Spacecraft approaching maneuver tracking control method based on observation and collision avoidance constraint

Abstract

The invention discloses a spacecraft approaching maneuver tracking control method based on observation and collision avoidance constraints, and the method comprises the steps: employing dual quaternion description to establish a relative kinematics and dynamics model, employing a relative pose dual quaternion to construct an observation sight line constraint and a collision avoidance safety constraint, designing an artificial potential function based on the two constraints, and carrying out the calculation of the artificial potential function. A near maneuver tracking control law is further designed, and the provided near maneuver tracking control method can enable the service spacecraft to approach the target spacecraft under the condition that observation and safety constraints are met all the time and finally keep stable tracking of the target spacecraft.

Description

Technical Field

[0001] The invention relates to the technical field of spacecraft tracking and observing targets, and in particular to a spacecraft proximity maneuver tracking control method with observation and collision avoidance constraints. Background Art

[0002] Spacecraft proximity maneuvers are usually defined as operations in which an on-orbit spacecraft flies close to another on-orbit object. Proximity maneuvers are a crucial prerequisite for implementing on-orbit service missions, such as monitoring, capture, refueling, facility maintenance, and debris removal. All of these operations require the construction of appropriate relative motion states based on actively controlled proximity maneuvers. Spacecraft proximity maneuver control is a key core technology to ensure the safety, efficiency, and accuracy of the approach process, and has attracted attention and attention in both theoretical research and engineering design. During the maneuver tracking process, the spacecraft has the strong coupling characteristics of attitude rotation and center of mass translation. Especially when the distance is short and the target volume is large, it is necessary to efficiently control and adjust the relative position and attitude simultaneously to ensure the safety of the spacecraft and meet the mission constraints. Proximity maneuvers are not just flying near the target, but usually also performing certain specific tasks, such as observation, docking, and refueling. The actuators installed on the tracking spacecraft will also have specific constraints on the position and attitude.

[0003] Generally speaking, solving the rotational and translational coupling control problem in close proximity maneuvers requires starting with relative motion modeling, followed by control law design. The rotational and translational coupling comes from the fact that the forces / torques on the spacecraft are closely related to the position / attitude, resulting in the mutual influence of the center of mass translation and attitude motion. At present, the actual needs of space missions drive the design and control of close proximity maneuvers to continue to move forward. Existing research results have effectively promoted the on-orbit application of close proximity maneuvers. On the one hand, the simultaneous coordinated control of relative position and attitude is still the focus of attention. On the other hand, the safety of the relative motion of the spacecraft and specific mission requirements are also commonly considered factors. Therefore, an improved technology is urgently needed to solve the problems existing in the existing technology. Summary of the invention

[0004] The object of the present invention is to provide a spacecraft proximity maneuver tracking control method with observation and collision avoidance constraints to solve the problems raised in the above-mentioned background technology.

[0005] To achieve the above object, the present invention provides the following technical solution: a spacecraft approaching maneuver tracking control method with observation and collision avoidance constraints, characterized in that: the spacecraft approaching maneuver tracking control method comprises:

[0006] The relative kinematics and dynamics models were established using dual quaternion description;

[0007] The relative position and posture dual quaternion is used to construct the observation line of sight constraint and collision avoidance safety constraint;

[0008] Artificial potential function and proximity maneuver tracking control law are designed based on constraints.

[0009] Preferably, the 6-DOF kinematic equation of the service spacecraft relative to the target spacecraft represented by the dual quaternion is:

[0010]

[0011] Preferably, the 6-DOF dynamic equation of the service spacecraft relative to the target spacecraft represented by the dual quaternion is:

[0012]

[0013] Preferably, in the design of constructing the observation line of sight constraint using the relative posture dual quaternion, the camera axis and the service spacecraft body coordinate system o S -x S y S z S o S z S The axes coincide, and the vertex N of the cone envelope is the intersection point of the lens surface and the axis, with coordinates (0,0,z N ) T represents the position coordinates of point N. The observation envelope of the camera is a cone of infinite height, and its half field of view angle is represented by θ;

[0014] The target spacecraft moves in the camera field of view. The envelope is designed as a perfect sphere. The new envelope considering the appearance can be regarded as the boundary of the field of view along o S z S The vertex of the new envelope is represented by N′, and its position coordinates are (0,0,z N +R T / sinθ) T , target centroid o T In the body coordinate system o S -x S y S z S The motion envelope equation in is:

[0015]

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

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

[0018]

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

[0020] In equation (4), for function, and use β FOV >0 as the target spacecraft mass center o T The position constraint of 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, Indicated by The generated quaternion is further:

[0023]

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

[0025]

[0026] In the formula, is a symmetric matrix, and we can further obtain:

[0027]

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

[0029]

[0030] In the formula, Formula (9) is the dual quaternion q S / T Represents the field of view constraint.

