Non-contact split satellite relative position and attitude calculation method of magnetic levitation stabilization mechanism

Abstract

This invention relates to a non-contact, split-type satellite relative position and attitude calculation method using a magnetic levitation stabilization mechanism, belonging to the field of aerospace technology; it establishes the dynamic equations for the position and attitude of the payload compartment; it establishes the relative dynamic equations between the payload compartment and the platform compartment; and it uses matrix F... L Represent 8 magnetic levitation forces; calculate the resultant force F formed by the magnetic levitation forces at the geometric center of the magnetic levitation system. A According to the resultant force F A Calculate the magnetic levitation force acting on the center of mass of the payload compartment. D F 磁上 Establish magnetic levitation force f Li The calculation equation is used to obtain the magnetic levitation force f. Li The relationship between the payload compartment and the magnetic levitation gap δ0 is established; the conversion relationship between the relative position of the payload compartment and the platform compartment and the magnetic levitation gap δ0 is established; the relationship between the relative position of the payload compartment and the platform compartment and the magnetic levitation force f is obtained. Li The relationship, that is, based on the magnetic levitation force f Li The relative position and attitude of the payload compartment relative to the platform compartment are calculated. This invention solves the problem of calculating the relative position and attitude of the payload compartment following the platform compartment based on the magnetic levitation stabilization mechanism, and provides a theoretical model for non-contact split-type satellite following control and vibration suppression system.

Description

Technical Field

[0001] This invention belongs to the field of aerospace technology and relates to a non-contact, split-type satellite relative position and attitude calculation method for magnetic levitation stabilization mechanism. Background Technology

[0002] For non-contact split-type satellites based on magnetic levitation stabilization mechanisms, the relative dynamics model between the two modules is of great significance for their high-precision pointing control.

[0003] Non-contact, separate-unit satellites utilize a magnetic levitation mechanism to stably connect the platform and payload modules, reducing vibration issues encountered during on-orbit operation, particularly impacting precise payload pointing. This design adapts to the complex dynamic environments encountered in different mission phases. During stable operation in orbit, the payload and platform modules are completely separated in space, maintaining a millimeter-level gap, creating a non-contact, relatively suspended state. This minimizes the interference of platform module micro-vibrations and flexural vibrations on payload module pointing control, ensuring the spacecraft's stability and accuracy during mission execution. Maintaining a millimeter-level distance between the two modules during stable on-orbit operation, especially during maneuvers, poses a significant challenge to controller design. Therefore, it is necessary to establish an accurate dynamic model to provide a precise theoretical model for the satellite pointing controller design.

[0004] Existing non-contact "dual-super" satellite actuators employ magnetic levitation mechanisms based on uniform magnetic field voice coil motors. Compared to magnetic levitation mechanisms based on magnetic bearings, these mechanisms, for the same volume, generate greater output and are applicable to a wider range of mission scenarios. Therefore, the non-contact satellite in this invention utilizes a magnetic levitation mechanism based on magnetic bearings. The magnetic levitation force generated by this structure is non-linearly related to the change in the magnetic bearing clearance. Consequently, to achieve relative stability between the two modules and precise pointing of the payload module, the conversion relationship between the payload module's position and attitude changes and the magnetic bearing clearance must be considered during the relative dynamics modeling process. Furthermore, to simplify controller design, the range of clearance changes required to linearize the magnetic levitation force needs to be determined. Summary of the Invention

[0005] The technical problem solved by this invention is to overcome the shortcomings of the prior art and propose a non-contact split-type satellite relative position and attitude calculation method based on the magnetic levitation stabilization mechanism. This method solves the problem of calculating the relative position and attitude of the payload cabin following the platform cabin based on the magnetic levitation stabilization mechanism, and provides a theoretical model for non-contact split-type satellite following control and vibration suppression system.

[0006] The solution of the present invention is:

[0007] A non-contact, split-type satellite relative position and attitude calculation method for magnetic levitation stabilization mechanisms, including:

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

[0009] Based on the laws of two-body motion, and using the dynamic equations of the payload compartment's position and attitude, the relative dynamic equations between the payload compartment and the platform compartment are established.

[0010] A magnetic levitation mechanism is installed between the payload compartment and the platform compartment; the magnetic levitation mechanism includes four sets of magnetic levitation bearings; the four sets of magnetic levitation bearings generate eight magnetic levitation forces f. Li Where i is the magnetic levitation index; and the matrix F L This represents 8 magnetic levitation forces;

[0011] According to F L Calculate the resultant force F generated by the magnetic levitation force at the geometric center of the magnetic levitation system. A According to the resultant force F A Calculate the magnetic levitation force acting on the center of mass of the payload compartment. D F 磁上 ;

[0012] Establish magnetic levitation force f Li The calculation equation is used to obtain the magnetic levitation force f. Li The relationship between the magnetic levitation gap δ0 and the magnetic levitation gap δ0;

[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 δ0;

[0014] Finally, the relative attitude of the payload compartment with respect to the platform compartment and the magnetic levitation force f are obtained. Li The relationship, that is, based on the magnetic levitation force f Li The relative pose of the payload compartment to the platform compartment is calculated.

