Magnetic levitation stability augmentation mechanism non-contact split type satellite relative position attitude calculation method

Abstract

The invention relates to a relative position attitude calculation method for a non-contact split type satellite of a magnetic levitation stability augmentation mechanism, and belongs to the technical field of spaceflight. Establishing a load cabin position attitude kinetic equation; establishing a relative kinetic equation between the load cabin and the platform cabin; representing eight magnetic levitation forces by using a matrix FL; calculating resultant force FA formed by magnetic levitation force in a magnetic levitation geometric center; according to the resultant force FA, calculating magnetic levitation power DF magnetic acting on the mass center of the load cabin; establishing a calculation equation of the magnetic levitation force fLi, and obtaining a relational expression between the magnetic levitation force fLi and the magnetic levitation gap delta0; establishing a conversion relation between the relative pose of the load cabin relative to the platform cabin and the magnetic levitation gap delta0; the relation between the relative pose of the load cabin relative to the platform cabin and the magnetic levitation force fLi is obtained, that is, the relative pose of the load cabin relative to the platform cabin is obtained through calculation according to the magnetic levitation force fLi; according to the method, the relative position and attitude calculation problem in the process that the load cabin follows the platform cabin based on the magnetic levitation stability augmentation mechanism is solved, and a theoretical model is provided for a non-contact split type satellite following control and vibration suppression system.

Description

Technical Field

[0001] The present invention belongs to the field of aerospace technology and relates to a method for calculating the relative position and attitude of a non-contact split satellite with a magnetic levitation and stabilization mechanism. Background Art

[0002] For a non-contact split satellite with a magnetic levitation and stabilization mechanism, establishing a relative dynamics model between two cabins is of great significance for its high-precision pointing control.

[0003] The non-contact split satellite is stably connected by a magnetic levitation mechanism between the platform cabin and the payload cabin, which can reduce the vibration problems faced during on-orbit operation, especially the impact on the precise pointing of the payload, and can adapt to the complex dynamic environment faced in different mission phases. During the stable operation phase in orbit, the payload cabin and the platform cabin are completely separated in space, and there is always a gap of millimeters, forming a non-contact relative suspension state, thereby minimizing the interference of the micro-vibration and flexible vibration of the platform cabin on the pointing control of the payload cabin and ensuring the stability and accuracy of the spacecraft during mission execution. For the stable operation of the satellite in orbit, especially during the maneuvering process, maintaining the distance between the two cabins at the millimeter level poses a great challenge to the controller design. Therefore, it is necessary to establish an accurate dynamics model to provide an accurate theoretical model for the design of the satellite pointing controller.

[0004] The existing non-contact "double ultra" satellite actuator adopts a magnetic levitation mechanism designed based on a uniform magnetic field voice coil motor. Compared with the magnetic levitation mechanism based on a magnetic levitation bearing, the actuator based on a magnetic levitation bearing has a greater output force under the same volume and can be applied to more mission scenarios. Therefore, in the present invention, the non-contact satellite adopts a magnetic levitation mechanism designed based on a magnetic levitation bearing. The magnetic buoyancy force generated by this structure is non-linearly related to the change in the gap of the magnetic levitation bearing. Therefore, to achieve the relative stability between the two cabins and the precise pointing of the payload cabin, the conversion relationship between the position and attitude change of the payload cabin and the gap of the magnetic bearing needs to be considered during the process of relative dynamics modeling between the cabins. And to simplify the difficulty of controller design, it is necessary to determine the range of gap change when the magnetic buoyancy force can be linearly processed. Summary of the Invention

[0005] The technical problem solved by the present invention is: overcoming the deficiencies of the prior art, proposing a method for calculating the relative position and attitude of a non-contact split satellite with a magnetic levitation and stabilization mechanism, solving the problems of relative position and attitude calculation during the process of the payload cabin following the platform cabin based on the magnetic levitation and stabilization mechanism, and providing a theoretical model for the following control and vibration suppression system of the non-contact split satellite.

[0006] The technical solution adopted by the present invention to solve the problem is:

[0007] A method for calculating the relative position and attitude of a non-contact split satellite with a magnetic levitation and stabilization mechanism, comprising:

[0008] Establish the dynamic equations of the position and attitude of the payload compartment;

[0009] According to the motion law of the dual-body, based on the dynamic equations of the position and attitude of the payload compartment, establish the relative dynamic equations between the payload compartment and the platform compartment;

[0010] There is a magnetic levitation mechanism between the payload compartment and the platform compartment; the magnetic levitation mechanism includes four groups of magnetic levitation bearings; the eight magnetic buoyancy forces f generated by the four groups of magnetic levitation bearings Li ; where i is the serial number of the magnetic buoyancy force; and use the matrix F L to represent the eight magnetic buoyancy forces;

[0011] According to F L calculate the resultant force F formed by the magnetic buoyancy forces at the magnetic levitation geometric center A ; According to the resultant force F A calculate the magnetic buoyancy force acting on the center of mass of the payload compartment D F 磁上 ;

[0012] Establish the calculation equation of the magnetic buoyancy force f Li to obtain the relationship between the magnetic buoyancy force f Li and the magnetic levitation gap δ 0 ;

[0013] Establish the conversion relationship between the relative position and attitude of the payload compartment relative to the platform compartment and the magnetic levitation gap δ 0 ;

[0014] Finally, obtain the relationship between the relative position and attitude of the payload compartment relative to the platform compartment and the magnetic buoyancy force f Li ; that is, calculate the relative position and attitude of the payload compartment relative to the platform compartment according to the magnetic buoyancy force f Li .

