A method for attitude and orbit coupling modeling and simulation of spacecraft formation

Abstract

This invention discloses a method for modeling and simulating the attitude-orbit coupling of spacecraft formations, comprising: establishing coupling models of the desired attitude and orbital parameters of the lead satellite, the actual attitude and orbital parameters of the lead satellite, the desired attitude and orbital parameters of the follower satellite, and the actual attitude and orbital parameters of the follower satellite; calculating the desired attitude and orbital parameters of the lead / follower satellites and the actual attitude and orbital parameters of the lead / follower satellites respectively based on the models; and performing flight formation control based on the calculated parameters to achieve formation flight of the follower satellites relative to the lead satellite. This invention can be used in satellite controller design. On the one hand, by modeling the attitude and orbital parameter information using dual quaternions, this method can more accurately establish a satellite dynamics model; on the other hand, by using the parameters of the lead satellite to determine the parameters of the follower satellites, the follower satellites can more accurately maintain their relative positional relationship with the lead satellite.

Description

Technical Field

[0001] This invention belongs to the field of satellite communication technology, and in particular relates to a method for modeling and simulating the attitude and orbit coupling of spacecraft formations. Background Technology

[0002] With the development of satellite technology, people have begun to consider space systems in which multiple satellites form a certain configuration, maintain a certain distance from each other, and cooperate to complete the same space mission. This method of satellite formation flying has the problem that the close distance between satellites leads to large changes in orbital position and relative attitude, and mutual coupling, which has a significant impact on our precise control of satellites.

[0003] To achieve precise control of satellite formations, establishing more accurate satellite motion models is a pressing issue. Traditional attitude and orbit control methods employ separate control approaches, often neglecting the coupling relationship between attitude and orbital motion. In close-range relative attitude control of spacecraft, the limitations of traditional separate modeling methods become increasingly apparent due to the high precision requirements. Models that consider attitude-orbit coupling often focus on the relative parameters between satellites, ultimately obtaining their relative distances and attitudes, but failing to capture the true parameters of individual satellites—that is, the actual motion of each satellite. This significantly hinders our observation of each satellite's actual situation. Furthermore, in practical applications, observation and control cannot be directly based on satellite relative parameters; models that directly obtain relative parameters present problems during actual control. Summary of the Invention

[0004] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a method for modeling and simulating the attitude and orbit coupling of spacecraft formations. This method can be used for satellite controller design. On the one hand, by modeling the attitude and orbital parameter information in the form of dual quaternions, the method can more accurately establish the satellite dynamics model. On the other hand, by using the parameters of the lead satellite to determine the parameters of the follower satellite, the follower satellite can more accurately maintain the relative position relationship with the lead satellite.

[0005] To address the aforementioned technical problems, this invention discloses a method for spacecraft formation attitude-orbit coupling modeling and simulation, comprising:

[0006] Establish coupling models of desired attitude and orbital parameters for the pilot satellite, actual attitude and orbital parameters for the pilot satellite, desired attitude and orbital parameters for the follower satellite, and actual attitude and orbital parameters for the follower satellite;

[0007] Based on the coupling model of the desired attitude and orbital parameters of the pilot satellite, the coupling model of the actual attitude and orbital parameters of the pilot satellite, the coupling model of the desired attitude and orbital parameters of the follower satellite, and the coupling model of the actual attitude and orbital parameters of the follower satellite, the desired attitude and orbital parameters of the pilot satellite, the actual attitude and orbital parameters of the pilot satellite, the desired attitude and orbital parameters of the follower satellite, and the actual attitude and orbital parameters of the follower satellite are calculated respectively.

[0008] Based on the calculated desired attitude and orbital parameters of the lead satellite, the actual attitude and orbital parameters of the lead satellite, the desired attitude and orbital parameters of the follower satellite, and the actual attitude and orbital parameters of the follower satellite, flight formation control is performed to achieve formation flight of the follower satellite relative to the lead satellite.

[0009] In the above-mentioned spacecraft formation attitude-orbit coupling modeling and simulation method, the process for establishing the coupling model of the desired attitude and orbital parameters of the pilot satellite is as follows:

[0010] Based on the definition of dual quaternions, we obtain the attitude dual quaternions that couple the desired attitude and orbital parameters of the pilot satellite's orbital motion around the Earth. And the velocity dual quaternion that couples the desired attitude and orbital parameters of the pilot satellite orbiting the Earth.

