Motion control method of four-axis attitude adjusting platform

Abstract

The invention discloses a motion control method of a four-axis attitude adjusting platform, and belongs to the field of precise instrument control. An objective function is constructed based on mechanical structure characteristics, a Newton iteration method is used for solving and continuously approaching a solution meeting precision requirements, so that accurate values of rotation and translation variables are determined, the movement distance and the angle adjustment amount of each axis are accurately calculated, and reverse solution from a target attitude to a driving parameter is realized. And constructing an equation according to geometric constraint conditions, solving a connecting rod included angle by using the Newton iteration method again, ensuring that a calculation result is highly matched with known position information, finally obtaining accurate attitude parameters of the platform, and completing forward derivation from the position information to the attitude. By constructing an accurate kinematic model and an efficient calculation method, high-precision displacement and angle change control of the platform in a three-dimensional space is realized, stable and accurate operation of the platform in different application scenes is ensured, and the quality and efficiency of precision machining and detection operation are improved.

Description

Technical Field

[0001] The present invention relates to the field of precision instrument control, and particularly to a motion control method for a four-axis pose adjustment platform. Background Art

[0002] In applications with extremely high precision requirements such as laser welding, micro-hole machining, and wafer inspection, although the existing pose adjustment platforms can achieve a certain degree of pose adjustment, when facing complex spatial layouts and high-precision motion requirements, traditional component combinations (such as electric cylinders, connecting rods, Hooke joints, etc.) are difficult to meet the requirements of precise pose fine-tuning. Through in-depth research on the four-axis linkage pose adjustment platform, this algorithm aims to solve this problem and ensure that the platform can achieve high-precision pose adjustment under various working conditions.

[0003] The kinematic calculation of a multi-axis motion platform involves multiple variables and complex geometric relationships. Traditional calculation methods often have complex calculations and difficult-to-guarantee accuracy when dealing with these problems. Summary of the Invention

[0004] The purpose of the present invention is to solve the problem of accuracy requirements existing in the existing pose adjustment platforms, and to provide a motion control method for a four-axis pose adjustment platform.

[0005] The purpose of the present invention is achieved through the following technical solutions:

[0006] A motion control method for a four-axis pose adjustment platform, the steps include:

[0007] Step 1: Definition of coordinate system and structural parameters: Refer to Figure 1 , around the static platform of the four-axis pose adjustment platform, construct a coordinate system for the motion axes and rotational motion axes (including X, Y, Z1, Z2, Z3, C axes, where the X and Y axes are two perpendicular directions along the edges of the base platform, the Z1, Z2, and Z3 axes are the connecting rod motion mechanisms, and the C axis is the rotational motion axis), determine the motion relationships of each axis and the structural parameters of the connecting rods, including the connecting rod length, the distance between the rotation centers of the upper and lower fulcrums, the circumradius of the hinge fulcrum, and the angle range between the connecting rod and the horizontal plane; lay a foundation for subsequent kinematic calculations; these parameters are used to accurately describe the mechanical structure characteristics of the platform;

[0008] Step 2: Inverse solution operation process: Based on the target three-dimensional displacement and the rotation angle around the axis, construct an initial transformation matrix and a normal vector to simulate the spatial transformation relationship in the ideal motion state of the platform;

[0009] Considering mechanical constraints, construct equations through rotation and translation variables, and calculate the key coordinate points after transformation through matrices. These coordinate points are used to reflect the possible position states of the platform under mechanical constraints;

[0010] Construct the objective function based on the mechanical structure characteristics, solve it using the Newton iteration method, continuously approximate the solution that meets the accuracy requirements, determine the exact values of the rotation and translation variables, and accurately calculate the movement distances and angle adjustment amounts of each axis for reverse solution from the target pose to the drive parameters;

[0011] Step 3: Forward solution operation process: Given the current position information of the platform, calculate the coordinates of the hinge points on the lower platform according to the geometric structure formula, set the key link angle variables based on this, and obtain the calculation path of the coordinates of the support points on the upper platform;

[0012] By projecting points onto a plane, constructing a new coordinate system and transformation matrix, realize the conversion and calculation between coordinate systems, and accurately solve the coordinates of each hinge point in the base coordinate system;

[0013] Construct equations according to the geometric constraint conditions, and use the Newton iteration method again to solve the link angles, ensuring that the calculation results are highly consistent with the known position information, and finally obtain the accurate pose parameters of the platform to complete the forward derivation from position information to pose.