[0015] In the above-mentioned calculation method of the relative position and attitude of the non-contact split satellite with magnetic levitation and stabilization mechanism, the method for establishing the dynamic equations of the position and attitude of the payload compartment is as follows:

[0016] Define 4 coordinate systems, namely the coordinate system fixedly connected to the inertial space the center-of-mass coordinate system of the platform compartment the coordinate system of the vibration isolation unit the center-of-mass coordinate system of the payload compartment Specifically:

[0017] The origin o of the coordinate system is located at the center of the earth; n The axis is located on the equatorial plane, and the positive direction points to the vernal equinox at 12:00 on January 1, 2000 AD; The positive direction of the axis points to the North Pole; The positive direction of the axis is determined by the right-hand rule;

[0018]

[0018] The coordinate system The origin O d is located at the centroid of the platform cabin; The axis is parallel to the bottom surface of the aircraft, and the positive direction points to the front of the aircraft; The positive direction of the axis points to the direction of the docking surface with other basic models; The positive direction of the axis is determined by the right - hand rule;

[0019] Coordinate system The origin O a is located at the magnetic levitation geometric center; The positive direction of the axis is consistent with the axis in the coordinate system O D in ; The positive direction of the axis is consistent with the axis in the coordinate system O D in ; The positive direction of the axis is determined by the right - hand rule;

[0020] Coordinate system The origin O c is located at the centroid of the payload cabin; The axis is parallel to the bottom surface of the aircraft, and the positive direction points to the front of the aircraft; The positive direction of the axis points to the magnetic levitation center plane; The positive direction of the axis is determined by the right - hand rule;

[0021] According to rigid - body motion, the dynamic equation of the payload cabin's position and attitude is:

[0022]

[0023] Wherein, D r CN is the expression of the vector from O in the inertial system to the centroid O of the payload cabin N in the coordinate system O C ; D ;

[0024] is the translational velocity of the payload cabin relative to the inertial system, that is D r CN the first - order derivative of with respect to time;

[0025] is the translational acceleration of the payload cabin relative to the inertial system, that is D r CN the second - order derivative of with respect to time;

[0026] D ε C is the expression of the Euler angles of the payload cabin relative to the inertial system in the coordinate system O D ;

[0027] D ωC is the expression of the angular velocity of the payload compartment relative to the inertial system in the coordinate system O D ;

[0028] is the expression of the angular acceleration of the payload compartment relative to the inertial system in the coordinate system O D ;

[0029] W C is the angular velocity transformation matrix;

[0030] M C is the mass of the payload compartment;

[0031] J C is the moment of inertia of the payload compartment;

[0032] D F C is the magnetic buoyancy force acting on the centroid of the payload compartment;

[0033] G is the universal gravitational constant;

[0034] M g is the mass of the earth.

[0035] In the above non-contact split satellite relative position and attitude calculation method of the magnetic levitation and stability augmentation mechanism, the method for establishing the relative dynamics equation between compartments is as follows:

[0036] According to the relative kinematic law of two bodies, the translational and rotational accelerations and velocities of the payload compartment in the O D coordinate system are expressed by the relative velocities and accelerations and the velocities and accelerations of the platform compartment, and the expressions are substituted into the attitude dynamics equation of the payload compartment; taking the relative 6-degree-of-freedom position and attitude variables as state variables, the relative dynamics equation between compartments is obtained:

[0037]

[0038] In the formula, D r CD is the vector from the centroid O D of the platform compartment to the centroid O C of the payload compartment;

[0039]

[0040] is the translational acceleration of the payload compartment relative to the platform compartment;

[0041] is the translational velocity of the payload compartment relative to the platform compartment;

[0042] D ε CD is the Euler angle of the payload compartment relative to the platform compartment;

[0043] D ω CD is the angular velocity of the payload compartment relative to the platform compartment;

[0044] is the angular acceleration of the payload compartment relative to the platform compartment;

[0045] D ω D is the expression of the angular velocity of the platform compartment relative to the inertial system in the coordinate system O D ;

[0046] is the angular acceleration of the platform compartment relative to the inertial system;

[0047] D r DN is the expression of the vector from the origin of the inertial system to the centroid of the payload compartment in the coordinate system O D ;

[0048] is the translational velocity of the platform compartment relative to the inertial system, that is D r DN the second derivative with respect to time;

[0049] is the translational velocity of the platform compartment relative to the inertial system, that is D r DN the first derivative with respect to time;

[0050] D ε D is the expression of the Euler angles of the platform compartment relative to the inertial system in the coordinate system O D ;

[0051] In the above calculation method of the relative position and attitude of the non-contact split satellite with a magnetic levitation stability augmentation mechanism, the 8 magnetic buoyancy forces generated by the four groups of magnetic levitation bearings are:

[0052]

[0053] where F L is the matrix of the 8 magnetic buoyancy forces;

[0054] is the i-th magnetic buoyancy force.

[0055] In the above calculation method of the relative position and attitude of the non-contact split satellite with a magnetic levitation stability augmentation mechanism, the calculation method of the resultant force F A formed by the magnetic buoyancy forces at the magnetic levitation geometric center is:

[0056]

[0057] where L z is the distance from the magnetic levitation output point to the magnetic levitation geometric center.

[0058] In the above non-contact split satellite relative position and attitude calculation method of the magnetic levitation stability enhancement mechanism, the acting planes of the eight magnetic buoyancy forces F L are always parallel to the installation interface of the platform module. Therefore, the geometric centers of the magnetic buoyancy forces coincide with the geometric center of the magnetic levitation mechanism of the platform module, the coordinate system of the magnetic buoyancy forces is fixedly connected to the coordinate system of the platform module, and the magnetic buoyancy force D F 磁上 acting on the center of mass of the payload module is calculated as follows:

[0059]

[0060] In the formula, D R A is the transformation matrix from the coordinate system O A to the coordinate system O D ;

[0061] I is the identity matrix;

[0062] D r AC is the vector from the center of mass of the payload module to the geometric center of the magnetic levitation mechanism;

[0063] ( D r AC ) × is the cross product matrix of the vector D r AC ;

[0064] D F 磁上 realizes replacing the magnetic buoyancy force D F C acting on the center of mass of the payload module in the relative dynamic equation between modules.