[0011] according to and Establish a coupled model of the desired attitude and orbital parameters of the navigation satellite.

[0012] In the aforementioned spacecraft formation attitude-orbit coupling modeling and simulation methods,

[0013] It is expressed as follows:

[0014]

[0015] Where, q DI The quaternion representing the expected attitude of the navigation satellite. ε represents the expected position vector of the navigation satellite relative to the Earth's inertial frame, and ε represents the dual unit.

[0016] It is expressed as follows:

[0017]

[0018] in, This represents the desired angular velocity vector of the navigation satellite relative to the Earth's inertial frame. This represents the desired linear velocity vector of the navigation satellite relative to the Earth's inertial frame.

[0019] In the above-mentioned spacecraft formation attitude-orbit coupling modeling and simulation method, the process for establishing the coupling model of the actual attitude and orbital parameters of the pilot satellite is as follows:

[0020] Based on the definition of dual quaternions, we obtain the attitude dual quaternions that couple the actual attitude and orbital parameters of the navigation satellite orbiting the Earth. And the velocity dual quaternion that couples the actual attitude and orbital parameters of the pilot satellite orbiting the Earth.

[0021] right Taking the derivative, we obtain the kinematic equations of the navigation satellite in dual quaternion form;

[0022] according to Determine the momentum spinor of the rigid body with reference to the center of mass of the navigation satellite.

[0023]

[0024] Where J represents the moment of inertia matrix of the rigid body in the fixed coordinate system, I 3×3 Let m represent a 3×3 identity matrix. L ε represents the mass of the pilot satellite, and ε represents the dual unit.

[0025] Differentiating both sides of equation (3) simultaneously yields the navigation satellite dynamics equation in dual quaternion form;

[0026] Based on the kinematic equations and dynamic equations of the navigation satellite in dual quaternion form, a coupled model of the actual attitude and orbital parameters of the navigation satellite is established.

[0027] In the aforementioned spacecraft formation attitude-orbit coupling modeling and simulation methods,

[0028] It is expressed as follows:

[0029]

[0030] Where, q BIL Indicates the actual attitude of the navigation satellite. This represents the actual position vector of the navigation satellite in the inertial frame. This represents the actual position vector of the navigation satellite within this system;

[0031] It is expressed as follows:

[0032]

[0033] in, This represents the actual angular velocity of the navigation satellite within this system. This represents the actual linear velocity of the navigation satellite within this system;

[0034] The kinematic equations of the pilot satellite in dual quaternion form are expressed as follows:

[0035]

[0036] The dual quaternion form of the navigation satellite dynamics equations is expressed as follows:

[0037]

[0038] in, The real part represents control. The dual part represents the control torque; The real part represents gravity. The dual part represents the gravitational gradient torque; This represents the dual interference force.

[0039] In the above-mentioned spacecraft formation attitude-orbit coupling modeling and simulation method, the process of establishing the coupling model between the desired attitude and orbital parameters of the following satellite is as follows:

[0040] Based on the definition of dual quaternions, we obtain the attitude dual quaternions that couple the desired attitude and orbital parameters of a satellite orbiting the Earth. And the velocity dual quaternion that couples the desired attitude and orbital parameters of the pilot satellite orbiting the Earth.

[0041] according to and Establish a coupled model of the desired attitude and orbital parameters of the following satellite.

[0042] In the aforementioned spacecraft formation attitude-orbit coupling modeling and simulation methods,

[0043] It is expressed as follows:

[0044]

[0045] Where, q DIF This represents the expected attitude quaternion for following the satellite's motion. ε represents the desired position vector of the satellite relative to the Earth's inertial frame, and ε represents the dual unit.

[0046] It is expressed as follows:

[0047]

[0048] in, This represents the expected angular velocity vector relative to the Earth's inertial frame of reference, following the satellite's motion. This represents the desired linear velocity vector relative to the Earth's inertial frame of reference as the satellite moves.

[0049] In the above-mentioned spacecraft formation attitude-orbit coupling modeling and simulation method, the process of establishing the coupling model between the actual attitude and orbital parameters of the following satellite is as follows:

[0050] Based on the definition of dual quaternions, we obtain the attitude dual quaternions that couple the actual attitude and orbital parameters of the satellite orbiting the Earth. And the velocity dual quaternion that couples the actual attitude and orbital parameters of the satellite orbiting the Earth.

[0051] right Taking the derivative, we obtain the kinematic equations of the following satellite in dual quaternion form;

[0052] according to Determine the momentum spinor of a rigid body with respect to the center of mass of the satellite.

