considering that the general Euler Lagrangian system form is convenient for controller design, and also convenient for migrating the control algorithm of the present invention to relative orbit controller design and robot control design with the same Euler Lagrangian model form, the present invention transforms the aforementioned spacecraft attitude kinematics and dynamics into a general Euler Lagrangian system, and gives 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 needs to be considered in the system. The general Eulerian Lagrangian model of the dynamics and kinematics of the relative motion of the dual spacecraft attitude is:

[0068]

[0069] in,

[0070]

[0071]

[0072]

[0073] 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 variable I3 is a 3×3 identity matrix with diagonal elements of 1, and the intermediate parameter 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 q evis the attitude tracking error of the service spacecraft relative to the target spacecraft. 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, that is, the shortest distance path. The relative attitude error converges to 0, which means that the service spacecraft body coordinate system By controlling, it rotates to the coordinate system of the target spacecraft coincide.

[0074] Step 2 (S2): Design a straight line trajectory / approximate shortest path sliding surface.

[0075]

[0076] Where ξ represents an arbitrary vector (the variable ξ is taken as the attitude tracking error q of the service spacecraft relative to the target spacecraft in step 1 ev ), α i and β are positive constant gains, which can be any positive constants, n is the number of sub-sliding surfaces, p i is a positive power exponent, p i The value range is usually from 0 to 1, sig NN (ξ) is the modulus normalized sign function with respect to ξ, which is defined in step 3.

[0077] It is worth noting that the design sliding surface in this step is an intermediate link in the controller design, and it does not have a physical meaning that corresponds to the spacecraft system model one by one. This sliding surface is mainly used for control signal adjustment. Its mathematical meaning is that for the first-order differential equation described by the formula in this step, the state vector ξ is stable and has the characteristic of finite time convergence, and its convergence trajectory is a straight line. In order to achieve the shortest path maneuver in the attitude tracking of the service spacecraft to the target spacecraft in the rendezvous and docking of the present invention, it is necessary to design the controller so that the closed-loop system has the form of the above differential equation, so that the finite time tracking control of the shortest trajectory of the spacecraft can be achieved. In "straight line trajectory / approximate shortest trajectory", the approximate shortest trajectory means that the actual trajectory is infinitely close to the straight line trajectory, and " / " represents the "or" relationship. Theoretically, the state of the above differential equation converges along a straight line, but there may be slight errors in the actual calculation. Therefore, the approximate shortest trajectory is used to describe more widely applicable situations, and the shortest trajectory is also acceptable in general applications.

[0078] Step 3 (S3): Based on the form of the sliding surface designed in step 2, combined with the dynamics and kinematics of the relative motion of the dual spacecraft attitudes in step 1, the variable ξ in step 2 is defined as the attitude tracking error q of the service spacecraft relative to the target spacecraft in step 1 ev, taking the number of sub-sliding mode surfaces n as 1, the straight line trajectory / approximate shortest track sliding mode variable s is designed for the spacecraft attitude model of rendezvous and docking as follows.

[0079]

[0080] Among them, κ1, κ3 are positive constant gains, and their values ​​can be freely adjusted according to the control effect. p1 is the power index related to the finite time convergence property, and its value range is between 0 and 1. NN (q ev ) is about q ev The modulus normalization sign function of is defined as follows:

[0081]

[0082]

[0083] Straight line / approximate shortest track, defined in the present invention as the spacecraft attitude error quaternion, in terms of q ev Vector three elements q ev1 ,q ev2 ,q ev3 In the rectangular coordinates of the coordinate axis, from the initial error point (q at the initial moment ev The straight line from the coordinate point in the service spacecraft's own system) to the origin (the origin in the service spacecraft's own system). Its physical manifestation is that the attitude of the service spacecraft maneuvers from the initial state to the desired attitude relative to the target spacecraft (the two spacecraft's own systems coincide) in the shortest path.

[0084] The straight line / approximate shortest trajectory of the service spacecraft relative to the target spacecraft attitude maneuver trajectory is expressed as follows: In the function, due to the sign NN (q ev ) has the following This function term will correct the direction of the control input so that the state of the spacecraft attitude error system tends to evolve in a straight line.