[0065] In the above non-contact split satellite relative position and attitude calculation method of the magnetic levitation stability enhancement mechanism, the calculation equation of the magnetic buoyancy force f Li is as follows:

[0066]

[0067] In the formula, μ 0 is the magnetic permeability of vacuum;

[0068] N S is the number of turns of the coil;

[0069] A S is the magnetic pole area;

[0070] I 0 is the bias current;

[0071] i x is the control current;

[0072] δ 0 is the magnetic levitation gap;

[0073] x is the change in the magnetic levitation gap.

[0074] In the above non-contact split satellite relative position and attitude calculation method of the magnetic levitation stability enhancement mechanism, since the magnetic buoyancy force is a non-linear force and the relative dynamics system is a non-linear system, the magnetic buoyancy force is linearized to solve the problem of difficult control design. The non-linear magnetic buoyancy force is expanded by the first-order Taylor expansion to obtain the linear expression between the magnetic buoyancy force and the current and gap changes:

[0075]

[0076] By comparing the non-linear and linear magnetic buoyancy force expressions, analyzing the deviation values between the linear and non-linear magnetic buoyancy forces under different currents and gap changes, the reasonable range of magnetic buoyancy force linearization is determined.

[0077] In the above non-contact split satellite relative position and attitude calculation method of the magnetic levitation stability enhancement mechanism, the relative position and attitude of the payload compartment relative to the platform compartment include the three-axis translational momentum of the payload compartment relative to the platform compartment and the three-axis rotational momentum of the payload compartment relative to the platform compartment.

[0078] In the above non-contact split satellite relative position and attitude calculation method of the magnetic levitation stability enhancement mechanism, the calculation method of the conversion relationship between the relative position and attitude of the payload compartment relative to the platform compartment and the magnetic levitation gap δ 0 is as follows:

[0079] In the platform compartment coordinate system, the translational and rotational change amount Δ D r CD of the centroid C of the payload compartment relative to the centroid D of the platform compartment is expressed as:

[0080]

[0081] In the formula, Δx CD is the translation amount of the centroid of the payload compartment relative to the centroid of the platform compartment in the axis direction;

[0082] Δy CD is the translation amount of the centroid of the payload compartment relative to the centroid of the platform compartment in the axis direction;

[0083] Δz CD is the translation amount of the centroid of the payload compartment relative to the centroid of the platform compartment in the axis direction;

[0084] is the rotation angle of the centroid of the payload compartment relative to the centroid of the platform compartment around the axis direction;

[0085] D θC is the rotation angle of the centroid of the payload compartment relative to the centroid of the platform compartment about the axis direction;

[0086] D ψ C is the rotation angle of the centroid of the payload compartment relative to the centroid of the platform compartment about the axis direction;

[0087] The 8 clearance amounts δ of the 4 magnetic levitation bearings measured are:

[0088] δ = [δx 1 , δz 1 , δy 2 , δz 2 , δx 3 , δz 3 , δy 4 , δz 4 T

[0089] In the formula, δx 1 , δz 1 , δy 2 , δz 2 , δx 3 , δz 3 , δy 4 , δz 4 are respectively the clearance change amounts of the 4 magnetic levitation bearings in the direction;

[0090] According to Δ D r CD and the geometric relationship, the magnetic levitation clearance is expressed; the initial position is considered that the magnetic levitation sleeve and the shaft are concentric, and the initial clearance is δ 0 , and the clearance change amount is caused by relative translation and rotation; considering that the relative rotation of the upper platform compartment is very small, Therefore the magnetic levitation clearance change amount is written as:

[0091]

[0092] In the formula, are respectively the components of the vector from the centroid of the payload compartment to the geometric center of the magnetic levitation in the direction;

[0093] The relative pose expressed by the clearance change amount:

[0094] Δd = [d 1 d 2 d 3 d 4 d 5 d 6 d​7 d 8 ] T

[0095]

[0096] The beneficial effects of the present invention compared with the prior art are as follows:

[0097] (1) The magnetic levitation mechanism of the present invention is composed of four magnetic levitation bearings, generating a relatively large driving force and being applicable to more flight missions.

[0098] (2) The output force of the magnetic bearing of the present invention is related to the bearing clearance. According to the rigid connection between the four magnetic bearings and the connection relationship between the load and the bearings, the conversion matrix between 8 clearances and the 6-degree-of-freedom pose of the load is determined to solve the position and attitude of the load.

[0099] (3) According to the non-linear relationship between the electromagnetic force and the current and clearance changes, the present invention analyzes the deviation between the linearization and non-linearity of the electromagnetic force under different current and clearance changes, and gives the current and clearance ranges in which the electromagnetic force can be linearized, providing a simplified dynamic model for the spacecraft control design. Brief Description of the Drawings

[0100] Figure 1 is the non-contact split satellite relative position and attitude calculation flow chart of the magnetic levitation and stability enhancement mechanism of the present invention;

[0101] Figure 2 is the structural schematic diagram of the non-contact split satellite of the present invention;

[0102] Figure 3 is the magnetic buoyancy distribution schematic diagram of the present invention. Detailed Embodiment

[0103] The present invention will be further described below in conjunction with embodiments.

[0104] The present invention provides a non-contact split satellite relative position and attitude calculation method for a magnetic levitation and stability enhancement mechanism, establishing a relative dynamic model that takes into account the relationship between relative position and clearance changes and the clearance change range in which the magnetic buoyancy can be linearized, solving the relative position and attitude calculation problem during the process of the load cabin following the platform cabin based on the magnetic levitation and stability enhancement mechanism, and providing a theoretical model for the non-contact split satellite following control and vibration suppression system.

