A 6DOF output feedback control method for spacecraft formation considering visibility constraints

Abstract

A 6DOF output feedback control method for a spacecraft formation considering visibility constraints belongs to the field of spacecraft formation control. The present invention is to solve the problems existing in the existing spacecraft formation control. The method of the present invention comprises the following steps: S1, establishing the dynamic equation of the tracking star relative to the space failure target spacecraft based on the Lie group SE (3); S2, introducing the configuration error potential function to obtain the configuration error vector; S3, establishing visibility constraints: constructing a field of view constraint to ensure that the target is always in the field of view of the kth tracking star, and an inter-satellite line of sight occlusion avoidance constraint based on the maximum observation cross section; S4, designing a potential function that satisfies the visibility constraint; S5, establishing an auxiliary power system based on the Lie group SE (3); S6, constructing a 6DOF output feedback control law for a spacecraft formation based on the auxiliary power system: #imgabs0#

Description

Technical Field

[0001] The invention relates to a spacecraft formation control method considering visibility constraints, and belongs to the field of spacecraft formation control. Background Art

[0002] With the development of space technology, on-orbit servicing of high-value or unique failed spacecraft in high-orbit orbits has become an indispensable technology. Relative orbit-attitude tracking control is a key enabling technology for on-orbit servicing operations such as spacecraft rendezvous and docking, and high-precision on-orbit monitoring. For failed spacecraft, they can be considered non-cooperative targets with known characteristics. Vision-based sensors are typically used to measure the relative position between spacecraft, but visual sensors lack direct linear and angular velocity measurements. Existing research on close-range on-orbit servicing operations in space assumes that linear and angular velocity information can be directly obtained. However, velocity measurement information may not be available due to sensor failures or limited onboard costs.

[0003] There are generally two solutions to the problem of unmeasurable velocity information: one is to use an observer to estimate the velocity information, and the other is to use a filter or dynamic auxiliary system to provide damping for the closed-loop system. For the case where angular velocity is unknown, the existing distributed finite-time attitude cooperative control scheme uses a finite-time distributed observer to enable all spacecraft in the formation to track the time-varying reference attitude without angular velocity measurement. The existing fixed-time stable controller proposed based on the state observer can be applied to more general second-order systems, but it does not consider the case where the relative linear velocity is unknown. None of the above methods can be directly extended to the case where 6DOF (six degrees of freedom tracking) velocity information is unknown. In order to solve the problem of unavailable agent velocity and acceleration during collision-free formation tracking of second-order multi-agent systems under communication constraints, a high-gain continuous-discrete-time observer is used to estimate the position and velocity of the agent and its neighbors in continuous time from discrete position data. Although the above-mentioned observer-based output feedback controller can achieve the goal of spacecraft attitude maneuvering, the designed observer structure is complex and requires unknown model information for accurate estimation, which makes it unfriendly in engineering practice.

[0004] Another way to solve the problem of unmeasurable velocity information is to design a filter or a dynamic auxiliary system. For the case where angular velocity measurement information is not required, a dynamic auxiliary system based on quaternion form can be used for indirect asymptotic estimation of angular velocity, providing the necessary damping for the closed-loop system to solve the problem of spacecraft attitude tracking when angular velocity information is unmeasurable. Furthermore, the problem of multi-agent attitude consistency can be solved by constructing a distributed quaternion filter. Based on this idea, a non-angular velocity attitude tracking control framework is proposed. This method represents attitude kinematics in Euler angles and can be implemented online in real time. It does not require expensive online calculations, making it easy to apply to actual large-angle attitude tracking maneuvers. Similarly, in order to solve the problem of non-angular velocity master-slave cooperative attitude tracking of rigid bodies, a distributed control algorithm based on local information exchange is proposed. It uses the nonlinear manifold SO(3) to represent the attitude of the rigid body and designs two auxiliary systems driven by specified inputs to solve the problem of unavailable absolute angular velocity and relative angular velocity. However, it cannot be directly applied to the problem of unknown 6DOF velocity.