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

[0016] Define four coordinate systems, which are fixed in inertial space. Platform cabin center of mass coordinate system Vibration Isolation Element Coordinate System Payload compartment center of mass coordinate system Specifically:

[0017] coordinate system The origin o n Located at the Earth's core; The axis is located on the equatorial plane, with its positive direction pointing to the vernal equinox at 12:00 on January 1, 2000. 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] coordinate system The origin o dLocated at the center of mass of the platform compartment; The axis is parallel to the bottom surface of the aircraft, and its positive direction points towards the front of the aircraft. The positive direction of the axis points towards the mating surface with other base types; The positive direction of the axis is determined by the right-hand rule;

[0019] coordinate system The origin o a Located at the geometric center of the maglev; Positive direction of axis and coordinate system O D middle Axis alignment; Positive direction of axis and coordinate system O D middle Axis alignment; The positive direction of the axis is determined by the right-hand rule;

[0020] coordinate system The origin o c Located at the center of mass of the payload compartment; The axis is parallel to the bottom surface of the aircraft, and its positive direction points towards the front of the aircraft. The positive direction of the axis points to the central plane of the magnetic levitation; The positive direction of the axis is determined by the right-hand rule;

[0021] Based on rigid body motion, the dynamic equations for the position and attitude of the payload compartment are as follows:

[0022]

[0023] In the formula, D r CN In an inertial frame of reference O N To the center of mass of the payload compartment O C The vector in coordinate system O D The following expression;

[0024] The translational velocity of the payload compartment relative to the inertial frame is, i.e. D r CN The first derivative with respect to time;

[0025] The translational acceleration of the payload compartment relative to the inertial frame is, i.e. D r CN The second derivative with respect to time;

[0026] D ε C The Euler angles of the payload compartment relative to the inertial frame in coordinate system O D The following expression;

[0027] D ω C The angular velocity of the payload compartment relative to the inertial frame in coordinate system OD The following expression;

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

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

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

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

[0032] D F C The magnetic levitation force acting on the center of mass of the payload compartment;

[0033] G is the gravitational constant;

[0034] M g The mass of Earth.

[0035] In the aforementioned non-contact, split-type satellite relative position and attitude calculation method for magnetic levitation stabilization mechanism, the method for establishing the inter-cabin relative dynamic equation is as follows:

[0036] According to the laws of relative kinematics of two bodies, in O D The translational rotational acceleration and velocity of the payload compartment in the coordinate system are expressed using relative velocity and acceleration, as well as the velocity and acceleration of the platform compartment. These expressions are then substituted into the payload compartment attitude dynamics equations. Using the relative 6-DOF position and attitude variables as state variables, the inter-compartment relative dynamics equations are obtained:

[0037]

[0038] In the formula, D r CD For the platform cabin center of mass O D The center of mass of the payload compartment O C ;

[0039]

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

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

[0042] D ε CD The Euler angle between the payload compartment and the platform compartment;

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

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

[0045] D ω D The angular velocity of the platform module relative to the inertial frame in coordinate system O D The following expression;

[0046] The angular acceleration of the platform cabin relative to the inertial frame;

[0047] D r DN The vector from the origin of the inertial frame to the center of mass of the payload chamber in coordinate system O D The following expression;

[0048] Let the platform module's translational velocity relative to the inertial frame be denoted as . D r DN The second derivative with respect to time;

[0049] Let the platform module's translational velocity relative to the inertial frame be denoted as . D r DN The first derivative with respect to time;

[0050] D ε D The Euler angles of the platform cabin relative to the inertial frame in coordinate system O D The expression below.

[0051] In the aforementioned non-contact, split-type satellite relative position and attitude calculation method for the magnetic levitation stabilization mechanism, the eight magnetic levitation forces generated by the four sets of magnetic levitation bearings are:

[0052]

[0053] In the formula, F L It is a matrix of 8 magnetic levitation forces;

[0054] Let be the i-th magnetic levitation force.

[0055] In the aforementioned non-contact, split-type satellite relative position and attitude calculation method for maglev stabilization mechanism, the resultant force F formed by the maglev force at the maglev geometric center... A The calculation method is as follows:

[0056]

[0057] In the formula, L z This is the distance from the maglev power output point to the maglev geometric center.

[0058] In the aforementioned non-contact, split-type satellite relative position and attitude calculation method for the magnetic levitation stabilization mechanism, eight magnetic levitation forces F... L The plane of action is always parallel to the platform cabin installation interface. Therefore, the geometric center of the magnetic levitation force coincides with the geometric center of the platform cabin's magnetic levitation mechanism, and the coordinate system of the magnetic levitation force is fixedly connected to the platform cabin's coordinate system. The magnetic levitation force acting on the center of mass of the load cabin... D F 磁上 The calculation method is as follows:

[0059]

[0060] In the formula, D R A Coordinate system O A To coordinate system O D The transformation matrix;

[0061] I is the identity matrix;

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

[0063] ( D r AC ) × For vectors D r AC The cross product matrix;

[0064] D F 磁上 To achieve the magnetic levitation force acting on the center of mass of the payload compartment in the relative dynamic equations between the two compartments. D F C .