[0085] Function Item We need to emphasize the correction of the control direction. In this step, define the sliding surface When the sliding surface converges to 0, we can get The differential equation has the same form as the sliding surface in step 2. The system is convergent. Because there is a function term Therefore, the mathematical transformation of this term is as follows The direction of the vector after q ev The same, which means that q ev The change is is always in the opposite direction to the state itself, then when q ev When converged, it must follow q ev The direction of the initial error point to the origin of the coordinate system changes, so that q ev The convergence process will appear as a straight line in the coordinate system, and it is the shortest path straight line.

[0086] Step 4 (S4): Considering the sliding surface design in step 3, when the sliding mode variable is differentiated, the derivative will appear as follows and The function term indicates a singular problem. In order to overcome the singular problem of variables, a non-singular control auxiliary switching function is designed as follows:

[0087]

[0088] Among them, ι and It is an auxiliary coefficient, which is a small positive constant used to prevent system singularity, and is usually 0.001.

[0089] Step 5 (S5): Based on Q a 、M a 、sig NN (·),s,φ,q ev , G a , Design of the shortest attitude path controller for spacecraft rendezvous and docking

[0090]

[0091] Among them, κ2 and κ4 are positive constant gains, and their value range can be designed accordingly according to the control effect of the closed-loop system. p2∈(0,1) is the positive constant power exponent.

[0092] The above five steps have a progressive logical relationship as follows: Step 1 (S1) provides the spacecraft system model and related parameter definitions required for the control system for controller design and subsequent steps. Based on step 1, a model-based controller and closed-loop system design are performed. In order to make the closed-loop system have a straight line / approximately shortest system trajectory, that is, the shortest trajectory of the attitude tracking error under the present invention, the present invention originally proposes a design method for a straight line trajectory / approximately shortest trajectory sliding surface in step 2, that is, according to the sliding surface proposed in step 2, different vectors, constant gains, power exponents and the number of sub-sliding surfaces can be defined for different application scenarios to form different sliding surfaces. For the problem of spacecraft attitude control, step 3 designs a sliding surface for spacecraft attitude control based on the spacecraft attitude vector on the basis of step 2. Considering that the sliding surface designed in step 3 has a singular problem when being derived, a non-singular control auxiliary switching function that avoids singularity is designed in step 4 and applied in the controller. Based on the designs of steps 1 to 4, step 5 proposes the shortest path controller for the attitude of the spacecraft during rendezvous and docking. The controller is introduced into the system of step 1 to obtain a closed-loop system, and this controller can be directly applied to the attitude control of the spacecraft or the relative attitude control of the spacecraft during rendezvous and docking. So far, the design of the entire control system of the present invention has been completed.

[0093] The method of the invention can be demonstrated as follows.

[0094] Select the Lyapunov function V1 about the sliding surface s and about q ev The Lyapunov function V2 is as follows

[0095]

[0096]

[0097] Taking the derivative of the above Lyapunov function with respect to time, we can get

[0098]

[0099]

[0100] According to the finite time stability theory, it can be known that the spacecraft 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. Through theoretical analysis, the error system serving the attitude control of the spacecraft will be stable and convergent in a finite time, and according to the characteristics of the modulus normalization function, the system state changes along the straight line / shortest path sign. Therefore, in the attitude motion of the spacecraft, the attitude maneuver of the shortest path will be exhibited.

[0101] The present invention also proposes a shortest path attitude control system in spacecraft rendezvous and docking, which includes: a motion model construction module, a sliding surface construction module, a sliding variable determination module, an auxiliary switching module, and a controller construction module.

[0102] Motion model building module: Based on the attitude tracking error q of the service spacecraft relative to the target spacecraft ev Establish the quaternion dynamics and kinematics model of dual spacecraft attitude.

[0103] Sliding surface construction module: According to the attitude tracking error q of the service spacecraft relative to the target spacecraft ev A straight line trajectory / approximate shortest track sliding mode surface is designed to achieve finite time tracking control of the spacecraft in the shortest track.

[0104] Sliding mode variable determination module: Based on the sliding mode surface, according to the attitude tracking error q of the service spacecraft relative to the target spacecraft ev , design the shortest track sliding mode variable s for the rendezvous and docking spacecraft;

[0105] Auxiliary switching module: According to the attitude tracking error q of the service spacecraft relative to the target spacecraft ev , a non-singular control auxiliary switching function φ is designed to eliminate the singularity of the shortest trace sliding mode variable s.