[0005] The above methods only consider the case where individual angular velocity information or linear velocity information is unmeasurable, and do not consider the case where all velocity information is missing in the orbit-attitude coupling scenario. Unlike existing work on spacecraft approach maneuvers, an adaptive output feedback safety control scheme is used to achieve simultaneous position and attitude tracking. This scheme eliminates the need for full state feedback (i.e., only attitude and position tracking errors are available) while ensuring that there will be no collision between the two spacecraft during the entire approach process. However, this method requires the design of separate observers for pose estimation and is not suitable for the pose coupling scenario. To avoid the above issues, based on a 6DOF dynamic model of a rigid spacecraft established based on dual quaternions, a pose tracking controller that does not require relative linear and angular velocity measurements is proposed.

[0006] In engineering practice, various state constraints often limit the position and attitude motion of spacecraft. Existing research has considered the problem of safe approach when linear velocity information is not required, or the problem of attitude maneuvering under motion constraints when angular velocity measurement is not required. For example, a control strategy based on an artificial potential function that does not use velocity information can enable all tracking satellites to achieve control objectives while avoiding collisions with other intelligent agents and obstacles in the environment. However, research on integrated spacecraft attitude and orbit control under motion constraints without velocity information has received little attention. Summary of the Invention

[0007] To address the challenges of existing spacecraft formation control, the present invention provides a 6DOF output feedback control method for spacecraft formations that considers visibility constraints. This invention proposes an integrated spacecraft posture control method that can be used under motion constraints when velocity measurement information is unavailable. The innovation of this invention lies in the fact that, for situations where velocity measurement information is unavailable, the designed output feedback controller is independent of the observer design, and no model information is required for velocity estimation, while ensuring that posture motion satisfies the corresponding motion constraints.

[0008] The present invention provides a 6DOF output feedback control method for spacecraft formation considering visibility constraints, the method comprising the following steps:

[0009] S1. Based on Lie group SE (3), the dynamic equations of the tracking satellite relative to the target spacecraft with space failure are established;

[0010] S2, introducing the configuration error potential function to obtain the configuration error vector;

[0011] S3. Establish visibility constraints: Construct a field of view constraint to ensure that the target is always in the field of view of the kth tracking star, and an inter-satellite line of sight occlusion avoidance constraint based on the maximum observation cross section;

[0012] S4. Design a potential function that satisfies the visibility constraint;

[0013] S5. Establish an auxiliary power system based on Lie group SE(3);

[0014] S6. Construct a 6DOF output feedback control law for spacecraft formation based on the auxiliary power system:

[0015]

[0016] Where:

[0017] is the control quantity generated on the kth tracking satellite by the motion constraint potential field between the tracking satellite and the target spacecraft;

[0018]

[0019] Where: It means to find the gradient about (·), is the attitude error of the kth tracking satellite relative to the target spacecraft, represents the position error of the kth tracking satellite relative to the target spacecraft, is the expected attitude of the kth tracking satellite relative to the target spacecraft, is the expected position of the kth tracking satellite relative to the target spacecraft; (·) ∨ Represents mapping, mapping (·) ∨ : Indicates that The matrix in is mapped to the isomorphic real space V m represents the visibility constraint potential function;

[0020] is an output feedback controller not related to the potential function,

[0021]

[0022] Where: k f 、k l is the positive definite control gain matrix to be designed, and

[0023] represents the configuration error vector between the actual configuration and the desired configuration,

[0024] Represents the configuration error vector of the auxiliary system relative to the actual motion system,

[0025] represents the gravitational effect on the k-th tracking star,

[0026] J k ,m k denote the moment of inertia and mass of the kth tracking star, respectively, and E3 denotes the third-order unit matrix;

[0027] Ad g is the adjoint operator of the element g on the Lie group SE(3), ad ξ is the adjoint operator of ξ;

[0028]

[0029] express relatively speed, and Respectively Relative to rotational speed and translational speed.

[0030] Preferably, the adjoint operator Ad g 、ad ξ The matrix expression of is:

[0031] (·) × Indicates the antisymmetric matrix.

[0032] Any Any ξ=[ω v], where R∈SO(3) represents the rotation matrix, represents the rotation vector, represents the angular velocity of rotation, Indicates the translational velocity.