[0065] In the aforementioned non-contact, split-type satellite relative position and attitude calculation method for magnetic levitation stabilization mechanism, the magnetic levitation force f... Li The calculation equation is as follows:

[0066]

[0067] In the formula, μ0 is the vacuum permeability;

[0068] N S This refers to the number of coil turns.

[0069] A S The area of ​​the magnetic poles;

[0070] I0 is the bias current;

[0071] i x To control the current;

[0072] δ0 is the magnetic levitation gap;

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

[0074] In the aforementioned non-contact, split-type satellite relative position and attitude calculation method for magnetic levitation stabilization mechanism, since the magnetic levitation force is a nonlinear force and the relative dynamic system is also a nonlinear system, the magnetic levitation force is linearized to solve the problem of control design difficulty. A first-order Taylor expansion is performed on the nonlinear magnetic levitation force to obtain a linear expression between the magnetic levitation force and the changes in current and gap:

[0075]

[0076] By comparing the nonlinear and linear magnetic levitation force expressions, the deviation values ​​between linear and nonlinear magnetic levitation forces under different current and gap variations are analyzed to determine the reasonable range for linearizing the magnetic levitation force.

[0077] In the above-mentioned non-contact split-type satellite relative position and attitude calculation method for magnetic levitation stabilization mechanism, the relative attitude of the payload compartment relative to the platform compartment includes the 3-axis translational amount of the payload compartment relative to the platform compartment and the 3-axis rotational amount of the payload compartment relative to the platform compartment.

[0078] In the aforementioned non-contact, split-type satellite relative position and attitude calculation method for the magnetic levitation stabilization mechanism, the calculation method for the conversion relationship between the relative attitude of the payload compartment relative to the platform compartment and the magnetic levitation gap δ0 is as follows:

[0079] In the platform module coordinate system, the translational rotational change Δ of the payload module's center of mass C relative to the platform module's center of mass D is... D r CD Represented as:

[0080]

[0081] In the formula, Δx CD For the payload compartment's center of mass relative to the platform compartment's center of mass in Translation along the axial direction;

[0082] Δy CD For the payload compartment's center of mass relative to the platform compartment's center of mass in Translation along the axial direction;

[0083] Δz CD For the payload compartment's center of mass relative to the platform compartment's center of mass in Translation along the axial direction;

[0084] The center of mass of the payload compartment is relative to the center of mass of the platform compartment. Rotation angle in the axial direction;

[0085] D θ C The center of mass of the payload compartment is relative to the center of mass of the platform compartment. Rotation angle in the axial direction;

[0086] D ψ C The center of mass of the payload compartment is relative to the center of mass of the platform compartment. Rotation angle in the axial direction;

[0087] The eight clearance values ​​δ of the four magnetic levitation bearings were measured as follows:

[0088] δ=[δx1, δz1, δy2, δz2, δx3, δz3, δy4, δz4] T

[0089] In the formula, δx1, δz1, δy2, δz2, δx3, δz3, δy4, and δz4 represent the four magnetic levitation bearings at... Change in directional clearance;

[0090] According to Δ D r CD The geometric relationship is used to express the maglev gap; the initial position is assumed to be that the maglev sleeve and the axis are concentric, 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 in the magnetic levitation gap is written as:

[0091]

[0092] In the formula, The vectors from the center of mass of the payload compartment to the geometric center of the maglev are respectively in Component of direction;

[0093] Relative pose expressed in terms of gap change:

[0094] Δd=[d1 d2 d3 d4 d5 d6 d7 d8] T

[0095]

[0096] The advantages of this invention compared to the prior art are:

[0097] (1) The magnetic levitation mechanism of the present invention uses four magnetic levitation bearings in combination, which is cost-effective and generates greater power, making it suitable for more flight missions;

[0098] (2) The magnetic bearing output of the present invention is related to the bearing clearance. Based on the rigid connection between the four magnetic bearings and the connection relationship between the load and the bearing, the transformation matrix between the eight clearances and the six degrees of freedom of the load pose is determined, so as to solve the load position and attitude.

[0099] (3) Based on the nonlinear relationship between electromagnetic force and current and gap changes, this invention analyzes the deviation between linearization and nonlinearity of electromagnetic force under different current and gap changes, and gives the range of current and gap for electromagnetic force linearization, providing a simplified dynamic model for spacecraft control design. Attached Figure Description

[0100] Figure 1 This is a flowchart of the non-contact split-type satellite relative position and attitude calculation for the magnetic levitation stabilization mechanism of the present invention;

[0101] Figure 2 This is a schematic diagram of the non-contact split-type satellite structure of the present invention;

[0102] Figure 3 This is a schematic diagram of the magnetic levitation force distribution of the present invention. Detailed Implementation

[0103] The present invention will be further described below with reference to the embodiments.