[0053]

[0054] Where J represents the moment of inertia matrix of the rigid body in the fixed coordinate system, I 3×3 Let m represent a 3×3 identity matrix. F ε represents the mass of the satellite following it, and ε represents the dual unit.

[0055] Differentiating both sides of equation (10) yields the dual quaternion form of the satellite dynamics equation;

[0056] Based on the kinematic equations and dynamic equations of the follower satellite in dual quaternion form, a coupled model of the actual attitude and orbital parameters of the follower satellite is established.

[0057] In the aforementioned spacecraft formation attitude-orbit coupling modeling and simulation methods,

[0058] It is expressed as follows:

[0059]

[0060] Where, q BIF This indicates that the satellite's actual attitude is being followed. This represents the actual position vector of the satellite in the inertial frame of reference. This represents the actual position vector of the satellite in this system;

[0061] It is expressed as follows:

[0062]

[0063] in, This indicates the actual angular velocity of the satellite following the system. This indicates the actual linear velocity of the satellite following the system.

[0064] The kinematic equations of the following satellite in dual quaternion form are expressed as follows:

[0065]

[0066] The dual quaternion form of the satellite tracking dynamics equations is expressed as follows:

[0067]

[0068] in, The real part represents control. The dual part represents the control torque; The real part represents gravity. The dual part represents the gravitational gradient torque; This represents the dual interference force.

[0069] In the aforementioned spacecraft formation attitude-orbit coupling modeling and simulation method, flight formation control is performed based on the calculated desired attitude and orbit parameters of the lead satellite, the actual attitude and orbit parameters of the lead satellite, the desired attitude and orbit parameters of the follower satellite, and the actual attitude and orbit parameters of the follower satellite. This enables the follower satellites to fly in formation relative to the lead satellite, including:

[0070] Based on the calculated desired attitude and orbital parameters of the navigation satellite and the actual attitude and orbital parameters of the navigation satellite, the difference between the desired attitude and orbital parameters of the navigation satellite and the actual attitude and orbital parameters of the navigation satellite is calculated and denoted as the first difference.

[0071] Based on the calculated desired attitude and orbital parameters of the following satellite and the actual attitude and orbital parameters of the following satellite, the difference between the desired attitude and orbital parameters of the following satellite and the actual attitude and orbital parameters of the following satellite is calculated and denoted as the second difference.

[0072] Based on the comparison results of the first and second differences, the attitude and orbit differences between the follower satellite and the pilot satellite are obtained;

[0073] Based on the attitude and orbit difference between the follower satellite and the pilot satellite, determine the motion state and relationship between the actual motion attitude and orbit of the follower satellite and the pilot satellite;

[0074] Based on the actual motion attitude and orbital state and relationship between the follower satellite and the leader satellite, flight formation control is performed to achieve formation flight of the follower satellite relative to the leader satellite.

[0075] The present invention has the following advantages:

[0076] 1. Combining satellite attitude and orbital parameters into a single expression for model design simplifies model derivation and subsequent controller design.

[0077] 2. The model uses the Earth's inertial frame as the reference frame, which can obtain the actual flight attitude and orbit information of the satellite.

[0078] 3. The difference between the actual flight attitude and orbital parameters of the satellite and the expected values ​​can be obtained directly from the model.

[0079] 4. Calculating the expected flight attitude and orbital parameters of the following satellite based on the actual flight attitude and orbital parameters of the lead satellite has practical application significance.

[0080] 5. This design is not limited to a single or two satellites; it can be applied to the formation flight of multiple satellites.

[0081] 6. This design is not limited to modeling and simulation of satellites flying in formation, but can also be applied to scenarios involving multiple satellites, such as satellite tracking and hovering. Attached Figure Description

[0082] Figure 1 This is a flowchart illustrating the steps of a spacecraft formation attitude-orbit coupling modeling and simulation method in an embodiment of the present invention. Detailed Implementation

[0083] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments disclosed in the present invention will be described in further detail below with reference to the accompanying drawings.

[0084] like Figure 1 In this embodiment, the spacecraft formation attitude-orbit coupling modeling and simulation method includes:

[0085] Step 1: Establish a coupled model of the desired attitude and orbital parameters of the navigation satellite.