[0033] Preferably, the dynamic equation of the tracking satellite relative to the target spacecraft with space failure established based on Lie group SE (3) in S1 is the dynamic equation of the relative motion system, which is expressed as:

[0034]

[0035] Where:

[0036]

[0037] Where, Represents the coordinate system of the kth tracking star Relative to the target spacecraft body coordinate system The velocity vector, and Respectively Relative to The rotational speed and translational speed;

[0038] R tk for arrive The coordinate transformation matrix, Indicates the relative position vector of the kth tracking satellite relative to the target spacecraft. The coordinates under R It Represents the target spacecraft body coordinate system To the Earth-centered inertial coordinate system The coordinate transformation matrix, r t I and The target spacecraft and the kth tracking satellite are respectively in the target spacecraft body coordinate system The position vector under

[0039] express relatively speed, and Respectively Relative to The rotational speed and translational speed;

[0040] The gravitational effect on the kth tracking star represents the gravity term, The direction of this vector is from the center of the Earth to the center of mass of the target spacecraft or the kth tracking satellite. μ represents the Earth's gravitational constant, μ = 398600.47 km 3 / s 2 , R Ik Represents the coordinate system of the kth tracking star To the Earth-centered inertial coordinate system The coordinate transformation matrix,

[0041] represents the external interference acting on the kth tracking satellite.

[0042] Preferably, the configuration error vector in S2 includes the configuration error vector between the actual configuration and the desired configuration and the configuration error vector of the auxiliary system relative to the actual motion system

[0043] The configuration error vector between the actual configuration and the expected configuration Get it as follows:

[0044]

[0045] and Represent the relative attitude error vector and relative position error vector respectively;

[0046] Configuration error vector of the auxiliary system relative to the actual motion system Get it as follows:

[0047]

[0048] Where R ak express To the coordinate system of the kth tracking star The coordinate transformation matrix, express Relative to The relative position vector is The coordinates below, Represents the coordinate system Estimates.

[0049] Preferably, S3 establishes visibility constraints, wherein a field of view constraint is constructed to ensure that the target is always in the field of view of the kth tracking star:

[0050]

[0051] Among them, α k represents the viewing angle, α k =arccos((x p ) T xk ), represents the desired LOS direction, Indicates The position vector of the next k-th tracking satellite relative to the target spacecraft, x k for The unit vector under is the half-apex angle of the camera field of view for tracking stars, f k >0, indicating that the target spacecraft is within the field of view of the tracking satellite;

[0052] Among them, the intersatellite line of sight obstruction avoidance constraints established based on the maximum observation cross section are:

[0053]

[0054] Where, Indicates the indicator function for judging whether the line of sight is blocked,

[0055]

[0056] Where,

[0057] A target spacecraft T and N tracking satellites with a total of N+1 ellipsoids are defined as an ellipsoidal spacecraft set R tj The j-th tracking star body coordinate system is The coordinate transformation matrix, The relative position vector of the j-th tracking satellite relative to the target spacecraft is The coordinates below,

[0058] W kj represents a symmetric matrix, is the half-vertex angle of the camera field of view of the j-th tracking star, ε kj is a slack variable and 0≤ε kj ≤1;

[0059] η kj =(x s ) T x c It is a prerequisite for avoiding the constraint of line of sight occlusion. represents the direction of the kth tracking star, represents the direction of the jth tracking star, when η kj When ≤0, h kj = 1, the kth tracking star and the jth tracking star are located on the opposite side of MOCS. At this time, there is no need to consider the line of sight between the kth tracking star and the jth tracking star. When h k >0, indicating that the kth tracking star does not block the view of the jth tracking star.

[0060] Preferably, the design in S4 satisfies the potential function V of the visibility constraint m for:

[0061] V m =φ ak +ψ k

[0062] Among them, φ ak is the potential function for the field of view constraint between the kth tracking satellite and the target spacecraft on SE(3),

[0063]

[0064] Where, l ak is the normal number to be designed, represents the attitude error function between the kth tracking satellite and the target spacecraft,

[0065] when When φ ak →∞, the kth tracking satellite will lose visibility of the target spacecraft;

[0066] Among them, ψ k is the potential function for avoiding line of sight occlusion,

[0067]

[0068] Where, γ kj and κ kj is a positive constant, represents the position error function between the kth tracking satellite and the target spacecraft;

[0069] When the kth tracking star blocks the line of sight between the jth tracking star and the target spacecraft, h kj →0,ψ kj →∞.