[0104] This invention provides a non-contact method for calculating the relative position and attitude of a split-type satellite using a magnetic levitation stabilization mechanism. The established relative dynamic model considers the relationship between relative position and gap changes, as well as the gap change range that can be linearized by magnetic levitation force. This solves the problem of calculating the relative position and attitude of the payload cabin following the platform cabin based on the magnetic levitation stabilization mechanism, and provides a theoretical model for non-contact split-type satellite following control and vibration suppression systems.

[0105] A non-contact, split-type satellite relative position and attitude calculation method for maglev stabilization mechanisms, such as... Figure 1 As shown, the specific steps include the following:

[0106] Establish the dynamic equations for the position and attitude of the payload compartment. The method for establishing the dynamic equations for the position and attitude of the payload compartment is as follows:

[0107] Based on the non-contact, split-type satellite structure, such as Figure 2 As shown, four coordinate systems are defined, which are fixed in inertial space. Platform cabin center of mass coordinate system Vibration Isolation Element Coordinate System Payload compartment center of mass coordinate system Specifically:

[0108] coordinate system The origin o n Located at the Earth's core; The axis is located on the equatorial plane, with its positive direction pointing to the vernal equinox at 12:00 on January 1, 2000. 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 Located at the center of mass of the platform compartment; The axis is parallel to the bottom surface of the aircraft, and its positive direction points towards the front of the aircraft. The positive direction of the axis points towards the mating surface with other base types; The positive direction of the axis is determined by the right-hand rule.

[0110] coordinate system The origin o a Located at the geometric center of the maglev; Positive direction of axis and coordinate system O D middle Axis alignment; Positive direction of axis and coordinate system O D middle Axis alignment; The positive direction of the axis is determined by the right-hand rule.

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

[0112] Based on rigid body motion, the dynamic equations for the position and attitude of the payload compartment are as follows:

[0113]

[0114] In the formula, D r CN In an inertial frame of reference O N To the center of mass of the payload compartment O C The vector in coordinate system O D The expression below.

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

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

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

[0118] D ωC The angular velocity of the payload compartment relative to the inertial frame in coordinate system O D The expression below.

[0119] The angular acceleration of the payload compartment relative to the inertial frame in coordinate system O D The expression below.

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

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

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

[0123] D F C The magnetic levitation force acting on the center of mass of the payload compartment.

[0124] G is the gravitational constant.

[0125] M g The mass of Earth.

[0126] Based on the laws of two-body motion, and using the dynamic equations of the payload compartment's position and attitude, the relative dynamic equations between the payload compartment and the platform compartment are established.

[0127] The method for establishing the relative dynamic equations between the compartments is as follows:

[0128] According to the laws of relative kinematics of two bodies, in O D The translational rotational acceleration and velocity of the payload compartment in the coordinate system are expressed using relative velocity and acceleration, as well as the velocity and acceleration of the platform compartment. These expressions are then substituted into the payload compartment attitude dynamics equations. Using the relative 6-DOF position and attitude variables as state variables, the inter-compartment relative dynamics equations are obtained:

[0129]

[0130] In the formula, D r CD For the platform cabin center of mass O D The center of mass of the payload compartment O C The vector.

[0131]

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

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

[0134] D ε CDThe Euler angle is the distance between the payload compartment and the platform compartment.

[0135] D ω CD ω represents the angular velocity of the payload compartment relative to the platform compartment.

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

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

[0138] Let be the angular acceleration of the platform cabin relative to the inertial frame.

[0139] D r DN The vector from the origin of the inertial frame to the center of mass of the payload chamber in coordinate system O D The expression below.

[0140] Let the platform module's translational velocity relative to the inertial frame be denoted as . D r DN The second derivative with respect to time.

[0141] Let the platform module's translational velocity relative to the inertial frame be denoted as . D r DN The first derivative with respect to time.

[0142] D ε D The Euler angles of the platform cabin relative to the inertial frame in coordinate system O D The expression below.

[0143] A magnetic levitation mechanism is installed between the payload compartment and the platform compartment; the magnetic levitation mechanism includes four sets of magnetic levitation bearings; the four sets of magnetic levitation bearings generate eight magnetic levitation forces f. Li ,like Figure 3 As shown. Where i is the magnetic levitation index; and represented by matrix F L This represents 8 magnetic levitation forces. The 8 magnetic levitation forces generated by the four sets of magnetic bearings are:

[0144]

[0145] In the formula, F L It is a matrix of 8 magnetic levitation forces;

[0146] Let be the i-th magnetic levitation force.

[0147] According to F L Calculate the resultant force F generated by the magnetic levitation force at the geometric center of the magnetic levitation system.A According to the resultant force F A Calculate the magnetic levitation force acting on the center of mass of the payload compartment. D F 磁上 .