[0086] Because the satellites in the formation are relatively close together, attitude-orbit coupling issues arise during actual flight. Therefore, this embodiment employs a dual quaternion method to directly combine orbital and attitude parameters. First, the desired orbital position and attitude of the lead satellite are determined, and a model coupling the lead satellite's desired attitude and orbital parameters is established. That is, given the ideal motion attitude and flight position of the lead satellite, the attitude and orbital parameters of the lead satellite, expressed in dual quaternion form, are calculated using dual quaternions. Specifically:

[0087] Based on the definition of dual quaternions, we obtain the attitude dual quaternions that couple the desired attitude and orbital parameters of the pilot satellite's orbital motion around the Earth. And the velocity dual quaternion that couples the desired attitude and orbital parameters of the pilot satellite orbiting the Earth.

[0088]

[0089] Where, q DI The quaternion representing the expected attitude of the navigation satellite. Let ε represent the desired position vector of the navigation satellite relative to the Earth's inertial frame, and let ε denote the dual unit. This represents the desired angular velocity vector of the navigation satellite relative to the Earth's inertial frame. This represents the desired linear velocity vector of the navigation satellite relative to the Earth's inertial frame.

[0090] Then, according to and Establish a coupled model of the desired attitude and orbital parameters of the navigation satellite.

[0091] Step 2: Establish a coupled model of the actual attitude and orbital parameters of the navigation satellite.

[0092] The kinematic and dynamic equations of the navigation satellite are obtained using the dual quaternion method. A simulation model is then established based on these equations, resulting in a coupled model of the navigation satellite's actual attitude and orbital parameters. In other words, a model of the navigation satellite's actual motion in space is established to represent its actual movement. Finally, the actual attitude and position of the navigation satellite during its motion can be obtained through calculation. Specifically:

[0093] Based on the definition of dual quaternions, attitude dual quaternions are the coupling between the actual attitude and orbital parameters of a navigation satellite orbiting the Earth. And the velocity dual quaternion that couples the actual attitude and orbital parameters of the pilot satellite orbiting the Earth.

[0094]

[0095] Where, q BIL Indicates the actual attitude of the navigation satellite. This represents the actual position vector of the navigation satellite in the inertial frame. This represents the actual position vector of the navigation satellite within this system. This represents the actual angular velocity of the navigation satellite within this system. This represents the actual linear velocity of the navigation satellite within this system.

[0096] right Differentiating, we obtain the kinematic equations of the navigation satellite in dual quaternion form:

[0097]

[0098] according to Determine the momentum spinor of the rigid body with reference to the center of mass of the navigation satellite.

[0099]

[0100] Where J represents the moment of inertia matrix of the rigid body in the fixed coordinate system, I 3×3 Let m represent a 3×3 identity matrix. L Indicates the quality of the navigation satellite.

[0101] Differentiating both sides of equation (3) simultaneously, we obtain the dual quaternion form of the navigation satellite dynamics equation:

[0102]

[0103] in, The real part represents control. The dual part represents the control torque; The real part represents gravity. The dual part represents the gravitational gradient torque; This represents the dual interference force.

[0104] Finally, based on the kinematic equations and dynamic equations of the navigation satellite in dual quaternion form, a coupled model of the actual attitude and orbital parameters of the navigation satellite is established.

[0105] Step 3: Establish a coupled model of the desired attitude and orbital parameters of the following satellite.

[0106] Based on the definition of dual quaternions, we obtain the attitude dual quaternions that couple the desired attitude and orbital parameters of a satellite orbiting the Earth. And the velocity dual quaternion that couples the desired attitude and orbital parameters of the pilot satellite orbiting the Earth.

[0107]

[0108] Where, q DIF This represents the expected attitude quaternion for following the satellite's motion. This represents the expected position vector of the satellite relative to the Earth's inertial frame. This represents the expected angular velocity vector relative to the Earth's inertial frame of reference, following the satellite's motion. This represents the desired linear velocity vector relative to the Earth's inertial frame of reference as the satellite moves.

[0109] according to and Establish a coupled model of the desired attitude and orbital parameters of the following satellite.

[0110] Step 4: Establish a coupled model of the actual attitude and orbital parameters of the following satellite.

[0111] The kinematic and dynamic equations of the following satellite are obtained using the dual quaternion method. A simulation model is then established based on these equations, resulting in a model coupling the actual attitude and orbital parameters of the following satellite. In other words, a model of the actual motion of the following satellite in space is established to represent its actual movement. Finally, the attitude and position of the following satellite during its actual motion can be obtained through calculation. Specifically:

[0112] Based on the definition of dual quaternions, we obtain the attitude dual quaternions that couple the actual attitude and orbital parameters of the satellite orbiting the Earth. The velocity dual quaternion that couples the actual attitude and orbital parameters of a satellite orbiting the Earth.