[0070] Preferably, the attitude error function between the kth tracking satellite and the target spacecraft is for:

[0071]

[0072] Position error function between the kth tracking satellite and the target spacecraft for:

[0073]

[0074] Preferably, the auxiliary power system based on Lie group SE (3) in S5 is Relative to The kinematic equation is expressed as:

[0075]

[0076] Where, F ka represents the system matrix;

[0077]

[0078] Intermediate variables

[0079] for Relative to The speed is The following expression.

[0080] Beneficial effects of the present invention: Compared with existing research aimed at close-range, fixed-point inspections of target spacecraft, the present invention has a wider range of application scenarios. Not only can it complete fixed-point hovering observations in one-to-one on-orbit service missions, but also, when multiple satellites are performing close-range operations on the same target spacecraft, it can prevent other tracking satellites from blocking the current tracking satellite's line of sight of the target spacecraft. In response to situations where velocity measurement information cannot be obtained, the present invention designs an output feedback control scheme that does not require an observer, and no model information is required in the process of estimating velocity information. The output feedback control strategy designed in combination with potential function saves more on-board computing resources when dealing with visibility constraints than other optimization-based methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 It is a structural diagram of a 6DOF output feedback control method for a spacecraft formation considering visibility constraints described in the present invention.

[0082] 1. Target spacecraft, 2. kth tracking satellite, 3. Possible line-of-sight obstruction scenarios between tracking satellites. DETAILED DESCRIPTION

[0083] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0084] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0085] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

[0086] Specific implementation method 1: Figure 1 This embodiment describes a 6DOF output feedback control method for a spacecraft formation considering visibility constraints, which includes the following steps:

[0087] S1. Based on Lie group SE (3), the dynamic equations of the tracking satellite relative to the target spacecraft with space failure are established;

[0088] S2, introducing the configuration error potential function to obtain the configuration error vector;

[0089] S3. Establish visibility constraints: Construct a field of view constraint to ensure that the target is always in the field of view of the kth tracking star, and an inter-satellite line of sight occlusion avoidance constraint based on the maximum observation cross section;

[0090] S4. Design a potential function that satisfies the visibility constraint;

[0091] S5. Establish an auxiliary power system based on Lie group SE(3);

[0092] S6. Construct a 6DOF output feedback control law for spacecraft formation based on the auxiliary power system.

[0093] Regarding step S1, in order to describe the motion of the tracking star, first define the target spacecraft body coordinate system The origin is located at the target spacecraft mass center, the z-axis is along the normal of the orbital plane, the x-axis is along the direction of the target spacecraft orbital radius, and the y-axis is determined by the right-hand rule. Suppose there are N tracking satellites, and the body coordinate system of the kth tracking satellite is defined as The origin is located at the center of mass of the tracking star, and its coordinate axes are along the direction of the principal axis of inertia. In the present invention, the symbols (k, t, I) written in the upper right corner of the characters represent the expression of the variable in the corresponding coordinate system. Down.

[0094] In order to establish the integrated dynamic model of spacecraft attitude and orbit, it is necessary to unify the parameters and model forms of the two motions of attitude and orbit. First, the kinematic equation of the kth tracking satellite relative to the target is expressed in the following compact form:

[0095]

[0096] in, represents the position configuration of the tracking satellite relative to the target spacecraft, R tk for arrive The coordinate transformation matrix. Indicates the relative position vector of the kth tracking satellite relative to the target spacecraft. The coordinates under R It Represents the target spacecraft body coordinate system To the Earth-centered inertial coordinate system The coordinate transformation matrix, r t I and The target spacecraft and the kth tracking satellite are respectively in the target spacecraft body coordinate system The position vector under (the direction of the vector is from the center of the earth to the center of mass of the target spacecraft and the center of mass of the k-th tracking satellite). and Respectively Relative to The rotational speed and translational speed of . Mapping (·) ∧ : Indicates that The vectors in are mapped to the isomorphic matrix space in(·) × Indicates that the antisymmetric matrix is ​​obtained.