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

[0149]

[0150] In the formula, L z This is the distance from the maglev power output point to the maglev geometric center.

[0151] 8 magnetic levitation forces F L The plane of action is always parallel to the platform cabin installation interface. Therefore, the geometric center of the magnetic levitation force coincides with the geometric center of the platform cabin's magnetic levitation mechanism, and the coordinate system of the magnetic levitation force is fixedly connected to the platform cabin's coordinate system. The magnetic levitation force acting on the center of mass of the load cabin... D F 磁上 The calculation method is as follows:

[0152]

[0153] In the formula, D R A Coordinate system O A To coordinate system O D The transformation matrix.

[0154] I is the identity matrix.

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

[0156] ( D r AC ) × For vectors D r AC The cross product matrix.

[0157] D F 磁上 To achieve the magnetic levitation force acting on the center of mass of the payload compartment in the relative dynamic equations between the two compartments. D F C .

[0158] Establish magnetic levitation force f Li The calculation equation is used to obtain the magnetic levitation force f. Li The relationship between the magnetic levitation gap δ0 and the magnetic levitation gap δ0.

[0159] Magnetic levitation force f Li The calculation equation is as follows:

[0160]

[0161] In the formula, μ0 is the vacuum permeability.

[0162] N S This represents the number of turns in the coil.

[0163] A S denoted as the magnetic pole area.

[0164] I0 is the bias current.

[0165] i x To control the current.

[0166] δ0 is the magnetic levitation gap.

[0167] x represents the change in the magnetic levitation gap.

[0168] Establish the conversion relationship between the relative position and attitude of the payload compartment relative to the platform compartment and the magnetic levitation gap δ0.

[0169] Since magnetic levitation force is a nonlinear force, and the relative dynamic system is also a nonlinear system, the magnetic levitation force is linearized to solve the problem of control design difficulties. A first-order Taylor expansion of the nonlinear magnetic levitation force is performed to obtain a linear expression between the magnetic levitation force and the changes in current and gap.

[0170]

[0171] By comparing the nonlinear and linear magnetic levitation force expressions, the deviation values ​​between linear and nonlinear magnetic levitation forces under different current and gap variations are analyzed to determine the reasonable range for linearizing the magnetic levitation force.

[0172] The relative position of the payload compartment to the platform compartment includes the 3-axis translational motion of the payload compartment relative to the platform compartment and the 3-axis rotational motion of the payload compartment relative to the platform compartment.

[0173] The calculation method for the conversion relationship between the relative position and attitude of the payload compartment and the platform compartment and the magnetic levitation gap δ0 is as follows:

[0174] In the platform module coordinate system, the translational rotational change Δ of the payload module's center of mass C relative to the platform module's center of mass D is... D r CD Represented as:

[0175]

[0176] In the formula, Δx CD For the payload compartment's center of mass relative to the platform compartment's center of mass in Translation along the axial direction.

[0177] Δy CD For the payload compartment's center of mass relative to the platform compartment's center of mass in Translation along the axial direction.

[0178] Δz CD For the payload compartment's center of mass relative to the platform compartment's center of mass in Translation along the axial direction.

[0179] The center of mass of the payload compartment is relative to the center of mass of the platform compartment. Rotation angle in the axial direction.

[0180] D θ C The center of mass of the payload compartment is relative to the center of mass of the platform compartment. Rotation angle in the axial direction.

[0181] D ψ C The center of mass of the payload compartment is relative to the center of mass of the platform compartment. Rotation angle in the axial direction.

[0182] The eight clearance values ​​δ of the four magnetic levitation bearings were measured as follows:

[0183] δ=[δx1, δz1, δy2, δz2, δx3, δz3, δy4, δz4] T

[0184] In the formula, δx1, δz1, δy2, δz2, δx3, δz3, δy4, and δz4 represent the four magnetic levitation bearings at... Change in directional clearance;

[0185] According to Δ D r CD The geometric relationship is used to express the maglev gap; the initial position is assumed to be that the maglev sleeve and the axis are concentric, 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 in the magnetic levitation gap is written as:

[0186]

[0187] In the formula, The vectors from the center of mass of the payload compartment to the geometric center of the maglev are respectively in Component of direction;

[0188] Relative pose expressed in terms of gap change:

[0189] Δd=[d1 d2 d3 d4 d5 d6 d7 d8] T

[0190]

[0191] Finally, the relative attitude of the payload compartment with respect to the platform compartment and the magnetic levitation force f are obtained. Li The relationship, that is, based on the magnetic levitation force f Li The relative pose of the payload compartment to the platform compartment is calculated.

[0192] Example

[0193] A schematic diagram of a non-contact, split-type satellite structure based on a magnetic levitation stabilization mechanism is shown below. Figure 2 As shown, the method for calculating the relative position and attitude of the payload compartment includes the following steps:

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

[0195] Coordinate system fixed in inertial space:

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

[0197] Platform cabin center of mass coordinate system It is fixed to the center of gravity of the platform module;

[0198] Vibration isolation unit coordinate system: It is fixed to the platform cabin, with its origin located at the geometric center of the maglev;

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

[0200] Payload compartment center of mass coordinate system: It is fixed to the center of mass of the load compartment.