[0031] Preferably, in the design of constructing collision avoidance safety constraints using relative posture dual quaternions, a perfect sphere is used as the envelope of the service spacecraft and the target spacecraft, and the sphere radii are R S and R T , with The function represents the condition that the two spacecraft will not collide:

[0032]

[0033] Further β CA Represented as q S / TThe function of , we get:

[0034]

[0035] Formula (11) is the dual quaternion q S / T Represents the collision avoidance safety constraint.

[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 the global minimum, and its negative gradient can drive the system state to move toward the desired state, as follows:

[0037]

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

[0039] The repulsive potential function increases as it approaches the constraint boundary and takes an infinite value on the boundary, so that the system motion state can never cross the boundary, thereby ensuring that the state meets the constraint requirements, as follows:

[0040]

[0041] In the formula, k r >0 is a custom coefficient;

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

[0043]

[0044] Since the repulsive potential function is introduced As a product term, the global situation function is still in q D / T There is a minimum value at the global situation function V p Satisfies: For any q S / T , both have V p ≥0; when q S / T =q D / T When V p =0.

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

[0046]

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

[0048]

[0049] Preferably, in the design of the proximity 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:

[0050]

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

[0052] It can be seen from formula (17) that the first two terms on the right side of the equal sign are positive definite matrices, and the last two matrices cannot be determined to be positive definite. FOV >0 and β CA >0 in the 6-DOF motion space, All scalar or matrix components contained in are always finite values, and the first term on the right side of equation (17) contains a constant coefficient k a , the last three terms contain constant coefficient k r According to matrix theory, when k a >>k r hour, is always a positive definite matrix, thus ensuring that V p Yes S / T Convex function of .

[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 control law (18), the relative motion state of the system will converge and stabilize to the desired state, that is, and And the line of sight observation constraint is satisfied during the movement, and collision can be effectively avoided, that is, β FOV >0 and β CA >0 is always true.

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] The control law included in this method can enable the service spacecraft to approach the target spacecraft while always satisfying observation and safety constraints, and ultimately maintain stable tracking of it. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1The present invention is a flow chart of the tracking control of the approaching maneuvering posture considering the observation and collision avoidance constraints;

[0059] Figure 2 A schematic diagram of the field of view constraints for the service spacecraft of the present invention to observe the target spacecraft;

[0060] Figure 3 For the present invention S -x S z S Schematic diagram of the field of view boundary cross section on a plane;

[0061] Figure 4 An image of attitude changes of the spacecraft relative to the target serving the present invention;

[0062] Figure 5 An image of the position change of the spacecraft relative to the target serving the present invention;

[0063] Figure 6 An image of the angular velocity variation of the spacecraft relative to the target serving the present invention;

[0064] Figure 7 An image of the linear velocity variation of the spacecraft relative to the target serving the present invention;

[0065] Figure 8 A three-dimensional trajectory image of the spacecraft relative to the target serving the present invention;

[0066] Fig. 9 is the constraint amount β of the present invention FOV and β CA The changing image;

[0067] Fig.10 It is the changing image of the active control torque of the present invention;

[0068] Fig.11 This is a graph showing the change in active control force of the present invention. DETAILED DESCRIPTION

[0069] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. 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 creative work are within the scope of protection of the present invention.

[0070] See also Figure 1-11 The present invention provides a technical solution: a spacecraft approaching maneuver tracking control method with observation and collision avoidance constraints, characterized in that: the spacecraft approaching maneuver tracking control method comprises:

[0071] The relative kinematics and dynamics models were established using dual quaternion description;

[0072] The relative position and posture dual quaternion is used to construct the observation line of sight constraint and collision avoidance safety constraint;

[0073] Artificial potential function and proximity maneuver tracking control law are designed based on constraints.

[0074] The 6-DOF kinematic equation of the service spacecraft relative to the target spacecraft expressed by the dual quaternion is:

[0075]

[0076] The 6-DOF dynamic equation of the service spacecraft relative to the target spacecraft expressed by dual quaternion is:

[0077]

[0078] In the design of constructing observation line of sight constraint using relative pose dual quaternion, the camera axis and the service spacecraft body coordinate system o S -x S y S z S o S z S The axes coincide, and the vertex N of the cone envelope is the intersection point of the lens surface and the axis, with coordinates (0,0,z N ) T represents the position coordinates of point N. The observation envelope of the camera is a cone of infinite height, and its half field of view angle is represented by θ;