[0097] At the same time, for any ξ=[ω v], where R∈SO(3) represents the rotation matrix, represents the rotation vector, represents the angular velocity of rotation, represents the translational velocity, and defines two adjoint operators as follows:

[0098]

[0099] And there

[0100] Secondly, when the relative velocity of the two spacecraft can be directly measured, the dynamic equation of the relative motion system can be expressed as follows:

[0101]

[0102] in, J k ,m k represent the moment of inertia and mass of the kth tracking star, represents the control input of the kth tracking star. express relatively speed. represents the gravitational effect on the k-th tracking star, represents the gravity term and is of the form

[0103]

[0104] R Ik Represents the coordinate system of the kth tracking star To the Earth-centered inertial coordinate system The coordinate transformation matrix.

[0105] The goal of this invention is to design a control strategy that enables each tracking satellite to achieve safe and continuous specific tracking of the target spacecraft. During the entire mission, all motion constraints should be complied with.

[0106] Regarding step S2, a configuration error potential function is introduced to obtain a configuration error vector;

[0107] Before performing motion constraint analysis, the expected relative configuration between the kth tracking satellite and the target spacecraft is given as follows:

[0108]

[0109] in, is the expected attitude of the kth tracking satellite relative to the target spacecraft, is the expected position of the kth tracking satellite relative to the target spacecraft. The design must satisfy the requirements of motion constraints.

[0110] Then, the group error is selected as follows

[0111]

[0112] in, represents the attitude error of the kth tracking satellite relative to the target spacecraft, Represents the position error of the kth tracking satellite relative to the target spacecraft.

[0113] Because the expected configuration given in equation (4) Is a constant matrix, so, taking the derivative of formula (5) we can get

[0114]

[0115] For the convenience of controller design, the following positive definite Morse potential function is defined to evaluate the configuration error between the kth tracking satellite and the target spacecraft:

[0116]

[0117] and Represent the error functions of the posture and position parts respectively.

[0118]

[0119] in, Express Find the trace of a matrix.

[0120]

[0121] The time derivative of formula (7) can be obtained

[0122]

[0123] Among them, the configuration error function Gradient Also called the configuration error vector, its form is as follows

[0124]

[0125] and Represent the relative attitude error vector and relative position error vector respectively.

[0126] Configuration error vector of the auxiliary system relative to the actual motion system Get it as follows:

[0127]

[0128] Where R ak express To the coordinate system of the kth tracking star The coordinate transformation matrix, express Relative to The relative position vector is The coordinates below, Represents the coordinate system Estimates.

[0129] Regarding step S3, establishing visibility constraints, visibility constraint function V m It includes the following two parts: a field of view constraint that ensures the target is always in the field of view of the kth tracking star, and an inter-satellite line of sight occlusion avoidance constraint based on the maximum observation cross section.

[0130] Visibility constraints and potential function design:

[0131] In order to facilitate the measurement of relative positions between satellites, The following field of view constraint is constructed to ensure that the target is always in the field of view of the kth tracking star

[0132]

[0133] Among them, α k represents the viewing angle, α k =arccos((x p ) T x k ), represents the desired LOS direction, Indicates The position vector of the next k-th tracking satellite relative to the target spacecraft, x k for The unit vector under is the half-apex angle of the camera field of view for tracking stars, f k >0, indicating that the target spacecraft is within the field of view of the tracking satellite.

[0134] When other tracking satellites appear in the field of view of the kth tracking satellite and block the target spacecraft, this will greatly affect the imaging quality of the kth tracking satellite on the target. In order to enhance the applicability of the line of sight blockage avoidance constraint to different formation configurations, the cross section obtained by the intersection of the field of view of the tracking satellite and the target ellipsoid envelope is defined as the maximum observable cross-section (MOCS) of the tracking satellite on the target spacecraft. When two tracking satellites are located on opposite sides of the MOCS (such as Figure 1 When ZoneA is selected, there is no need to consider line of sight occlusion. Therefore, the constructed line of sight occlusion avoidance constraints are as follows:

[0135]

[0136] Where, Indicates the indicator function for judging whether the line of sight is blocked,

[0137]