[0201] Based on rigid body motion, the dynamic equations for the position and attitude of the payload compartment can be written as:

[0202]

[0203] In the formula, D r CN In an inertial frame of reference O N To the center of mass of the payload compartment O C Vector in O D Representation in a coordinate system D ε C Euler angles of the payload compartment relative to the inertial frame in coordinate system O D The following expression; D ω C The angular velocity of the payload compartment relative to the inertial frame at O D Representation in a coordinate system, and W C M is the angular velocity transformation matrix; C J C For the mass and moment of inertia of the payload compartment, D FC The magnetic levitation force acting on the center of mass of the payload compartment.

[0204] Step S2: According to the laws of relative kinematics of two bodies, in O D The translational and rotational accelerations and velocities of the payload compartment in the coordinate system can be expressed using relative velocity and acceleration, as well as the velocity and acceleration of the platform compartment. These expressions are then substituted into the payload compartment's dynamic equations. Taking the relative 6-DOF position and attitude variables as state variables, the equations can be simplified as follows:

[0205]

[0206] In the formula, D r CD For the platform cabin center of mass O D The center of mass of the payload compartment O C The vector, D ε CD The Euler angles of the payload compartment relative to the platform compartment. D ω CD ω represents the angular velocity of the payload compartment relative to the platform compartment.

[0207] Step S3: The eight electromagnetic forces generated by the four sets of magnetic levitation bearings (such as...) Figure 3 As shown),

[0208]

[0209] The resultant force / torque generated by electromagnetic force at the geometric center of the magnetic levitation can be expressed as:

[0210]

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

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

[0213]

[0214] In the formula, D r AC Let the vector be the distance 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 , Dr CD The relative vector of the center of mass of the upper platform compartment.

[0215] Step S4: In the platform module coordinate system, the translational rotation of the payload module's center of mass C relative to the platform module's center of mass D is expressed as:

[0216]

[0217] Eddy current sensor measures 8 gap quantities for 4 magnetic levitations:

[0218] δ=[δx1, δz1, δy2, δz2, δx3, δz3, δy4, δz4] T

[0219] According to Δ D r CD The geometric relationship can be used to express the maglev gap. The initial position is assumed to be that the maglev sleeve and the axis are concentric, with an initial gap δ0. 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 in the magnetic levitation gap can be written as:

[0220]

[0221] Writing the gap change on the left side of the above equation as Δd=δ0-δ, we can obtain the relative pose expressed in terms of gap change:

[0222] Δd=[d1 d2 d3 d4 d5 d6 d7 d8] T

[0223]

[0224] Step S5: The magnetic levitation bearing generates electromagnetic force through differential operation. The electromagnetic force Fi is related to the vacuum permeability μ0, the number of coil turns NS, the magnetic pole area AS, the bias current I0, and the magnetic levitation gap δ0, and has a nonlinear relationship with the coil current ix and the gap change x.

[0225]

[0226] Since magnetic levitation force is a nonlinear force, and the relative dynamic system is also a nonlinear system, the controller design for this system is quite complex. Therefore, we consider linearizing the magnetic levitation force to solve the problem of control design difficulty. A first-order Taylor expansion of the nonlinear electromagnetic force yields a linear expression between the electromagnetic force and the changes in current and gap:

[0227]

[0228] By comparing the expressions for nonlinear and linear electromagnetic forces, and analyzing the deviations between the linear and nonlinear electromagnetic forces under different current and gap variations, a reasonable range for linearizing the electromagnetic force can be determined.

[0229] The specific simulation data is shown in the table below:

[0230] <![CDATA[Magnetic permeability of vacuum μ0 (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 I0 (A)]]> 1 <![CDATA[Magnetic levitation gap δ0 (mm)]]> 0.5

[0231] Considering the gap varies within the range [-0.45mm, 0.45mm], the error of the linear force relative to the nonlinear force can be obtained based on the linear and nonlinear expressions of electromagnetic force, as shown in the table below:

[0232] Gap variation 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] As can be seen from the table, when the gap variation is within [-0.09mm, 0.09mm], the error of linear and nonlinear electromagnetic forces is below 6.5%. Beyond this range, the error increases significantly. In other words, the linearized electromagnetic force is no longer applicable when the gap variation exceeds ±0.09mm. Therefore, the controller design needs to ensure that the gap between the load compartment and the platform compartment does not exceed this range during movement.

[0234] The magnetic levitation mechanism of this invention uses a combination of four magnetic levitation bearings, which reduces costs and generates greater working force, making it suitable for more flight missions. The output force of the magnetic bearings in this invention is related to the bearing clearance. Based on the rigid connection between the four magnetic bearings and the connection relationship between the load and the bearings, the transformation matrix between the eight clearances and the six degrees of freedom of the load's pose is determined, thereby solving for the load's position and attitude.