[0014] Furthermore, the platform pose is:

[0015] where move_x, move_y, and move_z are the displacement amounts in the X, Y, and Z axis directions respectively, and angle_x, angle_y, and angle_z are the rotation angles around the X, Y, and Z axes respectively. The mechanical structure obtains the transformation matrix: ;

[0016] The normal vector is:

[0017] where: ax = angle_x, ay = angle_y, az = 0.

[0018] Furthermore, after the target transformation, there will be slight displacements in the XYZ directions on the upper platform, but the movement of the hinge is mechanically restricted and can only be carried out within a specific plane. Assume that after the transformation, after rotating θ angle upward at the outer corner and translating by an amount of offset(XO, YO, ZO), it meets the mechanical hinge conditions and the pose Q. Then the constructed equation is:

[0019] ;

[0020] where:

[0021] ;

[0022] ;

[0023] According to the mechanical structure characteristics:

[0024] ;

[0025] The transformed coordinate points are calculated and :

[0026] ;

[0027] .

[0028] Furthermore, according to the mechanical structure characteristics:

[0029] ;

[0030] wherein, is the normal vector of the motion plane of the Z2 link, is the normal vector of the motion plane of the Z3 link; the equation of is obtained, and this equation is solved, and the approximate solution of the equation is solved by the Newton iteration method:

[0031] ;

[0032] ;

[0033] ;

[0034] ;

[0035] wherein, , are infinitesimals, until , is the solution accuracy, then satisfies the attitude Q, and the transformed coordinate points can be obtained:

[0036] ;

[0037] ;

[0038] .

[0039] Furthermore, the center position after transformation also shifts, and the current center position is:

[0040] ;

[0041] Since there is a distance difference h_thickness between the actual upper plane and the calculated upper plane, the offsets of the center point in the X, Y, and Z directions after deflection are respectively:

[0042] ;

[0043] ;

[0044] ;

[0045] The structure of the three-link not only realizes the yaw angle function but also takes into account the realization of the z-direction movement function. Then, the translation amount of the upper platform coordinates after transformation is:

[0046] ;

[0047] where h_0 is the platform height at zero position:

[0048] .

[0049] Furthermore, the coordinates of the hinge points on the upper platform are finally obtained as:

[0050] ;

[0051] ;

[0052] ;

[0053] Then, the coordinates of the hinge points on the lower plane:

[0054] ;

[0055] ;

[0056] ;

[0057] Then calculate the movement distance:

[0058] ;

[0059] ;

[0060] ;

[0061] Since the center point of the upper plane will move out of the original zero position after the attitude adjustment of the adjustment table, the displacement table that moves in the X and Y directions moves the zero point of the upper plane back to the original zero position, plus the displacement amounts required in the X and Y directions:

[0062] ;

[0063] ;

[0064] ;

[0065] Then the output , This is the position where the X-axis moves to.

[0066] Furthermore, the calculation of the correct solution in motion control refers to the process of calculating the platform attitude Q when the current position of the motion platform is known :

[0067] According to the platform geometry, the coordinates of the hinge points of the lower platform can be obtained as:

[0068] ;

[0069] ;

[0070] ;

[0071] Let the angle between the Z1 link and the horizontal plane at this time be . According to the mechanical relationship, it can be obtained that:

[0072] .

[0073] Furthermore, based on the fact that the link only moves within a plane, project point a onto the plane of motion of link Z2 for calculation. From , and , the point can be obtained as:

[0074] ;

[0075] ;

[0076] Draw the projection plane and establish a new coordinate system Rb at point B. Take the direction as the X'-axis; direction as the Z'-axis; the Y'-axis is perpendicular to the plane spanned by X' and Z', and the origin is point B:

[0077] ;

[0078] ;

[0079] Then the coordinate transformation matrix of the Rb coordinate system is:

[0080] ;

[0081] The homogeneous form is:

[0082] ;

[0083] First, transform the coordinates from the base coordinate system to the Rb coordinate system. The homogeneous form of the inverse transformation matrix is:

[0084] ;

[0085] The inverse matrix of the identity matrix is its transpose matrix:

[0086] ;

[0087] In the Rb coordinate system, the coordinates of point b_B are:

[0088] ;

[0089] where L_B is the line The projection in this plane is:

[0090] ;

[0091] edge is ;

[0092] The coordinates of point b in the base coordinate system can be calculated as:

[0093] ;

[0094] Calculate the coordinates of point c from this.