[0138] in, Represents the ellipsoidal spacecraft set, including the target spacecraft T and N tracking star spacecraft. is the half-vertex angle of the camera field of view of the j-th tracking star, ε kj is a slack variable and 0≤ε kj ≤1.η kj =(x s ) T x c It is a prerequisite for avoiding the constraint of line of sight occlusion. represents the direction of the kth tracking star, represents the direction of the jth tracking star, when η kj When ≤0, h kj = 1, the kth tracking star and the jth tracking star are located on the opposite side of MOCS. At this time, there is no need to consider the line of sight between the kth tracking star and the jth tracking star. When h k >0, indicating that the kth tracking star does not block the view of the jth tracking star.

[0139] Regarding step S4, designing a potential function that satisfies visibility constraints

[0140] In order to ensure that the tracking satellite always meets these motion constraints during the mission, this step will propose a control method based on APF. The potential function for the field of view constraint between the kth tracking satellite and the target spacecraft on SE(3) is designed as follows:

[0141]

[0142] Among them, l ak is the normal number to be designed, represents the attitude error function between the kth tracking satellite and the target spacecraft,

[0143] when When φ ak →∞, the kth tracking satellite will lose visibility of the target spacecraft.

[0144] In order to ensure that the inter-satellite line of sight occlusion avoidance constraint is always established, the line of sight occlusion avoidance potential function is designed as follows

[0145]

[0146] Among them, γ kj and κ kj is a positive constant, represents the position error function between the kth tracking star and the target spacecraft. When the kth tracking star blocks the line of sight between the jth tracking star and the target spacecraft, h kj →0,ψ kj →∞.

[0147] Let V m =φ ak +ψ k , taking the derivatives of equations (15) and (16), we can get the following form:

[0148]

[0149] For ease of writing, Indicates V m The Riemann gradient of .

[0150] In short:

[0151] Regarding step S5, establishing an auxiliary power system based on Lie group SE(3)

[0152] When the angular velocity information of the tracking satellite is unmeasurable, the relative velocity information between the tracking satellite and the target spacecraft cannot be used. To this end, the present invention designs an auxiliary dynamics system on SE (3) Perform indirect estimation. Define the coordinate system Represents the coordinate system The estimate will Relative to The configuration is denoted as g at The auxiliary dynamics system is defined as follows

[0153]

[0154] in, is the input of the auxiliary power system and is a parameter to be designed. In order to describe the error between the auxiliary power system and the actual relative motion system, the error relative configuration is defined. R ak express arrive The coordinate transformation matrix, express Relative to The relative position vector is The coordinates under. And the error relative to the configuration satisfies the following relationship

[0155]

[0156]

[0157] for Relative to The speed is Similarly, in order to design the controller more conveniently, the following position function ψ(g ka ) is used to measure the configuration deviation between the auxiliary power system and the actual relative motion system.

[0158]

[0159] ψ R (R ak ), Represent the error functions of the posture and position parts respectively;

[0160] Rewrite formula (19) to get Relative to The kinematic equations are as follows

[0161]

[0162] in, Represents the configuration error vector of the auxiliary system relative to the actual motion system,

[0163]

[0164] Where, F ka represents the system matrix;

[0165]

[0166] Intermediate variables

[0167] for Relative to The speed is The following expression.

[0168] Formula (22) is used to measure the estimated status of the auxiliary power system to the real system. Right now This means that Under this condition, the input of the auxiliary power system designed by the present invention can approach the real relative speed of the system, that is,

[0169] Regarding step S6, constructing the 6DOF output feedback control law for spacecraft formation based on the auxiliary power system:

[0170] In this step, an output feedback controller will be designed for the tracking satellites to control each tracking satellite to reach its desired state so as to carry out the corresponding observation task. At the same time, in the process of reaching the desired state, the tracking satellite needs to comply with the motion constraints (12) and (13). The relative motion system under the action of this control law is almost globally asymptotically convergent. The control law is designed as follows:

[0171]

[0172]

[0173]

[0174] in, is an output feedback controller that is not related to the potential function. The first term in represents the configuration error feedback term, and the second term represents the relative configuration feedback term between the auxiliary dynamics system and the actual motion system. represents the known gravity effect term, and the last two terms represent the nonlinear feedforward terms. is the control quantity generated on the kth tracking satellite by the motion constraint potential field between the tracking satellite and the target spacecraft. is the positive definite control gain matrix to be designed. Ask for information about The gradient, Ask for information about gradient.

