Spacecraft near-approach maneuver tracking control method with observation and collision avoidance constraints

Abstract

The application discloses a spacecraft near-maneuver tracking control method of observation and collision avoidance constraints, comprising the following steps: establishing a relative kinematics and dynamics model by using a dual quaternion description; constructing observation line-of-sight constraints and collision avoidance safety constraints by using relative position and posture dual quaternions; designing an artificial potential function based on the two constraints; and further designing a near-maneuver tracking control law. The near-maneuver tracking control method can make a service spacecraft approach a target spacecraft under the condition of always satisfying observation and safety constraints, and finally keep stable tracking of the target spacecraft.

Description

Technical Field

[0001] This invention relates to the field of spacecraft target tracking and observation technology, specifically a spacecraft proximity maneuvering tracking control method with observation and collision avoidance constraints. Background Technology

[0002] Spacecraft proximity maneuvers are generally defined as the maneuvers by which an on-orbit spacecraft approaches another on-orbit object. Proximity maneuvers are a crucial prerequisite for carrying out on-orbit servicing missions, such as surveillance, capture, refueling, facility maintenance, and debris removal. All these operations require the establishment of a suitable relative motion state based on actively controlled proximity maneuvers. Spacecraft proximity maneuver control is a key core technology for ensuring the safety, efficiency, and precision of the approach process, attracting significant attention in both theoretical research and engineering design. During maneuvering and tracking, spacecraft exhibit strong coupling characteristics of attitude rotation and center-of-mass translation. Especially when the distance between them is short and the target is large, efficient simultaneous control and adjustment of relative position and attitude are necessary to ensure spacecraft safety and meet mission constraints. Proximity maneuvers involve more than just flying near the target; they often involve performing specific tasks such as observation, docking, and refueling. The actuators installed on the tracking spacecraft also impose specific constraints on its position and attitude.

[0003] Typically, solving the rotational-translational coupling control problem in near-maneuvering requires starting with relative motion modeling, followed by control law design. Rotational-translational coupling stems from the close relationship between the forces / torques acting on the spacecraft and its position / attitude; the translational motion of the center of mass and attitude motion interact with each other. Currently, the practical needs of space missions are driving the continued development of near-maneuvering mission design and control. Existing research results have effectively promoted the on-orbit application of near-maneuvering. On the one hand, the simultaneous coordinated control of relative position and attitude remains a key focus; on the other hand, the safety of the spacecraft's relative motion and specific mission requirements are also commonly considered factors. Therefore, an improved technology is urgently needed to address the problems existing in current technologies. Summary of the Invention

[0004] The purpose of this invention is to provide a spacecraft proximity maneuver tracking control method with observation and collision avoidance constraints to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a spacecraft proximity maneuvering tracking control method with observation and collision avoidance constraints, characterized in that: the spacecraft proximity maneuvering tracking control method includes:

[0006] A relative kinematics and dynamics model is established using dual quaternions.

[0007] Construct observation line constraints and collision avoidance safety constraints using relative pose dual quaternions;

[0008] Based on the design of the artificial potential function and the near-maneuver tracking control law.

[0009] Preferably, the 6-DOF kinematic equations of the service spacecraft relative to the target spacecraft, represented by the dual quaternions, are as follows:

[0010]

[0011] Preferably, the 6-DOF dynamic equations of the service spacecraft relative to the target spacecraft, represented by the dual quaternions, are as follows:

[0012]

[0013] Preferably, in the design of constructing the observation line-of-sight constraint using relative pose dual quaternions, the camera axis is aligned with the service spacecraft body coordinate system. S -x S y S z S o S z S With the axes coinciding, the vertex N of the observed cone's envelope is the intersection point of the lens surface and the camera axis, represented by coordinates (0, 0, z). N ) T Let N represent the position coordinates. The observation envelope of the camera is an infinitely high cone, and its half field of view is represented by θ.