[0113]

[0114] Where, q BIF This indicates that the satellite's actual attitude is being followed. This represents the actual position vector of the satellite in the inertial frame of reference. This represents the actual position vector of the satellite within this system. This indicates the actual angular velocity of the satellite following the system. This indicates the actual linear velocity of the satellite following this system.

[0115] right Differentiating, we obtain the kinematic equations of the following satellite in dual quaternion form:

[0116]

[0117] according to Determine the momentum spinor of a rigid body with respect to the center of mass of the satellite.

[0118]

[0119] Where J represents the moment of inertia matrix of the rigid body in the fixed coordinate system, I 3×3 Let m represent a 3×3 identity matrix. F Indicates the mass of the satellite;

[0120] Differentiating both sides of equation (10), we obtain the dual quaternion form of the satellite tracking dynamics equation:

[0121]

[0122] Based on the kinematic equations and dynamic equations of the follower satellite in dual quaternion form, a coupled model of the actual attitude and orbital parameters of the follower satellite is established.

[0123] Step 5: Based on the coupling model of the desired attitude and orbital parameters of the pilot satellite, the coupling model of the actual attitude and orbital parameters of the pilot satellite, the coupling model of the desired attitude and orbital parameters of the follower satellite, and the coupling model of the actual attitude and orbital parameters of the follower satellite, respectively calculate the desired attitude and orbital parameters of the pilot satellite, the actual attitude and orbital parameters of the pilot satellite, the desired attitude and orbital parameters of the follower satellite, and the actual attitude and orbital parameters of the follower satellite.

[0124] Step 6: Based on the calculated desired attitude and orbital parameters of the lead satellite, the actual attitude and orbital parameters of the lead satellite, the desired attitude and orbital parameters of the follower satellite, and the actual attitude and orbital parameters of the follower satellite, perform flight formation control to achieve formation flight of the follower satellite relative to the lead satellite.

[0125] In this embodiment, firstly, based on the calculated desired attitude and orbit parameters of the lead satellite and its actual attitude and orbit parameters, the difference between the desired attitude and orbit parameters and the actual attitude and orbit parameters of the lead satellite is calculated and recorded as the first difference. This difference is used to observe the true attitude angle deviation and the true distance, and is subsequently used to guide the lead satellite to move according to the desired attitude and orbit values. Secondly, based on the calculated desired attitude and orbit parameters of the follower satellite and its actual attitude and orbit parameters, the difference between the desired attitude and orbit parameters and the actual attitude and orbit parameters of the follower satellite is calculated and recorded as the second difference. This difference is used to observe the true attitude angle deviation and the true distance, and is subsequently used to guide the follower satellite to move according to the desired attitude and orbit values. Then, based on the comparison result of the first difference and the second difference, the attitude and orbit difference between the follower satellite and the lead satellite is obtained. Further, based on the attitude and orbit difference between the follower satellite and the lead satellite, the motion state and relationship of the actual motion attitude and orbit of the follower satellite and the lead satellite are determined. Finally, based on the actual motion attitude and orbital motion and relationship between the follower satellite and the leader satellite, flight formation control is performed to achieve formation flight of the follower satellite relative to the leader satellite.

[0126] Based on the above embodiments, a specific example will be used for illustration below.

[0127] Step 1: First, establish a geocentric inertial coordinate system O-XYZ with the Earth's center as the origin O, the XY plane coinciding with the equatorial plane, the X-axis pointing to the vernal equinox γ, the Z-axis perpendicular to the equatorial plane pointing to the North Pole, and the Y-axis forming a right-handed orthogonal coordinate system with the X and Z axes; with the spacecraft's center of mass as the origin O. b The spacecraft's body coordinate system O, whose three coordinate axes coincide with the spacecraft's principal axes of inertia.b -X b Y b Z b In this design, the desired coordinate system for the navigator spacecraft is denoted as O. dl -X dl Y dl Z dl The coordinate system of the pilot spacecraft is O. bl -X bl Y bl Z bl The desired coordinate system for the spacecraft is O. df -X df Y df Z df The coordinate system following the spacecraft body is O bf -X bf Y bf Z bf .