[0105] The non-contact split satellite relative position and attitude calculation method for the magnetic levitation and stability enhancement mechanism, as Figure 1 shown, specifically includes the following steps:

[0106] Establish the dynamic equation of the load cabin position and attitude. The method for establishing the dynamic equation of the load cabin position and attitude is as follows:

[0107] According to the non-contact split satellite structure, such as Figure 2 shown, four coordinate systems are defined, namely the coordinate system fixed in the inertial space platform module centroid coordinate system vibration isolation unit coordinate system payload module centroid coordinate system Specifically:

[0108] coordinate system The origin o n is located at the center of the earth; The axis is located on the equatorial plane, and the positive direction points to the vernal equinox at 12:00 on January 1, 2000 AD; The positive direction of the axis points to the North Pole; The positive direction of the axis is determined by the right-hand rule.

[0109] coordinate system The origin o d is located at the centroid of the platform module; The axis is parallel to the bottom surface of the aircraft, and the positive direction points to the front of the aircraft; The positive direction of the axis points to the direction of the docking surface with other basic models; The positive direction of the axis is determined by the right-hand rule.

[0110] coordinate system The origin o a is located at the geometric center of the magnetic levitation; The positive direction of the axis is the same as the D in the coordinate system O axis; The positive direction of the axis is the same as the D in the coordinate system O axis; The positive direction of the axis is determined by the right-hand rule.

[0111] coordinate system The origin o c is located at the centroid of the payload module; The axis is parallel to the bottom surface of the aircraft, and the positive direction points to the front of the aircraft; The positive direction of the axis points to the magnetic levitation center plane; The positive direction of the axis is determined by the right-hand rule.

[0112] According to rigid body motion, the position and attitude dynamics equation of the payload module is:

[0113]

[0114] In the formula, D r CN is the vector from O N to the centroid O C of the payload module in the inertial system in the coordinate system OD The expression under

[0115] is the translational velocity of the payload compartment relative to the inertial system, i.e., D r CN The first derivative with respect to time.

[0116] is the translational acceleration of the payload compartment relative to the inertial system, i.e., D r CN The second derivative with respect to time.

[0117] D ε C is the expression of the Euler angles of the payload compartment relative to the inertial system in the coordinate system O D under.

[0118] D ω C is the expression of the angular velocity of the payload compartment relative to the inertial system in the coordinate system O D under.

[0119] is the expression of the angular acceleration of the payload compartment relative to the inertial system in the coordinate system O D under.

[0120] W C is the angular velocity transformation matrix.

[0121] M C is the mass of the payload compartment.

[0122] J C is the moment of inertia of the payload compartment.

[0123] D F C is the magnetic buoyancy force acting on the centroid of the payload compartment.

[0124] G is the universal gravitational constant.

[0125] M g is the mass of the Earth.

[0126] According to the two-body motion law, based on the position and attitude dynamics equation of the payload compartment, the relative dynamics equation between the payload compartment and the platform compartment is established.

[0127] The method for establishing the inter-compartment relative dynamics equation is as follows:

[0128] According to the two-body relative kinematics law, in the O D coordinate system, the translational and rotational accelerations and velocities of the payload compartment are expressed using relative velocities and accelerations as well as the velocities and accelerations of the platform compartment, and the expressions are substituted into the attitude dynamics equation of the payload compartment; taking the relative 6-degree-of-freedom position and attitude variables as state variables, the inter-compartment relative dynamics equation is obtained:​

[0129]

[0130] In the formula, D r CD is the vector from the centroid O of the platform module to the centroid O D of the payload module. C

[0131]

[0132] is the translational acceleration of the payload module relative to the platform module.

[0133] is the translational velocity of the payload module relative to the platform module.

[0134] D ε CD is the Euler angle of the payload module relative to the platform module.

[0135] D ω CD is the angular velocity of the payload module relative to the platform module.

[0136] is the angular acceleration of the payload module relative to the platform module.

[0137] D ω D is the expression of the angular velocity of the platform module relative to the inertial system in the coordinate system O D .

[0138] is the angular acceleration of the platform module relative to the inertial system.

[0139] D r DN is the expression of the vector from the origin of the inertial system to the centroid of the payload module in the coordinate system O D .

[0140] is the translational velocity of the platform module relative to the inertial system, that is, D r DN the second derivative with respect to time.

[0141] is the translational velocity of the platform module relative to the inertial system, that is, D r DN the first derivative with respect to time.

[0142] D ε D is the expression of the Euler angle of the platform module relative to the inertial system in the coordinate system O D .

[0143] A magnetic levitation mechanism is provided between the payload compartment and the platform compartment; the magnetic levitation mechanism includes four groups of magnetic levitation bearings; the eight magnetic buoyancy forces f generated by the four groups of magnetic levitation bearings Li , such as Figure 3 shown. Among them, i is the serial number of the magnetic buoyancy force; and the matrix F L is used to represent the eight magnetic buoyancy forces. The eight magnetic buoyancy forces generated by the four groups of magnetic levitation bearings are:

[0144]

[0145] In the formula, F L is the matrix of the eight magnetic buoyancy forces;

[0146] is the i-th magnetic buoyancy force.

[0147] According to F L , calculate the resultant force F A formed by the magnetic buoyancy forces at the magnetic levitation geometric center; according to the resultant force F A , calculate the magnetic buoyancy force D F 磁上 acting on the centroid of the payload compartment.

[0148] The calculation method of the resultant force F A formed by the magnetic buoyancy forces at the magnetic levitation geometric center is:

[0149]

[0150] In the formula, L z is the distance from the magnetic levitation output point to the magnetic levitation geometric center.