[0079] The target spacecraft moves in the camera field of view. The envelope is designed as a perfect sphere. The new envelope considering the appearance can be regarded as the boundary of the field of view along o S z S The vertex of the new envelope is represented by N′, and its position coordinates are (0,0,z N +R T / sinθ) T , target centroid o T In the body coordinate system o S -x S y S z S The motion envelope equation in is:

[0080]

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

[0082] To make o TAlways within the new envelope, need satisfy:

[0083]

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

[0085] In equation (4), for function, and use β FOV >0 as the target spacecraft mass center o T The position constraint of 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, Indicated by The generated quaternion is further:

[0088]

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

[0090]

[0091] In the formula, is a symmetric matrix, and we can further obtain:

[0092]

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

[0094]

[0095] In the formula, Formula (9) is the dual quaternion q S / T Represents the field of view constraint.

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

[0097]

[0098] Further β CA Represented as q S / T The function of , we get:

[0099]

[0100] Formula (11) is the dual quaternion q S / T Represents the collision avoidance safety constraint.

[0101] The artificial potential function based on constraint design is a combination of the attractive potential function and the repulsive potential function. The attractive potential function takes the desired state as the global minimum, and its negative gradient can drive the system state to move toward the desired state, as follows:

[0102]

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

[0104] The repulsive potential function increases as it approaches the constraint boundary and takes an infinite value on the boundary, so that the system motion state can never cross the boundary, thereby ensuring that the state meets the constraint requirements, as follows:

[0105]

[0106] In the formula, k r >0 is a custom coefficient;

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

[0108]

[0109] Since the repulsive potential function is introduced As a product term, the global situation function is still in q D / T There is a minimum value at the global situation function V p Satisfies: For any q S / T , both have V p ≥0; when q S / T =q D / T When V p =0.

[0110] In the design of the close 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 close-in maneuver tracking control law, the 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 About q S / T The Hessian matrix of

[0117] It can be seen from formula (17) that the first two terms on the right side of the equal sign are positive definite matrices, and the last two matrices cannot be determined to be positive definite. FOV >0 and β CA >0 in the 6-DOF motion space, All scalar or matrix components contained in are always finite values, and the first term on the right side of equation (17) contains a constant coefficient k a , the last three terms contain constant coefficient k r According to matrix theory, when k a >>k r hour, is always a positive definite matrix, thus ensuring that V p Yes S / T Convex function of .

[0118] The design of the approaching 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 control law (18), the relative motion state of the system will converge and stabilize to the desired state, that is, and And the line of sight observation constraint is satisfied during the movement, and collision can be effectively avoided, that is, β FOV >0 and β CA >0 is always true.

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

[0122]

[0123] It can be calculated that EJE = diag(JM ,J m ), obviously EJE is a symmetric positive definite matrix, then for any Both 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]

[0125] Substituting equations (1), (2) and (18) into (20) we obtain:

[0126]

[0127] The combined calculation of some terms in equation (21) is as follows:

[0128]

[0129] as well as

[0130]

[0131] According to equations (22) and (23), equation (21) is simplified to:

[0132]

[0133] Thus there is Established if and only if hour,

[0134] Since V ≥ 0 and V and the quantity V related to it p ,q S / T and are bounded, and Existence. p Bounded means that when t ≥ 0, β FOV ≠0 and β CA ≠0 is always true. Therefore, as long as the initial relative posture meets the constraint requirements, that is, β FOV (t=0)>0 and β CA (t=0)>0, since the constraint function changes continuously with time, β FOV (t)>0 and β CA(t)>0 always holds true, that is, the relative position of the two spacecraft will always meet the requirements of observation and collision avoidance constraints. Integrate both sides of equation (24) and take the limit. Since V(0) is bounded, If exists, Exists, according to Barbarat's lemma, Further V p ,q S / T and are all bounded, and from equation (2) we can get Bounded, take the derivative of equation (2), and then combine Bounded, obtained If bounded, Uniform continuity, using Barbarat's lemma, we can get Finally, the dynamic equation (2) and the control input (18) are combined to obtain and get It can be further deduced that

[0135] Therefore, the control law contained in this method can stabilize the relative motion system, ensure that the service spacecraft approaches the target spacecraft while always satisfying the observation and safety constraints, and ultimately maintain stable tracking of it.

[0136] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A spacecraft approaching maneuver tracking control method with observation and collision avoidance constraints, characterized by: The spacecraft proximity maneuver tracking control method comprises: The relative kinematic and dynamic models were established using dual quaternion description; The relative position and posture dual quaternion is used to construct the observation line of sight constraint and collision avoidance safety constraint; Artificial potential function and proximity maneuver tracking control law are designed based on constraints.