[0106] Controller building blocks: Based on the dual-spacecraft attitude quaternion dynamics and kinematics model, the attitude tracking error q of the service spacecraft relative to the target spacecraft ev , the shortest path sliding mode variable s, and the non-singular control auxiliary switching function φ are used to design the attitude shortest path controller for the rendezvous and docking of the service spacecraft and the target spacecraft, so that the attitude tracking error of the service spacecraft to the target spacecraft can converge within a finite time, and the attitude tracking trajectory is the shortest path.

[0107] The motion model building module establishes the dual spacecraft attitude quaternion dynamics and kinematics model specifically including:

[0108] The general Eulerian Lagrangian form of the dual-spacecraft attitude quaternion dynamics and kinematics model is:

[0109]

[0110] in,

[0111]

[0112]

[0113]

[0114] 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 variable I3 is a 3×3 identity matrix with diagonal elements of 1, and the intermediate parameter C a , G a , Q a is the nonlinear matrix 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 ev It is the attitude tracking error of the serving spacecraft relative to the target spacecraft.

[0115] The sliding surface construction module designs a straight line trajectory / approximate shortest path sliding surface specifically including:

[0116]

[0117] Among them, ξ represents an arbitrary vector, α i and β are positive constant gains, which can be any positive constants, n is the number of sub-sliding surfaces, p i is a positive power exponent, p i The value range is usually from 0 to 1, sig NN (ξ) is the modulus normalized sign function about ξ, and the variable ξ is taken as the attitude tracking error q of the service spacecraft relative to the target spacecraft. ev .

[0118] The sliding mode variable determination module designs the straight line trajectory / approximate shortest track sliding mode variable s including:

[0119] The number of sub-sliding surfaces n is set to 1, and the linear trajectory / approximate shortest trajectory sliding mode variable s is as follows:

[0120]

[0121] Among them, κ1, κ3 are positive constant gains, and their values ​​can be freely adjusted according to the control effect. p1 is the power index related to the finite time convergence property, and its value range is between 0 and 1. NN (q ev ) is about q evThe modulus normalization sign function of is defined as follows:

[0122]

[0123]

[0124] The auxiliary switching module designs a non-singular control auxiliary switching function φ as follows:

[0125]

[0126] Among them, ι and It is an auxiliary coefficient, which is a small positive constant used to prevent system singularity, and is usually 0.001.

[0127] The controller building module designs the attitude shortest path controller τ in the rendezvous and docking between the service spacecraft and the target spacecraft as follows:

[0128]

[0129] Among them, κ2 and κ4 are positive constant gains, and their value range is set accordingly according to the control effect of the closed-loop system, and p2∈(0,1) is the positive constant power exponent.

[0130] Based on the above implementation of the present invention, a simulation result of a method and system for controlling the shortest attitude path in spacecraft rendezvous and docking can be obtained as follows: Figures 3 to 6 shown. Figure 3 The simulation results of the attitude error motion trajectory using the control method of the present invention are shown, and a schematic comparison of the straight line / shortest trajectory with the traditional finite time algorithm is made. From this figure, it can be seen that compared with the traditional method, the present method has a shorter maneuvering path and more precise control effect in the trajectory direction (trajectory direction); Figure 4 The error quaternion vector part of the control method of the present invention is simulated to verify the convergence of the method of the present invention; Figure 5 The control input simulation results of the control method of the present invention are used to verify the feasibility of the method of the present invention; Figure 6 The energy consumption results of the control method of the present invention are compared with the traditional algorithm to verify the low energy consumption characteristics of the method of the present invention. The above simulation results fully demonstrate that the spacecraft rendezvous and docking mission can achieve high-precision attitude shortest path finite time control under the control method proposed by the present invention.

[0131] The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.