[0151] The acting planes of the eight magnetic buoyancy forces F L are always parallel to the installation interface of the platform compartment. Therefore, the geometric center of the magnetic buoyancy forces coincides with the geometric center of the magnetic levitation mechanism of the platform compartment, the coordinate system of the magnetic buoyancy forces is fixedly connected to the coordinate system of the platform compartment, and the calculation method of the magnetic buoyancy force D F 磁上 acting on the centroid of the payload compartment is:

[0152]

[0153] In the formula, D R A is the transformation matrix from the coordinate system O A to the coordinate system O D .

[0154] I is the identity matrix.

[0155] D r AC is the vector from the centroid of the payload compartment to the geometric center of the magnetic levitation mechanism.

[0156] ( D rAC ) × is the cross - product matrix of the vector D r AC .

[0157] D F 磁上 realizes replacing the magnetic buoyancy force acting on the centroid of the payload compartment in the relative dynamics equation of the cabin D F C .

[0158] Establish the calculation equation of the magnetic buoyancy force f Li and obtain the relationship between the magnetic buoyancy force f Li and the magnetic levitation gap δ 0 .

[0159] The calculation equation of the magnetic buoyancy force f Li is as follows:

[0160]

[0161] where μ 0 is the magnetic permeability of vacuum.

[0162] N S is the number of turns of the coil.

[0163] A S is the pole area.

[0164] I 0 is the bias current.

[0165] i x is the control current.

[0166] δ 0 is the magnetic levitation gap.

[0167] x is the change amount of the magnetic levitation gap.

[0168] Establish the conversion relationship between the relative pose of the payload compartment relative to the platform compartment and the magnetic levitation gap δ 0 .

[0169] Since the magnetic buoyancy force is a non - linear force and the relative dynamics system is a non - linear system, in order to solve the problem of difficult control design, the magnetic buoyancy force is linearized. Perform a first - order Taylor expansion on the non - linear magnetic buoyancy force to obtain a linear expression between the magnetic buoyancy force and the current and gap change:

[0170]

[0171] By comparing the non - linear and linear magnetic buoyancy force expressions, analyze the deviation values between the linear and non - linear magnetic buoyancy forces under different current and gap change amounts, and determine the reasonable range of magnetic buoyancy force linearization.

[0172] The relative position and attitude of the payload cabin with respect to the platform cabin include the three-axis translational momentum of the payload cabin relative to the platform cabin and the three-axis rotational momentum of the payload cabin relative to the platform cabin.

[0173] The calculation method for the conversion relationship between the relative position and attitude of the payload cabin with respect to the platform cabin and the magnetic levitation gap δ 0 is as follows:

[0174] In the platform cabin coordinate system, the translational and rotational change amount Δ D r CD of the centroid C of the payload cabin relative to the centroid D of the platform cabin is expressed as:

[0175]

[0176] In the formula, Δx CD is the translation amount of the centroid of the payload cabin relative to the centroid of the platform cabin in the axis direction.

[0177] Δy CD is the translation amount of the centroid of the payload cabin relative to the centroid of the platform cabin in the axis direction.

[0178] Δz CD is the translation amount of the centroid of the payload cabin relative to the centroid of the platform cabin in the axis direction.

[0179] is the rotation angle of the centroid of the payload cabin relative to the centroid of the platform cabin around the axis direction.

[0180] D θ C is the rotation angle of the centroid of the payload cabin relative to the centroid of the platform cabin around the axis direction.

[0181] D ψ C is the rotation angle of the centroid of the payload cabin relative to the centroid of the platform cabin around the axis direction.

[0182] The eight gap amounts δ of the four magnetic levitation bearings measured are:

[0183] δ = [δx 1 , δz 1 , δy 2 , δz 2 , δx 3 , δz 3 , δy 4 , δz 4 T

[0184] In the formula, δx 1 , δz 1 , δy​2 , δz 2 , δx 3 , δz 3 , δy 4 , δz 4 are the variation amounts of the directional clearances of the four magnetic levitation bearings respectively in direction;

[0185] According to Δ D r CD and the geometric relationship, the magnetic levitation clearance is expressed; the initial position is considered that the magnetic levitation sleeve and the shaft are concentric, and the initial clearance δ 0 , and the clearance variation is caused by relative translation and rotation; considering that the relative rotation of the upper platform cabin is very small, Therefore the magnetic levitation clearance variation is written as:

[0186]

[0187] In the formula, are respectively the components of the vector from the centroid of the load cabin to the magnetic levitation geometric center in the direction;

[0188] The relative pose expressed by the clearance variation:

[0189] Δd = [d 1 d 2 d 3 d 4 d 5 d 6 d 7 d 8 T

[0190]

[0191] Finally, the relationship between the relative pose of the load cabin relative to the platform cabin and the magnetic levitation force f Li is obtained, that is, the relative pose of the load cabin relative to the platform cabin is calculated according to the magnetic levitation force f Li .

[0192] Embodiment

[0193] The schematic diagram of the non-contact split satellite structure based on the magnetic levitation stability enhancement mechanism is as shown in Figure 2 and the relative position and attitude calculation method of the load cabin includes the following steps:

[0194] Step S1: Define four coordinate systems in the magnetic levitation vibration isolation system, and their definitions are as follows:

[0195] The coordinate system fixed in the inertial space: ​

[0196] The two coordinate systems fixed to the satellite platform (platform cabin) are defined as:

[0197] Platform cabin centroid coordinate system Fixedly connected to the center of mass of the platform cabin;

[0198] Vibration isolation unit coordinate system: It is fixed on the platform cabin, and its origin is located at the geometric center of the magnetic levitation;

[0199] The coordinate system fixed to the load compartment is defined as:

[0200] Coordinate system of the center of mass of the payload compartment: Fixedly connected to the center of mass of the payload compartment.