[0095] Furthermore, the calculated results need to satisfy: ; Solve value, using the Newton iteration method, let:

[0096] ;

[0097] Obtain the equation ;

[0098] ;

[0099] ;

[0100] until ( is the solution accuracy) then Satisfy position P; then obtain the fulcrum coordinates of the upper plane at this position; then the center point of the upper plane at this position is:

[0101] ;

[0102] The normal vector of the upper plane is:

[0103] ;

[0104] Obtain:

[0105] ;

[0106] ;

[0107] ;

[0108] ;

[0109] ;

[0110] ;

[0111] The current platform attitude is obtained as:

[0112] .

[0113] The beneficial effects of the present invention are:

[0114] (1) Through the inverse solution operation and the forward solution operation process, the movement distances and angles of each movement axis can be accurately calculated according to the given platform attitude or position information, realizing high-precision adjustment of the platform attitude; in practical applications, the displacement and rotation angle control of the platform in three-dimensional space can reach extremely high precision, meeting the strict requirements in fields such as precision machining and detection;

[0115] (2) The flexibility and adaptability of the algorithm are improved. This algorithm is not only applicable to the independent operation of the four-axis attitude adjustment platform, but can also be used in combination with the XY movement axis, greatly enhancing the movement flexibility and adaptability of the platform; in different application scenarios, the appropriate movement mode can be selected according to specific requirements, improving the versatility and practicality of the platform;

[0116] (3) The movement control precision is improved. During the movement control process, by accurately calculating and controlling the movement of each movement axis, the error during the platform movement is effectively reduced, improving the precision and stability of the movement control; it is of great significance for ensuring the quality of machining and detection and improving production efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0118] Figure 1 The directional axis construction diagram of the four-axis attitude adjustment platform control algorithm provided for the embodiment;

[0119] Figure 2 The mechanical structure set relationship diagram provided for this embodiment;

[0120] Figure 3 The plan view with point B as the origin drawn by projection provided for this embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0122] The technical solutions of the present invention will be clearly and completely described below in conjunction with the embodiments. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative efforts belong to the scope of protection of the present invention.

[0123] To achieve a high-precision attitude adjustment effect, the four-axis attitude adjustment platform adopts high-precision motion components and high-precision encoders; a mathematical model that meets high-precision adjustment is established based on the mechanical structure characteristics. This mathematical model mainly realizes the inverse kinematics solution (calculating the motion amounts of each axis of the platform through the attitude of the end of the platform) and the forward kinematics solution (calculating the attitude of the end of the platform through the motion amounts of each axis). In control, the inverse solution is the conversion from mechanical intuitive motion to controlling the motion of each axis, and the forward solution is for the controller to obtain the information of the machine at any position to prevent the machine from running away and over-travel; neither of them can be missing.

[0124] Therefore, a motion control method for a four-axis attitude adjustment platform is provided, and the steps include:

[0125] (1) Definition of coordinate system and structural parameters:

[0126] A coordinate system is constructed around the four-axis attitude adjustment platform (including the X, Y, Z1, Z2, Z3, and C axes) to determine the motion relationships of each axis and the structural parameters of the connecting rods, including the connecting rod length, the distance between the rotation centers of the upper and lower fulcrums, the circumradius of the hinge fulcrum, and the range of the angle between the connecting rod and the horizontal plane; this lays a foundation for subsequent kinematic calculations; these parameters are used to accurately describe the characteristics of the mechanical structure (static platform, motion axes, and rotational motion axes) of the platform.

[0127] This algorithm is based on the four-axis attitude adjustment platform and adds a kinematic algorithm for XY-direction motion. The algorithm can be decomposed for the independent use of the four-axis attitude adjustment platform or used in combination with the XY motion axes.