[0014] The target spacecraft moves within the camera's field of view, and the envelope is designed as a perfect sphere. Considering the target's appearance, the new observation envelope can be viewed as the boundary of the field of view along o. S z S The vertex of the new observation envelope, obtained by axial translation, is denoted by N′, and its position coordinates are (0,0,z). N +R T / sinθ) T Target centroid o T In volume coordinate system o S -x S y S z S The motion envelope equation in the equation is:

[0015]

[0016] In the formula, z N′ =z N +R T / sinθ;

[0017] To make o T Always within the new envelope, requires satisfy:

[0018]

[0019] In the formula, U = diag(1,1,0);

[0020] In equation (4), for The function, and using β FOV >0 is the center of mass of the target spacecraft. T Position constraints, further limiting β FOV Represented as q S / T function β FOV =β FOV (q S / T The specific derivation is as follows:

[0021]

[0022] In the formula, Indicates by The generated quaternions further include:

[0023]

[0024] In the formula, From equations (5) and (6), we obtain:

[0025]

[0026] In the formula, Since it is a symmetric matrix, we further obtain:

[0027]

[0028] Combining equations (4), (7), and (8), we get:

[0029]

[0030] In the formula, Equation (9) is the dual quaternion q S / T The observation line of sight is constrained.

[0031] Preferably, the design for constructing collision avoidance safety constraints using relative pose dual quaternions employs a perfect sphere as the envelope of the service spacecraft and the target spacecraft, with sphere radii R and R, respectively. S and R T , with The function represents the condition under which the two spacecraft will not collide:

[0032]

[0033] Further β CA Represented as qS / T The function yields:

[0034]

[0035] Equation (11) is the dual quaternion q S / T This indicates the collision avoidance safety constraints.

[0036] Preferably, the artificial potential function based on constraint design is a combination of an attractive potential function and a repulsive potential function. The attractive potential function takes the desired state as its global minimum, and its negative gradient can drive the system's relative motion state to move towards the desired state, as detailed below:

[0037]

[0038] In the formula, k a >0 is a custom coefficient.

[0039] The repulsive potential function increases as the system's relative motion state approaches the constraint boundary, and takes an infinite value at the boundary, ensuring that the system's relative motion state can never cross the boundary, thus guaranteeing that the system's relative motion state satisfies the constraint requirements, as detailed below:

[0040]

[0041] In the formula, k r >0 is a user-defined coefficient;

[0042] Further, based on equations (12) and (13), the global situation function is designed as follows:

[0043]

[0044] Due to the introduction of the repulsive potential function As a product term, the global situation function remains in q D / T It has a local minimum at a certain point, and the global situation function V p Satisfy: for any q S / T All have V p ≥0; when q S / T =q D / T At that time, V p =0.

[0045] Preferably, the design of the proximity maneuver tracking control law requires the use of The calculation is as follows:

[0046]

[0047] In the formula, and The calculation is as follows:

[0048]

[0049] Preferably, the design of the proximity maneuver tracking control law requires a potential function V. p It is a convex function, which can be verified by calculating its Hessian matrix:

[0050]

[0051] In the formula, the matrix and β FOV and β CA Regarding q S / T The Hessian matrix;

[0052] From equation (17), it can be seen that the first two terms on the right side of the equation are positive definite matrices, while the positive definiteness of the last two terms cannot be determined. FOV >0 and β CA In the 6-DOF motion space defined by >0, All scalars or matrix components contained in the equation are finite values, and the first term on the right-hand side of equation (17) contains a constant coefficient k. a The last three terms contain a constant coefficient k. r According to matrix theory, when k a >>k r hour, It is always a positive definite matrix, thus guaranteeing V. p It is q S / T A convex function.

[0053] Preferably, the design of the proximity maneuver tracking control law is as follows:

[0054]

[0055] In the formula, k p >0 and k d >0 is a constant coefficient. Under the near-maneuver tracking control law (18), the relative motion state of the system will converge and stabilize to the desired state, that is... and Furthermore, the movement satisfies the observation line-of-sight constraint while effectively avoiding collisions, i.e., β FOV >0 and β CA >0 is always true.

[0056] Compared with the prior art, the beneficial effects of the present invention are:

[0057] The approach maneuver tracking control law included in this method enables the servicing spacecraft to approach the target spacecraft while always meeting observation and safety constraints, and ultimately maintain stable tracking of it. Attached Figure Description

[0058] Figure 1 The flowchart of the proximity maneuver pose tracking control for this invention takes into account observation and collision avoidance constraints;

[0059] Figure 2 A schematic diagram illustrating the line-of-sight constraint of the spacecraft used for observing the target spacecraft in this invention;

[0060] Figure 3 For the present invention o S -x S z S A schematic diagram of the field of view boundary on a plane;

[0061] Figure 4 Images showing the attitude change of the spacecraft relative to the target spacecraft for this invention;

[0062] Figure 5 Images showing the positional changes of the spacecraft relative to the target spacecraft, serving the purpose of this invention;

[0063] Figure 6 Images showing the change in angular velocity of the spacecraft relative to the target spacecraft, used in this invention;

[0064] Figure 7 The image showing the change in linear velocity of the spacecraft relative to the target spacecraft is provided for this invention.