[0235] Based on the nonlinear relationship between electromagnetic force and changes in current and gap, this invention analyzes the deviation between linearization and nonlinearity of electromagnetic force under different changes in current and gap, and gives the range of current and gap for linearization of electromagnetic force, providing a simplified dynamic model for spacecraft control design.

[0236] 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.

Claims

1. A non-contact, split-type satellite relative position and attitude calculation method for magnetic levitation stabilization mechanism, characterized in that: include: Establish the dynamic equations for the position and attitude of the payload compartment; Based on the laws of two-body motion, and using the dynamic equations of the payload compartment's position and attitude, the relative dynamic equations between the payload compartment and the platform compartment are established. A magnetic levitation mechanism is installed between the payload compartment and the platform compartment; the magnetic levitation mechanism includes four sets of magnetic levitation bearings; the four sets of magnetic levitation bearings generate eight magnetic levitation forces. ;in, The magnetic levitation index is used; and a matrix is ​​used. This represents 8 magnetic levitation forces; according to Calculate the resultant force of the magnetic levitation force at the geometric center of the magnetic levitation system. According to the resultant force Calculate the magnetic levitation force acting on the center of mass of the payload compartment. ; Establishing magnetic levitation The calculation equations are used to obtain the magnetic levitation force. Gap with maglev Relationship; Establish the relative attitude of the payload compartment with respect to the platform compartment and the magnetic levitation clearance. The transformation relationship; Finally, the relative attitude and magnetic levitation force of the payload compartment relative to the platform compartment are obtained. The relationship, that is, based on magnetic levitation force The relative pose of the payload compartment to the platform compartment is calculated.

2. The non-contact, split-type satellite relative position and attitude calculation method for the magnetic levitation stabilization mechanism according to claim 1, characterized in that: The method for establishing the dynamic equations of the payload compartment's position and attitude is as follows: Define four coordinate systems, which are fixed in inertial space. Platform cabin center of mass coordinate system Vibration isolation unit coordinate system Payload cabin center of mass coordinate system Specifically: coordinate system The origin Located at the Earth's core; The axis is located on the equatorial plane, with its positive direction pointing to the vernal equinox at 12:00 on January 1, 2000. 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 The origin Located at the center of mass of the platform compartment; The axis is parallel to the bottom surface of the aircraft, and its positive direction points towards the front of the aircraft. The positive direction of the axis points towards the mating surface with other base types; The positive direction of the axis is determined by the right-hand rule; coordinate system The origin Located at the geometric center of the maglev; Positive direction of axis and coordinate system middle Axis alignment; Positive direction of axis and coordinate system middle Axis alignment; The positive direction of the axis is determined by the right-hand rule; coordinate system The origin Located at the center of mass of the payload compartment; The axis is parallel to the bottom surface of the aircraft, and its positive direction points towards the front of the aircraft. The positive direction of the axis points to the central plane of the magnetic levitation; The positive direction of the axis is determined by the right-hand rule; Based on rigid body motion, the dynamic equations for the position and attitude of the payload compartment are as follows: In the formula, In an inertial frame to the center of mass of the payload compartment The vector in the coordinate system The following expression; The translational velocity of the payload compartment relative to the inertial frame is, i.e. The first derivative with respect to time; The translational acceleration of the payload compartment relative to the inertial frame is, i.e. The second derivative with respect to time; The Euler angles of the payload compartment relative to the inertial frame in the coordinate system The following expression; The angular velocity of the payload compartment relative to the inertial frame in the coordinate system The following expression; The angular acceleration of the payload compartment relative to the inertial frame in the coordinate system The following expression; For the mass of the payload compartment; The moment of inertia of the payload compartment; The magnetic levitation force acting on the center of mass of the payload compartment; It is the gravitational constant; It is the mass of Earth.

3. The non-contact, split-type satellite relative position and attitude calculation method for the magnetic levitation stabilization mechanism according to claim 2, characterized in that: The method for establishing the relative dynamic equations between the compartments is as follows: According to the laws of relative kinematics of two bodies, The translational and rotational accelerations and velocities of the payload compartment in the coordinate system are expressed using relative velocities and accelerations, as well as the velocities and accelerations of the platform compartment. These expressions are then substituted into the payload compartment's position and attitude dynamics equations. Using the relative 6-DOF position and attitude variables as state variables, the inter-compartment relative dynamics equations are obtained: In the formula, For the platform cabin center of mass The center of mass of the payload compartment ; This refers to the translational acceleration of the payload compartment relative to the platform compartment; The translational velocity of the payload compartment relative to the platform compartment; The Euler angle between the payload compartment and the platform compartment; The angular velocity of the payload compartment relative to the platform compartment; This refers to the angular acceleration of the payload compartment relative to the platform compartment; The angular velocity of the platform module relative to the inertial frame in the coordinate system The following expression; The angular acceleration of the platform cabin relative to the inertial frame; The vector from the origin of the inertial frame to the center of mass of the payload compartment in the coordinate system. The following expression; Let the platform module's translational velocity relative to the inertial frame be denoted as . The second derivative with respect to time; Let the platform module's translational velocity relative to the inertial frame be denoted as . The first derivative with respect to time; Euler angles of the platform module relative to the inertial frame in the coordinate system The expression below.