[0201] According to the rigid body motion, the dynamic equations of the position and attitude of the payload cabin can be written as:

[0202]

[0203] In the formula, D r CN O is the inertial system N To the center of mass of the payload compartment O C The vector in O D The expression in the coordinate system is D ε C The Euler angle of the payload cabin relative to the inertial system in coordinate system O D The following expression; D ω C is the angular velocity of the payload cabin relative to the inertial system at O D coordinate system, and W C is the angular velocity conversion matrix; M C , J C is the mass and moment of inertia of the payload cabin, D F C is the magnetic buoyancy force acting on the center of mass of the payload module.

[0204] Step S2: According to the relative kinematics law of two bodies, D The translational and rotational acceleration and velocity of the payload cabin in the coordinate system can be expressed by the relative velocity and acceleration and the velocity and acceleration of the platform cabin, and the expressions are substituted into the dynamic equation of the payload cabin. The relative 6-DOF position and attitude variables are used as state quantities, which can be organized into the following form:

[0205]

[0206] In the formula, D r CD is the center of mass of the platform cabin O D to the center of mass of the payload compartment OC vector D ε CD is the Euler angle of the payload compartment relative to the platform compartment D ω CD is the angular velocity of the payload compartment relative to the platform compartment

[0207] Step S3: The 8 electromagnetic forces generated by the four groups of magnetic bearings (as shown in Figure 3 )

[0208]

[0209] The resultant force / moment formed by the electromagnetic forces at the magnetic levitation geometric center can be expressed as:

[0210]

[0211] In the formula, LZ is the distance from the magnetic levitation output point to the magnetic levitation geometric center

[0212] The 8 electromagnetic forces F are provided by the magnetic levitation hardware L The acting plane is always parallel to the installation interface of the platform compartment. Therefore, the geometric center of the magnetic buoyancy coincides with the geometric center of the magnetic levitation mechanism of the platform compartment, and the coordinate system of the magnetic buoyancy is fixedly connected to the coordinate system of the platform compartment D R A = I, and the magnetic buoyancy acting on the center of mass of the payload compartment can be expressed as:

[0213]

[0214] In the formula D r AC is the vector from the center of mass of the payload compartment to the geometric center of the magnetic levitation mechanism D r AC = D r AD - D r CD , D r CD is the relative vector of the center of mass of the upper platform compartment

[0215] Step S4: Under the coordinate system of the platform compartment, the translational and rotational change amounts of the center of mass C of the payload compartment relative to the center of mass D of the platform compartment are expressed as:

[0216]

[0217] The 8 gap amounts of the 4 magnetic levitations measured by the eddy current sensors:

[0218] δ = [δx 1 , δz 1 , δy 2 , δz 2 , δx 3 , δz3 , δy 4 , δz 4 T

[0219] According to Δ D r CD and geometric relationships, the magnetic levitation gap can be expressed. The initial position assumes that the magnetic levitation sleeve and the shaft are concentric, and the initial gap is δ 0 , and the change in the gap is caused by relative translation and rotation. Considering that the relative rotation of the upper platform cabin is very small, Therefore the change in the magnetic levitation gap can be written as:

[0220]

[0221] Writing the change in the gap on the left side of the above formula as Δd = δ 0 - δ, the relative pose expressed in terms of the change in the gap can be obtained:

[0222] Δd = [d 1 d 2 d 3 d 4 d 5 d 6 d 7 d 8 T

[0223]

[0224] Step S5: The magnetic levitation bearing generates electromagnetic force through a differential method. The electromagnetic force Fi is related to the vacuum permeability μ 0 , the number of coil turns NS, the pole area AS, the bias current I0, and the magnetic levitation gap δ 0 , and has a non-linear relationship with the coil current ix and the gap change x:

[0225]

[0226] Since the magnetic levitation force is a non-linear force and the relative dynamic system is a non-linear system, the design of the controller for this system is relatively complex. Therefore, it is considered to linearize the magnetic levitation force to solve the problem of difficult control design. Perform a first-order Taylor expansion on the non-linear electromagnetic force to obtain a linear expression between the electromagnetic force and the current and gap changes:

[0227]

[0228] Compare the non-linear and linear electromagnetic force expressions, and analyze the deviation values between the linear and non-linear electromagnetic forces under different current and gap change amounts to determine the reasonable range of electromagnetic force linearization. ​​

[0229] The specific simulation data is as follows:

[0230] <![CDATA[Magnetic permeability in vacuum μ 0 (H / m)]]> <![CDATA[4π×10 -7 > <![CDATA[Number of turns N of the coil S > 300 <![CDATA[Magnetic pole area A S (mm 2 )]]> 30×35 <![CDATA[Bias current I 0 (A)]]> 1 <![CDATA[Magnetic levitation gap δ 0 (mm)]]> 0.5

[0231] Considering that the gap changes within the interval [-0.45mm, 0.45mm], according to the linear and nonlinear expressions of electromagnetic force, the error of the linear force relative to the nonlinear force can be obtained, as shown in the following table:

[0232] Clearance change x (m) Nonlinear force (N / m) Linear force (N / m) Error (%) -0.00045 -11842.3 -427.508 -96.39 -0.00036 -1474.56 -342.006 76.8061 -0.00027 -511.138 -256.505 49.8169 -0.00018 -225.718 -171.003 24.2404 -9.00E-05 -91.3235 -85.5016 6.37502 0 0 0 \ 9.00E-05 91.32348 85.50159 6.37502 0.00018 225.7181 171.0032 24.2404 0.00027 511.1382 256.5048 49.8169 0.00036 1474.556 342.0063 76.8061 0.00045 11842.32 427.5079 -96.39

[0233] It can be seen from the table that when the gap change is within [-0.09mm, 0.09mm], the error between the linear and nonlinear electromagnetic forces is below 6.5%. Beyond this range, the error increases significantly. That is to say, the linearized electromagnetic force is no longer applicable when the gap change exceeds ±0.09mm. Therefore, the design of the controller needs to ensure that the gap between the payload compartment and the platform compartment does not exceed this range during movement.