[0065] Figure 8 The three-dimensional trajectory image of the spacecraft relative to the target spacecraft is provided for the purposes of this invention;

[0066] Figure 9 β is the constraint quantity of this invention. FOV and β CA The changing image;

[0067] Figure 10 This is a graph showing the change in the active control torque of the present invention;

[0068] Figure 11 This is a graph showing the change in the active control force of the present invention. Detailed Implementation

[0069] 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 only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0070] Please see Figure 1-11This invention provides a technical solution: a spacecraft proximity maneuvering tracking control method with observation and collision avoidance constraints, characterized in that: the spacecraft proximity maneuvering tracking control method includes:

[0071] A relative kinematics and dynamics model is established using dual quaternions.

[0072] Construct observation line constraints and collision avoidance safety constraints using relative pose dual quaternions;

[0073] Based on the design of the artificial potential function and the near-maneuver tracking control law.

[0074] The 6-DOF kinematic equations of the service spacecraft relative to the target spacecraft, represented in dual quaternion form, are:

[0075]

[0076] The 6-DOF dynamic equations of the service spacecraft relative to the target spacecraft, represented in dual quaternion form, are as follows:

[0077]

[0078] In the design of constructing observation line-of-sight constraints using relative pose dual quaternions, the camera axis is aligned with the service spacecraft body coordinate system. S -x S y S z S o S z S With the axes coinciding, the vertex N of the observed cone's envelope is the intersection point of the lens surface and the axis, represented by coordinates (0, 0, z). N ) T Let N represent the position coordinates. The observation envelope of the camera is an infinitely high cone, and its half field of view is represented by θ.

[0079] The target spacecraft moves within the camera's field of view, and the envelope is designed as a perfect sphere. Considering the target's appearance, the new observation envelope can be viewed as the boundary of the field of view along o. S z S The vertex of the new observation envelope, obtained by axial translation, is denoted by N′, and its position coordinates are (0,0,z). N +R T / sinθ) T Target centroid o T In volume coordinate system o S -x S y S z S The motion envelope equation in the equation is:

[0080]

[0081] In the formula, zN′ =z N +R T / sinθ;

[0082] To make o T Always within the new envelope, requires satisfy:

[0083]

[0084] In the formula, U = diag(1,1,0);

[0085] In equation (4), for The function, and using β FOV >0 is the center of mass of the target spacecraft. T Position constraints, further limiting β FOV Represented as q S / T function β FOV =β FOV (q S / T The specific derivation is as follows:

[0086]

[0087] In the formula, Indicates by The generated quaternions further include:

[0088]

[0089] In the formula, From equations (5) and (6), we obtain:

[0090]

[0091] In the formula, Since it is a symmetric matrix, we further obtain:

[0092]

[0093] Combining equations (4), (7), and (8), we get:

[0094]

[0095] In the formula, Equation (9) is the dual quaternion q S / T The observation line of sight is constrained.

[0096] In the design of collision avoidance safety constraints using relative pose dual quaternions, a perfect sphere is used as the envelope of the service spacecraft and the target spacecraft, with radii R and R, respectively.S and R T , with The function represents the condition under which the two spacecraft will not collide:

[0097]

[0098] Further β CA Represented as q S / T The function yields:

[0099]

[0100] Equation (11) is the dual quaternion q S / T This indicates the collision avoidance safety constraints.

[0101] The artificial potential function based on constraint design is a combination of an attractive potential function and a repulsive potential function. The attractive potential function takes the desired state as its global minimum, and its negative gradient can drive the system's relative motion state to shift towards the desired state, as detailed below:

[0102]

[0103] In the formula, k a >0 is a custom coefficient.