2. The spacecraft approaching maneuver tracking control method with observation and collision avoidance constraints according to claim 1, characterized in that: The 6-DOF kinematic equation of the service spacecraft relative to the target spacecraft expressed by the dual quaternion is:

3. The spacecraft approaching maneuver tracking control method with observation and collision avoidance constraints according to claim 1, characterized in that: The 6-DOF dynamic equation of the service spacecraft relative to the target spacecraft expressed by the dual quaternion is:

4. The spacecraft approaching maneuver tracking control method with observation and collision avoidance constraints according to claim 1, characterized in that: In the design of constructing the observation line of sight constraint using relative pose dual quaternion, the camera axis and the service spacecraft body coordinate system o S -x S y S z S o S z S The axes coincide, and the vertex N of the cone envelope is the intersection point of the lens surface and the axis, with coordinates (0,0,z N ) T represents the position coordinates of point N. The observation envelope of the camera is a cone of infinite height, and its half field of view angle is represented by θ; The target spacecraft moves in the camera field of view. The envelope is designed as a perfect sphere. The new envelope considering the appearance can be regarded as the boundary of the field of view along o S z S The vertex of the new envelope is represented by N′, and its position coordinates are (0,0,z N +R T / sinθ) T , target centroid o T In the body coordinate system o S -x S y S z S The motion envelope equation in is: where z N′ = z N + R T / sinθ; To make o T Always within the new envelope, need satisfy: In the formula, U = diag(1,1,0); In equation (4), for function, and use β FOV >0 as the target spacecraft mass center o T The position constraint of β FOV Represented as q S / T Function β FOV =β FOV (q S / T ), the specific derivation is as follows: In the formula, Indicated by The generated quaternion is further: In the formula, From equations (5) and (6), we can obtain: In the formula, is a symmetric matrix, and we can further obtain: Combining equations (4), (7) and (8) we obtain: In the formula, Formula (9) is the dual quaternion q S / T Represents the field of view constraint.

5. The method for tracking and controlling a spacecraft approaching maneuver with observation and collision avoidance constraints according to claim 1, characterized in that: In the design of using relative posture dual quaternion to construct collision avoidance safety constraints, a perfect sphere is used as the envelope of the service spacecraft and the target spacecraft, and the sphere radius is R S and R T , with The function represents the condition that the two spacecraft will not collide: Further β CA Represented as q S / T The function of , we get: Formula (11) is the dual quaternion q S / T Represents the collision avoidance safety constraint.

6. The spacecraft approaching maneuver tracking control method with observation and collision avoidance constraints according to claim 1, characterized in that: 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 the global minimum, and its negative gradient can drive the system state to move toward the desired state, as follows: In the formula, k a >0 is a custom coefficient, The repulsive potential function increases as it approaches the constraint boundary and takes an infinite value on the boundary, so that the system motion state can never cross the boundary, thereby ensuring that the state meets the constraint requirements, as follows: In the formula, k r >0 is a custom coefficient; Further, according to equations (12) and (13), the global situation function is designed as follows: Since the repulsive potential function is introduced As a product term, the global situation function is still in q D / T There is a minimum value at the global situation function V p Satisfies: For any q S / T , both have V p ≥0; when q S / T =q D / T When V p =0.

7. The spacecraft approaching maneuver tracking control method with observation and collision avoidance constraints according to claim 1, characterized in that: In the design of the approaching maneuver tracking control law, it is necessary to use The calculation is as follows: In the formula, and The calculation is as follows:

8. The method for tracking and controlling a spacecraft approaching maneuver with observation and collision avoidance constraints according to claim 1, characterized in that: In the design of the close-in maneuver tracking control law, the potential function V p It is a convex function, which can be verified by calculating its Hessian matrix: In the formula, the matrix and They are β FOV and β CA About q S / T The Hessian matrix of It can be seen from formula (17) that the first two terms on the right side of the equal sign are positive definite matrices, and the last two matrices cannot be determined to be positive definite. FOV >0 and β CA >0 in the 6-DOF motion space, All scalar or matrix components contained in are always finite values, and the first term on the right side of equation (17) contains a constant coefficient k a , the last three terms contain constant coefficient k r According to matrix theory, when k a >>k r hour, is always a positive definite matrix, thus ensuring that V p Yes S / T Convex function of .

9. The spacecraft approaching maneuver tracking control method with observation and collision avoidance constraints according to claim 1, characterized in that: The design of the close-in maneuver tracking control law is as follows: In the formula, k p >0 and k d >0 is a constant coefficient. Under the control law (18), the relative motion state of the system will converge and stabilize to the desired state, that is, and And the line of sight observation constraint is satisfied during the movement, and collision can be effectively avoided, that is, β FOV >0 and β CA >0 is always true.

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