[0175] The input of the auxiliary power system is given below The design process. First, define the Lyapunov candidate function as follows

[0176]

[0177] Derivative (26) and substitute relevant terms, we can get

[0178]

[0179] Taking the definite integral of the above formula in [0, t] we can get

[0180]

[0181] It is not difficult to find that formula (28) is a standard dissipation inequality, V is the energy storage function, is the input of the dissipative system, is the output of the dissipative system. That is, (18) constructs a arrive Passive mapping, V(t) and V(0) are the two endpoint values ​​of [0,t]. Then, by designing the input of the auxiliary power system, damping can be injected into the closed-loop system and the stability of the system can be guaranteed. Therefore, Designed as follows

[0182]

[0183] in, is a constant gain matrix.

[0184] According to the definition of adjoint operator (24) Expressed as:

[0185]

[0186] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely illustrative of the principles and applications of the invention. It should be understood that many modifications may be made to the illustrative embodiments, and that other arrangements may be devised, without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in ways other than those described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be used in conjunction with other described embodiments.

Claims

1. A 6DOF output feedback control method for spacecraft formation considering visibility constraints, characterized by: The method comprises the following steps: S1. Based on Lie group SE (3), the dynamic equations of the tracking satellite relative to the target spacecraft with space failure are established; S2, introduce the configuration error potential function to obtain the configuration error vector; S3. Establish visibility constraints: Construct a field of view constraint to ensure that the target is always in the field of view of the kth tracking star, and an inter-satellite line of sight occlusion avoidance constraint based on the maximum observation cross section; S3 establishes visibility constraints, which constructs a field of view constraint to ensure that the target is always in the field of view of the kth tracking star: Among them, α k represents the viewing angle, α k =arccos((x p ) T x k ), represents the desired LOS direction, Indicates The position vector of the next k-th tracking satellite relative to the target spacecraft, x k for The unit vector under is the half-apex angle of the camera field of view for tracking stars. f k >0, indicating that the target spacecraft is within the field of view of the tracking satellite; Among them, the intersatellite line of sight obstruction avoidance constraints established based on the maximum observation cross section are: Where, Indicates the indicator function for judging whether the line of sight is blocked, Where, A target spacecraft T and N tracking satellites with a total of N+1 ellipsoids are defined as an ellipsoidal spacecraft set R tj The j-th tracking star body coordinate system is The coordinate transformation matrix, The relative position vector of the j-th tracking satellite relative to the target spacecraft is The coordinates below, W kj represents a symmetric matrix, is the half-vertex angle of the camera field of view of the j-th tracking star, ε kj is a slack variable and 0≤ε kj ≤1; η kj =(x s ) T x c It is a prerequisite for avoiding the constraint of line of sight occlusion. represents the direction of the kth tracking star, represents the direction of the jth tracking star, when η kj When ≤0, h kj = 1, the kth tracking star and the jth tracking star are located on the opposite side of MOCS. At this time, there is no need to consider the line of sight between the kth tracking star and the jth tracking star. When h k >0, indicating that the kth tracking star does not block the view of the jth tracking star; S4. Design a potential function that satisfies the visibility constraint; S5. Establish an auxiliary power system based on Lie group SE(3); S6. Construct a 6DOF output feedback control law for spacecraft formation based on the auxiliary power system: Where: is the control quantity generated on the kth tracking satellite by the motion constraint potential field between the tracking satellite and the target spacecraft; Where: It means to find the gradient about (·), is the attitude error of the kth tracking satellite relative to the target spacecraft, represents the position error of the kth tracking satellite relative to the target spacecraft, is the expected attitude of the kth tracking satellite relative to the target spacecraft, is the expected position of the kth tracking satellite relative to the target spacecraft; (·) ∨ Represents mapping, mapping Indicates that The matrix in is mapped to the isomorphic real space V m represents the visibility constraint potential function; is an output feedback controller not related to the potential function, Where: k f 、k l is the positive definite control gain matrix to be designed, and represents the configuration error vector between the actual configuration and the desired configuration, Represents the configuration error vector of the auxiliary system relative to the actual motion system, represents the gravitational effect on the k-th tracking star, J k ,m k denote the moment of inertia and mass of the kth tracking star, respectively, and E3 denotes the third-order unit matrix; Ad g is the adjoint operator of the element g on the Lie group SE(3), ad ξ is the adjoint operator of ξ; express relatively speed, and Respectively Relative to rotational speed and translational speed.