[0234] The magnetic levitation mechanism of the present invention is composed of four magnetic levitation bearings combined, generating a relatively large driving force and being applicable to more flight missions; the output force of the magnetic bearings of the present invention is related to the bearing gap. According to the rigid connection between the four magnetic bearings and the connection relationship between the load and the bearings, the conversion matrix between eight gaps and the six-degree-of-freedom pose of the load is determined to solve the position and attitude of the load.

[0235] Based on the nonlinear relationship between electromagnetic force, current, and gap change, the present invention analyzes the deviation between the linearization and nonlinearity of electromagnetic force under different currents and gap changes, and gives the current and gap ranges in which the electromagnetic force can be linearized, providing a simplified dynamic model for spacecraft control design.

[0236] Although the present invention has been disclosed above with 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 solution of the present invention using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modification, equivalent change, and decoration made to the above embodiments based on the technical essence of the present invention without departing from the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

Claims

1. A method for calculating relative position and attitude of non-contact split satellites using a magnetic levitation stabilization mechanism, characterized in that: include: Establish the dynamic equations of the position and attitude of the payload cabin; According to the motion law of the double body and based on the dynamic equation of the position and attitude of the payload cabin, the relative dynamic equation between the payload cabin and the platform cabin is established; A magnetic levitation mechanism is set between the payload cabin and the platform cabin; the magnetic levitation mechanism includes four sets of magnetic levitation bearings; the four sets of magnetic levitation bearings generate 8 magnetic levitation forces f Li ; where i is the magnetic buoyancy number; and the matrix F L Indicates 8 magnetic buoyancy forces; According to F L Calculate the resultant force F generated by the magnetic levitation force at the magnetic levitation geometric center A ; According to the resultant force F A Calculate the magnetic buoyancy force acting on the center of mass of the payload module D F 磁上 ; Establishing magnetic buoyancy f Li The calculation equation for the magnetic buoyancy force f is obtained Li The relationship between the magnetic levitation gap δ0; Establish the conversion relationship between the relative posture of the payload cabin relative to the platform cabin and the magnetic levitation gap δ0; Finally, the relative position of the payload cabin relative to the platform cabin and the magnetic buoyancy force f are obtained. Li According to the relationship between the magnetic buoyancy force f Li The relative position of the payload cabin relative to the platform cabin is calculated.

2. The method for calculating relative position and attitude of non-contact split satellites using a magnetic levitation stabilization mechanism according to claim 1 is characterized by: The method for establishing the dynamic equation of the position and attitude of the payload cabin is: Define 4 coordinate systems, which are the coordinate systems fixed in the inertial space Platform cabin centroid coordinate system Vibration isolation unit coordinate system Load cell center of mass coordinate system Specific: Coordinate system Origin o n Located at the center of the earth; The axis is located on the equatorial plane, with the positive direction pointing to the vernal equinox at 12:00 on January 1, 2000 AD; The positive direction of the axis points to the North Pole; The positive direction of the axis is determined by the right-hand rule; Coordinate system Origin o d Located at the center of mass of the platform cabin; The axis is parallel to the bottom of the aircraft, and the positive direction points to the front of the aircraft; The positive direction of the axis points to the direction of the docking surface with other base types; The positive direction of the axis is determined by the right-hand rule; Coordinate system Origin o a Located at the geometric center of Maglev; Axis positive direction and coordinate system O D middle Axis consistent; Axis positive direction and coordinate system O D middle Axis consistent; The positive direction of the axis is determined by the right-hand rule; Coordinate system Origin o c Located at the center of mass of the payload compartment; The axis is parallel to the bottom of the aircraft, and the positive direction points to the front of the aircraft; The positive direction of the axis points to the center plane of the magnetic levitation; The positive direction of the axis is determined by the right-hand rule; According to the rigid body motion, the dynamic equation of the position and attitude of the payload cabin is: In the formula, D r CN O is the inertial system N To the center of mass of the payload compartment O C The vector in the coordinate system O D The following expression; is the translational velocity of the payload cabin relative to the inertial system, that is D r CN First derivative with respect to time; is the translational acceleration of the load cabin relative to the inertial system, that is D r CN The second derivative with respect to time; D ε C is the Euler angle of the payload cabin relative to the inertial system in coordinate system O D The following expression; D ω C is the angular velocity of the payload cabin relative to the inertial system in coordinate system O D The following expression; is the angular acceleration of the payload cabin relative to the inertial system in coordinate system O D The following expression; W C is the angular velocity conversion matrix; M C is the mass of the payload compartment; J C is the moment of inertia of the load compartment; D F C is the magnetic buoyancy force acting on the mass center of the payload cabin; G is the gravitational constant; M g The mass of the earth.