[0128] The satellite's motion relative to the Earth can be viewed as a helical motion of the satellite's own coordinate system relative to the Earth's inertial frame; that is, the satellite's rotational motion around the Earth is coupled with translational motion. Therefore, the attitude dual quaternion, which couples the desired attitude and orbital parameters of the navigation satellite's motion around the Earth, can be obtained using the definition of dual quaternions:

[0129]

[0130] Similarly, the velocity dual quaternion, which couples the desired attitude and orbital parameters of a pilot satellite orbiting the Earth, can be obtained according to the definition of dual quaternions:

[0131]

[0132] The coupling model of the desired attitude and orbital parameters of the navigation satellite can be established based on equations (1) and (2).

[0133] Step 2, Equation (1) is also the definition of attitude dual quaternion and velocity dual quaternion. According to the above definitions, we can define the attitude dual quaternion form of the actual attitude of the navigation satellite orbiting the Earth and the orbital parameters as follows:

[0134]

[0135] Differentiating both sides of equation (4) and combining them with the quaternion attitude kinematics equations:

[0136]

[0137] The satellite kinematic equations in dual quaternion form can be obtained:

[0138]

[0139] Similarly, equation (2) is the definition of velocity dual quaternion. Based on the above definition, we can define the velocity dual quaternion form of the coupling between the actual attitude and orbital parameters of the navigation satellite orbiting the Earth as follows:

[0140]

[0141] Given that the momentum spinor of a rigid body with its center of mass as the reference point is:

[0142]

[0143] Differentiating both sides of equation (3) yields the dual form of the dynamic equation:

[0144]

[0145] Based on the equations, a model can be established that couples the attitude and orbital parameters of the navigation satellite in space, representing the actual motion of the satellite in space.

[0146] In order to combine attitude and orbit, the satellite's attitude and orbit parameters were processed into dual quaternion form. This form brings great benefits to the derivation of equations and subsequent controller design. However, the actual attitude and position of the satellite cannot be directly obtained using the dual quaternion form. Therefore, the results obtained from the model in the dual quaternion form are solved.

[0147] The satellite attitude and orbital parameters updated by equation (6) can be solved using the attitude dual quaternion definition defined by equation (4). Therefore, the actual attitude q of the navigation satellite BIL That is The actual position of the navigation satellite in the Earth's inertial frame is... The actual position of the navigation satellite in this satellite system is in Let be the real part of the attitude dual quaternion. This is the dual part of the attitude dual quaternion. The satellite velocity dual quaternion updated by equation (7) can be used to calculate the actual flight angular velocity of the navigation satellite and the angular velocity affected by rotation. Since the updated values ​​obtained by equation (7) are parameters under this system, while in practical applications, parameters under the inertial frame are required. Therefore, according to: The velocity dual quaternions in this system are transformed to the inertial frame for solution, yielding the actual angular velocity in the navigation satellite's inertial frame: The actual linear velocity of the navigation satellite in its inertial frame affected by rotation is in, Let the real part be the velocity dual quaternion. For the dual part of the velocity dual quaternion.

[0148] Step 3: Subtract the actual attitude and orbital parameters of the pilot satellite in the inertial frame from the desired attitude and orbital parameters to obtain the actual difference between the actual and desired parameters of the pilot satellite in the inertial frame.

[0149] Step 4: To achieve formation flight, this design employs a distributed method, using a lead satellite to determine the desired position and attitude of the follower satellites. Step 2 yields the actual attitude quaternions, actual position, and actual angular velocity of the lead satellite. Based on the desired configuration, the desired attitude quaternions, desired position, desired linear velocity, and desired angular velocity of the follower satellites are calculated. For example, if it is desired that multiple satellites maintain a "line-like" flight and point in the same direction towards the Earth, a definite constant (which can be determined based on different actual conditions) can be added to a certain coordinate axis direction based on the actual position of the lead satellite obtained in Step 2. The specific implementation method is as follows: in To track the desired position of the satellite in the inertial frame, Differentiation yields the desired linear velocity of the satellite in the inertial frame, unaffected by attitude-orbit coupling. To ensure consistent pointing with the Earth, set the desired attitude quaternion for the satellite. With desired angular velocity Consistent with the lead satellite. Once the required parameter values ​​are obtained, a model coupling the desired attitude and orbital parameters of the following satellite can be constructed as described in step 1.