[0104] The repulsive potential function increases as the system's relative motion state approaches the constraint boundary, and takes an infinite value at the boundary, ensuring that the system's relative motion state can never cross the boundary, thus guaranteeing that the system's relative motion state satisfies the constraint requirements, as detailed below:

[0105]

[0106] In the formula, k r >0 is a user-defined coefficient;

[0107] Further, based on equations (12) and (13), the global situation function is designed as follows:

[0108]

[0109] Due to the introduction of the repulsive potential function As a product term, the global situation function remains in q D / T It has a local minimum at a certain point, and the global situation function V p Satisfy: for any q S / T All have V p ≥0; when q S / T =q D / T At that time, V p =0.

[0110] In the design of the near-maneuver tracking control law, it is necessary to use The calculation is as follows:

[0111]

[0112] In the formula, and The calculation is as follows:

[0113]

[0114] In the design of the near-maneuver tracking control law, a potential function V is required. p It is a convex function, which can be verified by calculating its Hessian matrix:

[0115]

[0116] In the formula, the matrix and β FOV and β CA Regarding q S / T The Hessian matrix;

[0117] From equation (17), it can be seen that the first two terms on the right side of the equation are positive definite matrices, while the positive definiteness of the last two terms cannot be determined. FOV >0 and β CA In the 6-DOF motion space defined by >0, All scalars or matrix components contained in the equation are finite values, and the first term on the right-hand side of equation (17) contains a constant coefficient k. a The last three terms contain a constant coefficient k. r According to matrix theory, when k a >>k r hour, It is always a positive definite matrix, thus guaranteeing V. p It is q S / T A convex function.

[0118] The design of the proximity maneuver tracking control law is as follows:

[0119]

[0120] In the formula, k p >0 and k d >0 is a constant coefficient. Under the near-maneuver tracking control law (18), the relative motion state of the system will converge and stabilize to the desired state, that is... and Furthermore, the movement satisfies the observation line-of-sight constraint while effectively avoiding collisions, i.e., β FOV >0 and β CA >0 is always true.

[0121] Furthermore, to prove the stability of the relative motion system under the proximity maneuver tracking control law (18), consider the following candidate Lyapunov function:

[0122]

[0123] EJE = diag(J) can be calculated. M J m Since EJE is clearly a symmetric positive definite matrix, then for any... All If and only if hour, Therefore, V≥0 for any q S / T and It holds true if and only if q S / T =q D / T and When V = 0, the derivative of V with respect to time is calculated as follows:

[0124] Substituting equations (1), (2), and (18) into (20) yields:

[0125] The following calculations are performed by combining some terms in equation (21):

[0126]

[0127] as well as

[0128] Based on equations (22) and (23), equation (21) is simplified to:

[0129] Therefore, It is valid if and only if hour,

[0130] Since V≥0 and Then V and related quantities V p q S / T and Both are bounded, and It exists. V p Boundedness indicates that when t≥0, β FOV ≠0 and β CA The condition ≠ 0 always holds true. Therefore, as long as the initial relative pose satisfies the constraint requirement, i.e., β... FOV (t=0)>0 and β CA (t=0)>0, since the constraint function changes continuously with time, then β FOV (t)>0 and β CA(t)>0 always holds, meaning that the relative pose of the two spacecraft will always meet the requirements of observation and collision avoidance constraints. Integrating both sides of equation (24) and taking the limit, since V(0) is bounded, If it exists, then It exists, and according to the Barbarath lemma, we can obtain... Further V p q S / T and Both are bounded, as can be obtained from equation (2). Bounded, differentiate equation (2), and then combine... Bounded, obtained If it is bounded, then Uniformly continuous, we can obtain using the Barbarat lemma. Finally, the dynamic equation (2) and the proximity maneuver tracking control law (18) are combined, and... and It can be obtained Further derivation can be obtained

[0131] Therefore, the proximity maneuvering tracking control law included in this method can stabilize the relative motion system, ensuring that the servicing spacecraft approaches the target spacecraft while always meeting observation and safety constraints, and ultimately maintains stable tracking of it.