[0128] According to Figure 1 Figure 2 , the motion axis bodies are set as follows: the one for Y-direction motion is the Y axis; the one for X-direction motion is the X axis; the three connecting rod motion mechanisms are the Z1, Z2, and Z3 axes; the rotational motion axis is the C axis;

[0129] A simple model is constructed, and the coordinate system is defined and the model is simplified:

[0130] The lower rotation shaft of the connecting rod of the Z1 motion axis is A; the upper rotation shaft of the connecting rod of the Z1 motion axis is a; the lower rotation shaft of the connecting rod of the Z2 motion axis is B; the upper rotation shaft of the connecting rod of the Z2 motion axis is b; the lower rotation shaft of the connecting rod of the Z3 motion axis is C; the upper rotation shaft of the connecting rod of the Z3 motion axis is c; the circumradius of the circumcircle of the upper rotation shafts of the three connecting rods is r; the connecting rod lengths are l1 = l2 = l3 = l;

[0131] The moving distances of the X, Y, Z1, Z2, Z3, and C axes are move_X, move_Y, move_Z1, move_Z2, move_Z3, and move_C respectively; the angles formed by the connecting rods of the Z1, Z2, and Z3 axes with the XOY plane are θZ1, θ_Z2, and θ_Z3 respectively.

[0132] According to the established coordinate system, the intersection coordinates are calculated as follows:

[0133] As shown in the figure Figure 2 Based on the structural geometric relationship shown, the coordinates of the upper hinge support zero position state in the base coordinate system are:

[0134] ;

[0135] ;

[0136] ;

[0137] where: r is the radius of the circumscribed circle of the upper hinge support, l is the length between the rotation centers of the upper and lower supports, trip_z is the stroke of the Z axis, and angle_max is the maximum angle formed by the connecting rod with the horizontal plane;

[0138] The coordinates of the lower hinge support in the zero position state base coordinate system are:

[0139] ;

[0140] ;

[0141] ;

[0142] where: r is the radius of the circumscribed circle of the upper hinge support, l is the length between the rotation centers of the upper and lower supports, trip_z is the stroke of the Z axis, and angle_max is the maximum angle formed by the connecting rod with the horizontal plane.

[0143] (2) Inverse solution operation process:

[0144] Based on the target three-dimensional displacement and the rotation angle around the axis, an initial transformation matrix and a normal vector are constructed to simulate the spatial transformation relationship in the ideal motion state of the platform;

[0145] Considering mechanical constraints, equations are constructed through rotation and translation variables, and the key coordinate points after transformation are calculated through matrices. These coordinate points are used to reflect the possible position states of the platform under mechanical limitations;

[0146] Construct the objective function based on the mechanical structure characteristics, solve it using the Newton iteration method, continuously approximate the solution that meets the accuracy requirements, determine the exact values of the rotation and translation variables, and accurately calculate the movement distances and angle adjustment amounts of each axis for reverse solving from the target pose to the drive parameters;

[0147] The specific implementation is as follows:

[0148] The moving platform has an attitude (move_x, move_y, move_z are the displacements in the XYZ three directions respectively, unit: mm; angle_x, angle_y, angle_z are the angles of rotation around the XYZ axes respectively, and the right-hand rule is followed for the positive direction, unit: deg). And it is stated that this Euler angle is an interior angle (rotation around the coordinate axis after the previous transformation), and the rotation sequence is Z - Y - X. From the mechanical structure, the transformation matrix is obtained:

[0149] ;

[0150] The normal vector is:

[0151] ;

[0152] Where: ax = angle_x; ay = angle_y; az = 0;

[0153] After the transformation, there will be slight displacements in the XYZ directions on the upper platform, but the movement of the hinge is mechanically restricted and can only be carried out within a specific plane. That is, it is assumed that after the transformation, it rotates by θ angle on the outer corner and then translates by offset(XO, YO, ZO) amount to meet the mechanical hinge conditions, and the attitude meets Q. That is, the equation is constructed:

[0154] ;

[0155] Where: ;

[0156] ;

[0157] According to the mechanical structure characteristics: ;

[0158] Then the transformed coordinate points are obtained: , ;

[0159] According to the mechanical structure characteristics: ;

[0160] Where: is the normal vector of the movement plane of the Z2 connecting rod;

[0161] is the normal vector of the motion plane of the Z3 link;

[0162] obtain the equation of, and solve , and use the Newton iteration method to solve the approximate solution of the equation:

[0163] ;

[0164] ;

[0165] where represents the tangent line of the function curve corresponding to a certain value at a certain point, which intersects the axis at the point; similarly;

[0166] Due to the difficulty of taking the derivative, here let:

[0167] ;

[0168] ;

[0169] where , are infinitesimals; loop multiple times until ( is the solution accuracy), then satisfies the attitude Q, and the transformed coordinate points are obtained:

[0170] ;

[0171] ;

[0172] ;

[0173] Up to here, it is only to calculate the values of the three points a′, b′, c′ of the upper loading platform of the end attitude in the base coordinate system. Then calculate the offset position of the platform center when calculating the end attitude through these three points, and add the offset caused by other factors to obtain the final values of the three points av, bv, cv of the upper loading platform of the end attitude in the base coordinate system.