2. The 6DOF output feedback control method for spacecraft formation considering visibility constraints according to claim 1, characterized in that: Adjoint operator Ad g 、ad ξ The matrix expression of is: (·) × Indicates the antisymmetric matrix. Any Any ξ=[ωv], where R∈SO(3) represents the rotation matrix, represents the rotation vector, represents the angular velocity of rotation, Indicates the translational velocity.

3. The 6DOF output feedback control method for spacecraft formation considering visibility constraints according to claim 2, characterized in that: The dynamic equation of the tracking satellite relative to the target spacecraft with space failure established based on Lie group SE (3) in S1 is the dynamic equation of the relative motion system, which is expressed as: Where: Where, Represents the coordinate system of the kth tracking star Relative to the target spacecraft body coordinate system The velocity vector, and Respectively Relative to The rotational speed and translational speed; R tk for arrive The coordinate transformation matrix, Indicates the relative position vector of the kth tracking satellite relative to the target spacecraft. The coordinates under R It Represents the target spacecraft body coordinate system To the Earth-centered inertial coordinate system The coordinate transformation matrix, and The target spacecraft and the kth tracking satellite are respectively in the target spacecraft body coordinate system The position vector under express relatively speed, and Respectively Relative to The rotational speed and translational speed; The gravitational effect on the kth tracking star represents the gravity term, The direction of this vector is from the center of the Earth to the center of mass of the target spacecraft or the kth tracking satellite. μ represents the Earth's gravitational constant, μ = 398600.47 km 3 / s 2 , R Ik Represents the coordinate system of the kth tracking star To the Earth-centered inertial coordinate system The coordinate transformation matrix, represents the external interference acting on the kth tracking satellite.

4. The 6DOF output feedback control method for spacecraft formation considering visibility constraints according to claim 3, characterized in that: The configuration error vector in S2 includes the configuration error vector between the actual configuration and the expected configuration and the configuration error vector of the auxiliary system relative to the actual motion system The configuration error vector between the actual configuration and the expected configuration Get it as follows: and Represent the relative attitude error vector and relative position error vector respectively; Configuration error vector of the auxiliary system relative to the actual motion system Get it as follows: Where R ak express To the coordinate system of the kth tracking star The coordinate transformation matrix, express Relative to The relative position vector is The coordinates below, Represents the coordinate system Estimates.

5. The 6DOF output feedback control method for spacecraft formation considering visibility constraints according to claim 4, characterized in that: The potential function V designed in S4 satisfies the visibility constraint m for: V m =φ ak +ψ k Among them, φ ak is the potential function for the field of view constraint between the kth tracking satellite and the target spacecraft on SE(3), Where, l ak is the normal number to be designed, represents the attitude error function between the kth tracking satellite and the target spacecraft, when When φ ak →∞, the kth tracking satellite will lose visibility of the target spacecraft; Among them, ψ k is the potential function for avoiding line of sight occlusion, Where, γ kj and κ kj is a positive constant, represents the position error function between the kth tracking satellite and the target spacecraft; When the kth tracking star blocks the line of sight between the jth tracking star and the target spacecraft, h kj →0,ψ kj →∞.

6. The 6DOF output feedback control method for spacecraft formation considering visibility constraints according to claim 5, characterized in that: Attitude error function between the kth tracking satellite and the target spacecraft for: Position error function between the kth tracking satellite and the target spacecraft for:

7. The 6DOF output feedback control method for spacecraft formation considering visibility constraints according to claim 6, characterized in that: The auxiliary power system based on Lie group SE(3) in S5 is used Relative to The kinematic equation is expressed as: Where, F ka represents the system matrix; Intermediate variables for Relative to The speed is The following expression.

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