[0132] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A spacecraft close-proximity maneuver tracking control method with observation and collision avoidance constraints, characterized in that: The spacecraft proximity maneuvering tracking control method comprises: The relative kinematics and dynamics models are established by using dual quaternion description, and the 6-DOF kinematics equation of the service spacecraft relative to the target spacecraft represented by dual quaternion is as follows: The 6-DOF dynamics equation of the service spacecraft represented by dual quaternions with respect to the target spacecraft is The observation line-of-sight constraint is constructed using relative pose dual quaternions, with the camera axis aligned with the service spacecraft body coordinate system. S -x S y S z S o S z S With the axes coinciding, the vertex N of the observed cone's envelope is the intersection point of the lens surface and the camera axis, represented by coordinates (0, 0, z). N ) T The position coordinates of point N are represented by θ. The camera's observation envelope is an infinitely high cone, and its half-field of view is denoted by θ. The target spacecraft moves within the camera's field of view, and the envelope is designed as a perfect sphere. Considering the target's appearance, the new observation envelope can be regarded as the field of view boundary along θ. S z S The vertex of the new observation envelope, obtained by axial translation, is denoted by N′, and its position coordinates are (0,0,z). N +R T / sinθ) T Target centroid o T In volume coordinate system o S -x S y S z S The motion envelope equation in the equation is: where z N′ = z N + R T / sin θ; so that o T is always within the new envelope, it is necessary that the following is satisfied: In the formula, U = diag(1,1,0); In equation (4), for The function, and using β FOV >0 is the center of mass of the target spacecraft. T Position constraints, further limiting β FOV Represented as q S / T function β FOV =β FOV (q S / T The derivation is as follows: wherein represents a quaternion generated by the vector v, further having: wherein From equations (5) and (6) we get: wherein is a symmetric matrix, and further that Combined with equations (4), (7) and (8), the following equation is obtained: wherein Formula (9) is a dual quaternion q S / T the observation line-of-sight constraint represented by The relative pose dual quaternion is used to construct the safety constraint of collision avoidance. The regular sphere is used as the envelope of the service spacecraft and the target spacecraft, and the radii of the spheres are R S and R T , respectively. The function containing is used to represent the condition that the two spacecrafts will not collide. Further, β CA is expressed as a function of q S / T , we obtain: Formula (11) is a dual quaternion q S / T collision avoidance safety constraints The artificial potential function is designed based on the two constraints, and the proximity maneuvering tracking control law is obtained.

2. The spacecraft close proximity maneuver tracking control method with observation and collision avoidance constraints according to claim 1, characterized in that: The observation line-of-sight constraint and the collision avoidance safety constraint, the artificial potential function is designed based on the two constraints, the artificial potential function is a combination of attractive potential function and repulsive potential function, the attractive potential function takes the expected state as the global minimum value, and the negative gradient can drive the system relative motion state to move to the expected state, and the specific is as follows: wherein k a >0 is a user-defined coefficient, The repulsive potential function increases with the system relative motion state approaching the constraint boundary, and takes infinite value on the boundary, so that the system relative motion state cannot cross the boundary, thereby ensuring that the system relative motion state meets the constraint requirement, and the specific is as follows: wherein k r >0 is a custom coefficient; Further according to equations (12) and (13), the global potential function is designed as follows: Introducing As a product term, the global potential function still has a minimum at q D / T The global potential function V p satisfies: for any q S / T , V p ≥ 0; when q S / T = q D / T , V p = 0.

3. The spacecraft close proximity maneuver tracking control method with observation and collision avoidance constraints according to claim 2, characterized in that: the global potential function, which is calculated as follows: wherein and are calculated as follows: obtained For the design of the near motor tracking control law.

4. The spacecraft close proximity maneuver tracking control method with observation and collision avoidance constraints according to claim 3, characterized in that: The global potential function, which needs to be convex, is based on The Hessian matrix is computed to verify it: where the matrix and are respectively β FOV and β CA . The Hessian matrix of q S / T ; as can be seen from equation (17), the first two terms on the right side are positive definite matrices, and the last two terms cannot be determined as positive definite matrices, when β FOV > 0 and β CA > 0, all the scalar or matrix components contained in the equation (17) are finite values, the first term on the right side contains a constant coefficient k a , and the last three terms contain a constant coefficient k r , according to the matrix theory, when k a > k r , is always a positive definite matrix, thereby ensuring that V p is a convex function of q S / T .

5. The spacecraft close proximity maneuver tracking control method with observation and collision avoidance constraints according to claim 3, wherein: The near-miss maneuver tracking control law is based on And designed, as follows: where k p >0 and k d >0 are constant coefficients, under the near- miss control law (18), the relative motion state of the system will converge and stabilize to the desired state, i.e. and and the observation line-of-sight constraint is satisfied during the motion, while effectively avoiding collision, i.e. β FOV >0 and β CA >0 always hold.

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