4. The non-contact, split-type satellite relative position and attitude calculation method for the magnetic levitation stabilization mechanism according to claim 3, characterized in that: The eight magnetic levitation forces generated by the four sets of magnetic bearings are: In the formula, It is a matrix of 8 magnetic levitation forces; Let be the i-th magnetic levitation force.

5. The non-contact, split-type satellite relative position and attitude calculation method for the magnetic levitation stabilization mechanism according to claim 4, characterized in that: The resultant force formed by the magnetic levitation force at the geometric center of the magnetic levitation The calculation method is as follows: In the formula, This is the distance from the maglev power output point to the maglev geometric center.

6. The non-contact, split-type satellite relative position and attitude calculation method for the magnetic levitation stabilization mechanism according to claim 5, characterized in that: 8 magnetic levitation forces The plane of action is always parallel to the platform cabin installation interface. Therefore, the geometric center of the magnetic levitation force coincides with the geometric center of the platform cabin's magnetic levitation mechanism, and the coordinate system of the magnetic levitation force is fixedly connected to the platform cabin's coordinate system. The magnetic levitation force acting on the center of mass of the load cabin... The calculation method is as follows: In the formula, coordinate system To coordinate system The transformation matrix; It is the identity matrix; The vector from the center of mass of the payload compartment to the geometric center of the magnetic levitation mechanism; For vectors The cross product matrix; To achieve the magnetic levitation force acting on the center of mass of the payload compartment in the relative dynamic equations between the two compartments. .

7. The non-contact, split-type satellite relative position and attitude calculation method for the magnetic levitation stabilization mechanism according to claim 1, characterized in that: Magnetic levitation The calculation equation is as follows: In the formula, The vacuum permeability; This refers to the number of coil turns. The area of ​​the magnetic poles; This is the bias current; To control the current; For magnetic levitation gap; This represents the change in the gap between magnetic levitation ...

8. The non-contact, split-type satellite relative position and attitude calculation method for the magnetic levitation stabilization mechanism according to claim 7, characterized in that: Since magnetic levitation force is a nonlinear force, and the relative dynamic system is also a nonlinear system, the magnetic levitation force is linearized to solve the problem of control design difficulties. A first-order Taylor expansion of the nonlinear magnetic levitation force is performed to obtain a linear expression between the magnetic levitation force and the changes in current and gap. By comparing the nonlinear and linear magnetic levitation force expressions, the deviation values ​​between linear and nonlinear magnetic levitation forces under different current and gap variations are analyzed to determine the reasonable range for linearizing the magnetic levitation force.

9. The non-contact, split-type satellite relative position and attitude calculation method for the magnetic levitation stabilization mechanism according to claim 8, characterized in that: The relative position of the payload compartment to the platform compartment includes the 3-axis translational motion of the payload compartment relative to the platform compartment and the 3-axis rotational motion of the payload compartment relative to the platform compartment.

10. The non-contact, split-type satellite relative position and attitude calculation method for the magnetic levitation stabilization mechanism according to claim 9, characterized in that: Relative position and attitude of the payload compartment relative to the platform compartment and the magnetic levitation clearance The method for calculating the conversion relationship is as follows: In the platform module coordinate system, the payload module's center of mass... C Relative platform cabin center of mass D Translational rotational change Represented as: In the formula, For the payload compartment's center of mass relative to the platform compartment's center of mass in Translation along the axial direction; For the payload compartment's center of mass relative to the platform compartment's center of mass in Translation along the axial direction; For the payload compartment's center of mass relative to the platform compartment's center of mass in Translation along the axial direction; The center of mass of the payload compartment is relative to the center of mass of the platform compartment. Rotation angle in the axial direction; The center of mass of the payload compartment is relative to the center of mass of the platform compartment. Rotation angle in the axial direction; The center of mass of the payload compartment is relative to the center of mass of the platform compartment. Rotation angle in the axial direction; Eight clearance measurements were taken from four sets of magnetic levitation bearings. for: In the formula, , , , , , , , Four sets of magnetic levitation bearings are respectively in , , Change in directional clearance; according to The geometric relationship expresses the maglev gap; the initial position assumes that the maglev sleeve and the shaft are concentric, and the maglev gap at this time... The change in clearance is caused by relative translation and rotation; considering that the relative rotation of the upper platform compartment is very small, ,therefore , The change in the magnetic levitation gap is written as: In the formula, , , The vectors from the center of mass of the payload compartment to the geometric center of the maglev are respectively in , , Component of direction; Relative pose expressed by the change in gap: 。

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