[0150] Step 5: Construct a model coupling the desired attitude and orbital parameters of the follower satellite using the method described in Step 2. Similar to defining the attitude dual quaternion coupling the actual attitude and orbital parameters of the pilot satellite orbiting the Earth, the attitude dual quaternion coupling the actual attitude and orbital parameters of the follower satellite orbiting the Earth is defined as follows:

[0151]

[0152] The satellite kinematic equations in dual quaternion form are obtained as described in step 2:

[0153]

[0154] Similarly, the velocity dual quaternion form, which couples the actual attitude and orbital parameters of a satellite orbiting the Earth, is defined as follows:

[0155]

[0156] The dual-form dynamic equations obtained as described in step 2 are as follows:

[0157]

[0158] Based on the equations, a model can be established that couples the attitude and orbital parameters of the satellite as it moves in space, representing the actual motion of the satellite in space.

[0159] Similarly, we need to solve the dual quaternion form of the result obtained from the model.

[0160] Step 6: Subtract the desired attitude and orbital parameters of the following satellite in the inertial frame obtained in Step 4 from the actual attitude and orbital parameters of the following satellite in the inertial frame obtained in Step 5 to obtain the actual difference between the actual parameters and the desired parameters of the following satellite in the inertial frame.

[0161] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

[0162] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A method for modeling and simulating the attitude-orbit coupling of a spacecraft formation, characterized in that, The method comprises the following steps: establishing a coupling model of a navigation satellite's nominal attitude and orbit parameters, a coupling model of a navigation satellite's actual attitude and orbit parameters, a coupling model of a follower satellite's nominal attitude and orbit parameters, and a coupling model of a follower satellite's actual attitude and orbit parameters; solving the coupling model of the navigation satellite's nominal attitude and orbit parameters, the coupling model of the navigation satellite's actual attitude and orbit parameters, the coupling model of the follower satellite's nominal attitude and orbit parameters, and the coupling model of the follower satellite's actual attitude and orbit parameters to obtain the navigation satellite's nominal attitude and orbit parameters, the navigation satellite's actual attitude and orbit parameters, the follower satellite's nominal attitude and orbit parameters, and the follower satellite's actual attitude and orbit parameters respectively; controlling the flight formation according to the navigation satellite's nominal attitude and orbit parameters, the navigation satellite's actual attitude and orbit parameters, the follower satellite's nominal attitude and orbit parameters, and the follower satellite's actual attitude and orbit parameters to realize the formation flight of the follower satellite relative to the navigation satellite, which comprises the following steps: calculating the difference between the navigation satellite's nominal attitude and orbit parameters and the navigation satellite's actual attitude and orbit parameters according to the navigation satellite's nominal attitude and orbit parameters and the navigation satellite's actual attitude and orbit parameters, and recording the difference as a first difference; calculating the difference between the follower satellite's nominal attitude and orbit parameters and the follower satellite's actual attitude and orbit parameters according to the follower satellite's nominal attitude and orbit parameters and the follower satellite's actual attitude and orbit parameters, and recording the difference as a second difference; obtaining the attitude and orbit difference between the follower satellite and the navigation satellite according to the comparison result of the first difference and the second difference; determining the motion state and relationship of the actual motion attitude and orbit of the follower satellite and the navigation satellite according to the attitude and orbit difference between the follower satellite and the navigation satellite; and controlling the flight formation according to the motion state and relationship of the actual motion attitude and orbit of the follower satellite and the navigation satellite to realize the formation flight of the follower satellite relative to the navigation satellite.

2. The method of claim 1, wherein, The establishment process of the coupling model of the navigation satellite's nominal attitude and orbit parameters is as follows: According to the definition of dual quaternion, the attitude dual quaternion of the desired attitude coupled with the orbit parameters of the navigation satellite moving around the earth is obtained , and the velocity dual quaternion of the desired attitude coupled with the orbit parameters of the navigation satellite moving around the earth ; According to and , the coupling model of navigation satellite's attitude and orbit parameters is established.

3. The spacecraft formation attitude and orbit coupling modeling and simulation method according to claim 2, characterized in that is represented as follows: ···（1） wherein, qdes represents a desired attitude quaternion of the navigation satellite motion, rdes represents a desired position vector of the navigation satellite relative to the Earth's inertial frame, represents a dual unit; is represented as follows: ···（2） wherein, represents the desired angular velocity vector of the motion of the navigation satellite relative to the Earth's inertial system, represents the desired linear velocity vector of the motion of the navigation satellite relative to the Earth's inertial system.