3. The method for calculating relative position and attitude of non-contact split satellites using a magnetic levitation stabilization mechanism according to claim 2 is characterized in that: The method for establishing the relative dynamic equation between cabins is: According to the relative kinematics law of two bodies, D The translational and rotational accelerations and velocities of the payload cabin in the coordinate system are expressed by the relative velocity and acceleration and the velocity and acceleration of the platform cabin, and the expressions are substituted into the attitude dynamics equation of the payload cabin; the relative 6-DOF position attitude variables are used as state quantities to obtain the relative dynamics equation between cabins: In the formula, D r CD is the center of mass of the platform cabin O D to the center of mass of the payload compartment O C A vector of is the translational acceleration of the payload cabin relative to the platform cabin; is the translational velocity of the payload cabin relative to the platform cabin; D ε CD is the Euler angle of the payload cabin relative to the platform cabin; D ω CD is the angular velocity of the payload cabin relative to the platform cabin; is the angular acceleration of the payload cabin relative to the platform cabin; D ω D is the angular velocity of the platform cabin relative to the inertial system in the coordinate system O D The following expression; is the angular acceleration of the platform cabin relative to the inertial system; D r DN is the vector from the origin of the inertial system to the center of mass of the payload compartment in the coordinate system O D The following expression; is the translational velocity of the platform cabin relative to the inertial system, that is D r DN The second derivative with respect to time; is the translational velocity of the platform cabin relative to the inertial system, that is D r DN First derivative with respect to time; D ε D is the Euler angle of the platform cabin relative to the inertial system in coordinate system O D The following expression.

4. The method for calculating relative position and attitude of non-contact split satellites of magnetic levitation stabilization mechanism according to claim 3 is characterized by: The eight magnetic buoyancy forces generated by the four sets of magnetic bearings are: In the formula, F L is the matrix of 8 magnetic buoyancy forces; is the i-th magnetic buoyancy force.

5. The method for calculating relative position and attitude of non-contact split satellites of magnetic levitation stabilization mechanism according to claim 4 is characterized by: The resultant force F formed by the magnetic levitation force at the magnetic levitation geometric center A The calculation method is: Where, L z It is the distance from the maglev output point to the maglev geometric center.

6. The method for calculating relative position and attitude of non-contact split satellites of magnetic levitation stabilization mechanism according to claim 5 is characterized by: 8 Magnetic buoyancy F L The action plane is always parallel to the installation interface of the platform cabin. Therefore, the geometric center of the magnetic buoyancy force coincides with the geometric center of the magnetic levitation mechanism of the platform cabin. The coordinate system of the magnetic buoyancy force is fixedly connected to the coordinate system of the platform cabin. The magnetic buoyancy force acting on the center of mass of the payload cabin is D F 磁上 The calculation method is: In the formula, D R A is the coordinate system O A To coordinate system O D The transformation matrix of I is the identity matrix; D r AC is the vector from the mass center of the payload cabin to the geometric center of the magnetic levitation mechanism; ( D r AC ) × For vector D r AC The cross product matrix of D F 磁上 Realize the replacement of the magnetic buoyancy force acting on the center of mass of the payload cabin in the relative dynamic equation between cabins D F C .

7. The method for calculating relative position and attitude of non-contact split satellites of magnetic levitation stabilization mechanism according to claim 1 is characterized by: Magnetic buoyancy f Li The calculation equation is: Where μ0 is the vacuum magnetic permeability; N S is the number of coil turns; A S is the magnetic pole area; I0 is the bias current; i x To control the current; δ0 is the magnetic levitation gap; x is the change in the magnetic levitation gap.

8. The method for calculating relative position and attitude of non-contact split satellites of magnetic levitation stabilization mechanism according to claim 7 is characterized by: Since the magnetic buoyancy force is a nonlinear force and the relative dynamic system is a nonlinear system, the magnetic buoyancy force is linearized to solve the problem of difficult control design. The nonlinear magnetic buoyancy force is expanded by the first-order Taylor to obtain the linear expression between the magnetic buoyancy force and the current and gap changes: By comparing the nonlinear and linear magnetic buoyancy expressions, the deviation between the linear and nonlinear magnetic buoyancy under different current and gap changes is analyzed, and the reasonable range of magnetic buoyancy linearization is determined.

9. The method for calculating relative position and attitude of non-contact split satellites of magnetic levitation stabilization mechanism according to claim 8 is characterized by: The relative position of the payload cabin relative to the platform cabin includes the three-axis translation of the payload cabin relative to the platform cabin and the three-axis rotation of the payload cabin relative to the platform cabin.

10. The method for calculating relative position and attitude of non-contact split satellites of magnetic levitation stabilization mechanism according to claim 9, characterized in that: The conversion relationship between the relative position of the payload cabin to the platform cabin and the magnetic levitation gap δ0 is calculated as follows: In the platform cabin coordinate system, the translational rotation change Δ of the load cabin mass center C relative to the platform cabin mass center D D r CD It is expressed as: In the formula, Δx CD The center of mass of the load cabin is relative to the center of mass of the platform cabin. The amount of translation in the axis direction; Δy CD The center of mass of the load cabin is relative to the center of mass of the platform cabin. The amount of translation in the axis direction; Δz CD The center of mass of the load cabin is relative to the center of mass of the platform cabin. The amount of translation in the axis direction; The center of mass of the load cabin is around the center of mass of the platform cabin. The rotation angle of the axis; The center of mass of the load cabin is around the center of mass of the platform cabin. The rotation angle of the axis; D ψ C The center of mass of the load cabin is around the center of mass of the platform cabin. The rotation angle of the axis; The 8 gaps δ of the 4 magnetic bearings measured are: δ=[δx1,δz1,δy2,δz2,δx3,δz3,δy4,δz4] T Where, δx1, δz1, δy2, δz2, δx3, δz3, δy4, δz4 are the four magnetic bearings in Directional gap change; According to Δ D r CD The geometric relationship expresses the magnetic levitation gap; the initial position assumes that the magnetic levitation sleeve is co-centered with the shaft, the initial gap is δ0, and the gap change is caused by relative translation and rotation; considering that the relative rotation of the upper platform cabin is very small, therefore The change of magnetic levitation gap is written as: In the formula, are the vectors from the mass center of the payload cabin to the geometric center of the magnetic levitation. Directional component; Relative pose expressed by gap change: Δd=[d1 d2 d3 d4 d5 d5 d6 d7 d8 T

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