Claims

1. A method for controlling the shortest path of attitude in spacecraft rendezvous and docking, characterized in that: include: Step 1: Based on the attitude tracking error q of the service spacecraft relative to the target spacecraft ev Establish dual spacecraft attitude quaternion dynamics and kinematics model; Step 2: Based on the attitude tracking error q of the service spacecraft relative to the target spacecraft ev Design the shortest-track sliding surface to achieve finite-time tracking control of the spacecraft in the shortest track direction; Step 3: Based on the sliding surface, according to the attitude tracking error q of the service spacecraft relative to the target spacecraft ev , design the shortest track sliding mode variable s for the rendezvous and docking spacecraft; Step 4: Based on the attitude tracking error q of the service spacecraft relative to the target spacecraft ev , design a non-singular control auxiliary switching function φ to eliminate the singularity of the shortest-trace sliding mode variable s; Step 5: Based on the dual-spacecraft attitude quaternion dynamics and kinematics model, the attitude tracking error q of the service spacecraft relative to the target spacecraft ev , the shortest path sliding mode variable s, the non-singular control auxiliary switching function φ, design the attitude shortest path controller τ in the rendezvous and docking between the service spacecraft and the target spacecraft, so that the attitude tracking error of the service spacecraft to the target spacecraft can converge within a limited time, and the attitude tracking trajectory is the shortest; The general Eulerian Lagrangian form of the dual-spacecraft attitude quaternion dynamics and kinematics model described in step 1 is: 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 variable I3 is a 3×3 identity matrix with diagonal elements of 1, and the intermediate parameter C a , G a , Q a is the nonlinear matrix 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, q ev The attitude tracking error of the serving spacecraft relative to the target spacecraft; The shortest sliding surface in step 2 is: Among them, ξ represents an arbitrary vector, α i and β are positive constant gains, is an arbitrary positive constant, n is the number of sub-sliding surfaces, p i is a positive power exponent, p i The value range is 0 to 1, sig NN (ξ) is the modulus normalized sign function about ξ, and the variable ξ is taken as the attitude tracking error q of the service spacecraft relative to the target spacecraft. ev ; The shortest track sliding mode variable s in step 3 includes: The number of sub-sliding surfaces n is set to 1, Among them, κ1, κ3 are positive constant gains, p1 is the power index related to the finite time convergence property, and its value range is between 0 and 1, sign NN (q ev ) is about q ev The modulus normalized sign function of The non-singular control auxiliary switching function φ in step 4 is specifically: Among them, ι and is the auxiliary coefficient, which is a normal number used to prevent system singularity and is set to 0.001; The attitude shortest path controller τ in the rendezvous and docking between the service spacecraft and the target spacecraft in step 5 is: Among them, κ2 and κ4 are positive definite constant gains, and p2∈(0,1) is a positive definite constant power exponent.

2. A shortest path control system for attitude in spacecraft rendezvous and docking, characterized in that: include: Motion model building module, sliding surface building module, sliding variable determination module, auxiliary switching module, controller building module, wherein: Motion model building module: Based on the attitude tracking error q of the service spacecraft relative to the target spacecraft ev Establish dual spacecraft attitude quaternion dynamics and kinematics model; Sliding surface construction module: According to the attitude tracking error q of the service spacecraft relative to the target spacecraft ev Design the shortest-track sliding surface to achieve finite-time tracking control of the spacecraft in the shortest track direction; Sliding mode variable determination module: Based on the sliding mode surface, according to the attitude tracking error q of the service spacecraft relative to the target spacecraft ev , design the shortest track sliding mode variable s for the rendezvous and docking spacecraft; Auxiliary switching module: According to the attitude tracking error q of the service spacecraft relative to the target spacecraft ev , design a non-singular control auxiliary switching function φ to eliminate the singularity of the shortest-trace sliding mode variable s; Controller building blocks: Based on the dual-spacecraft attitude quaternion dynamics and kinematics model, the attitude tracking error q of the service spacecraft relative to the target spacecraft ev , the shortest path sliding mode variable s, the non-singular control auxiliary switching function φ, design the attitude shortest path controller τ in the rendezvous and docking between the service spacecraft and the target spacecraft, so that the attitude tracking error of the service spacecraft to the target spacecraft can converge within a limited time, and the attitude tracking trajectory is the shortest; It is characterized in that the motion model building module establishes the quaternion dynamics and kinematics model of the dual spacecraft attitude, and the general Euler Lagrangian form is: 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 variable I3 is a 3×3 identity matrix with diagonal elements of 1, and the intermediate parameter C a , G a , Q a is the nonlinear matrix 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, q ev The attitude tracking error of the serving spacecraft relative to the target spacecraft; It is characterized in that the sliding mode variable determination module designs the shortest trace sliding mode variable s including: The number of sub-sliding surfaces n is set to 1, Among them, κ1, κ3 are positive constant gains, p1 is the power index related to the finite time convergence property, and its value range is between 0 and 1, sign NN (q ev ) is about q ev The modulus normalized sign function of is defined as follows: It is characterized in that the controller construction module designs the attitude shortest path controller τ in the rendezvous and docking between the service spacecraft and the target spacecraft, specifically: Among them, κ2 and κ4 are positive definite constant gains, and p2∈(0,1) is a positive definite constant power exponent.

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