4. The method of claim 1, wherein, The establishment process of the coupling model of the navigation satellite's actual attitude and orbit parameters is as follows: According to the definition of dual quaternion, the attitude dual quaternion of the actual attitude and the orbit parameters coupling of the navigation satellite moving around the earth is obtained , and the velocity dual quaternion of the actual attitude and the orbit parameters coupling of the navigation satellite moving around the earth ; For Taking derivative, the navigation satellite kinematic equation in dual quaternion form is obtained. According to , the momentum spin of the rigid body is determined with the reference point being the center of mass of the leader satellite : ···（3） wherein denotes the matrix of the moment of inertia of the rigid body in the fixed coordinate system, denotes the identity matrix, denotes the mass of the navigation satellite, denotes the dual identity; deriving the navigation satellite's dynamics equation in the form of dual quaternions by simultaneously deriving both sides of equation (3); establishing the coupling model of the navigation satellite's actual attitude and orbit parameters according to the navigation satellite's kinematics equation in the form of dual quaternions and the navigation satellite's dynamics equation in the form of dual quaternions.

5. The spacecraft formation attitude and orbit coupling modeling and simulation method according to claim 4, characterized in that is represented as follows: ···（4） wherein, represents the actual attitude of the navigation satellite, represents the actual position vector of the navigation satellite in the inertial system, represents the actual position vector of the navigation satellite in the body system; is represented as follows: ···（5） wherein, represents the actual angular velocity of the lead satellite in the system, represents the actual linear velocity of the lead satellite in the system; The navigation satellite's kinematics equation in the form of dual quaternions is expressed as follows: ···（6） The navigation satellite's dynamics equation in the form of dual quaternions is expressed as follows: ···（7） wherein, , the real part of the dual part of the real part of the dual part of denotes the dual disturbance force.

6. The method of claim 1, wherein, The establishment process of the coupling model of the follower satellite's nominal attitude and orbit parameters is as follows: According to the dual quaternion definition, the attitude dual quaternion coupled with the desired attitude and the orbit parameters of the satellite moving around the earth is obtained , and the velocity dual quaternion coupled with the desired attitude and the orbit parameters of the satellite moving around the earth is obtained ; According to and , the coupled model of the tracking attitude and orbit parameters is established.

7. The spacecraft formation attitude and orbit coupling modeling and simulation method according to claim 6, characterized in that is represented as follows: ···（8） wherein, qdesire represents the desired attitude quaternion following the satellite motion, rdesire represents the desired position vector of the satellite relative to the Earth's inertial frame, represents the dual unit; is represented as follows: ···（9） wherein, represents the desired angular velocity vector of the satellite motion relative to the Earth Inertial Frame, represents the desired linear velocity vector of the satellite motion relative to the Earth Inertial Frame.

8. The method of claim 1, wherein, The establishment process of the coupling model of the follower satellite's actual attitude and orbit parameters is as follows: According to the definition of dual quaternion, the attitude dual quaternion coupled with the actual attitude and orbit parameters of the satellite around the earth is obtained , and the velocity dual quaternion coupled with the actual attitude and orbit parameters of the satellite around the earth is obtained ​ right Taking the derivative, we obtain the kinematic equations of the following satellite in dual quaternion form; According to , the rigid body is determined to follow the momentum spin of the satellite center of mass as the reference point : ···（10） wherein, denotes the matrix of the moment of inertia of the rigid body in the fixed coordinate system, denotes the identity matrix, denotes the mass of the follower satellite, denotes the dual identity; deriving the follower satellite's dynamics equation in the form of dual quaternions by simultaneously deriving both sides of equation (10); According to the dual quaternion form of the follower satellite kinematics equation and the dual quaternion form of the follower satellite dynamics equation, a coupling model of the actual attitude and the orbit parameters of the follower satellite is established.

9. The spacecraft formation attitude and orbit coupling modeling and simulation method according to claim 8, characterized in that, is represented as follows: ···（11） wherein, represents the actual attitude of the follower satellite, represents the actual position vector of the follower satellite in the inertial system, represents the actual position vector of the follower satellite in the body system; is represented as follows: ···（12） wherein, represents the actual angular velocity of the follower satellite in the system, represents the actual linear velocity of the follower satellite in the system; The dual quaternion form of the follower satellite kinematics equation is expressed as follows: ···（13） The dual quaternion form of the follower satellite dynamics equation is expressed as follows: The dual quaternion form of the follower satellite kinematics equation is expressed as follows: ···（14） wherein, , the real part of the dual part of the real part of the dual part of denotes the dual disturbance force.

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