[0174] The center position after transformation also shifts, and the current center position is:

[0175] ;

[0176] Since there is a distance difference of h_thickness between the actual upper plane and the calculated upper plane, the offsets of the center point in the XYZ directions after deflection are respectively:

[0177] ;

[0178] ;

[0179] ;

[0180] The structure of the three-link not only realizes the yaw angle function, but also takes into account the realization of the z-direction movement function. Therefore, the upper platform coordinates need to be translated after transformation:

[0181] ;

[0182] Where: h_0 is the platform height at zero position: ;

[0183] Finally, the coordinates of the hinge points on the upper platform are:

[0184] ;

[0185] ;

[0186] ;

[0187] Then the coordinates of the hinge points on the lower plane:

[0188] ;

[0189] ;

[0190] ;

[0191] Then calculate the movement distance of the Z axis , , and c:

[0192] ;

[0193] ;

[0194] ;

[0195] ;

[0196] End the operation part of the four-axis adjustment table. If used with an XY platform, additional calculations are required to calculate the movement distances of the XY axes , .

[0197] After the adjustment table adjusts its attitude, the center point of the upper plane will be translated out of the original zero position. At this time, it is necessary to cooperate with the displacement table that moves in the X and Y directions to move the zero point of the upper plane back to the original zero position, plus the displacement required in the X and Y directions.

[0198] ;

[0199] ;

[0200] Then the output is:

[0201] ;

[0202] ( That is, the position where the X-axis moves to.)

[0203] (III) Correct solution calculation process:

[0204] Given the current position information of the platform, calculate the coordinates of the hinge points on the lower platform according to the geometric structure formula. Based on this, set the key link angle variables and obtain the calculation path of the coordinates of the support points on the upper platform;

[0205] By projecting points onto a plane, constructing a new coordinate system and transformation matrix, realize the conversion and calculation between coordinate systems, and accurately solve the coordinates of each support point in the base coordinate system;

[0206] Construct equations according to geometric constraint conditions, and use the Newton iteration method to solve the link angle again to ensure that the calculation results are highly consistent with the known position information, and finally obtain the accurate attitude parameters of the platform to complete the forward derivation from position information to attitude.

[0207] The specific implementation is as follows:

[0208] The calculation of the correct solution in motion control refers to the process of solving the attitude Q of the platform when the current position of the moving platform is known in this case.

[0209] According to the geometric structure of the platform, the coordinates of the hinge points on the lower platform can be obtained as:

[0210] ;

[0211] ;

[0212] ;

[0213] First: By knowing the movement distances of each axis, obtain the values of the intersection points A′, B′, and C′ on the lower plane in the base coordinate system under the end attitude. Then assume the angle between the Z1 link and the horizontal plane to calculate the value of the coordinate a′ of the intersection point of Z1 and the upper plane in the base coordinate system under the end attitude.

[0214] Let the angle between the Z1 connecting rod and the horizontal plane at this time ; According to the mechanical relationship, it can be obtained that:

[0215] ;

[0216] Then, according to the fact that the connecting rod can only move in a certain plane, project point a onto the plane where the Z2 connecting rod moves for calculation. From , and , the point is:

[0217] ;

[0218] ;

[0219] Draw the projection plane, as shown in Figure 3 . Then establish a new coordinate system Rb at point B, with the direction as the X'-axis; direction as the Z'-axis; the Y'-axis is perpendicular to the plane spanned by X' and Z'; the origin is point B, Convert the vector into a column vector:

[0220] ;

[0221] ;

[0222] Then the transformation matrix of the Rb coordinate system is written as:

[0223] ;

[0224] Written in homogeneous form:

[0225] ;

[0226] First, transform the coordinates from the base coordinate system to the Rb coordinate system. The homogeneous form of the inverse transformation matrix is:

[0227] ;

[0228] (The inverse matrix of the identity matrix = its transpose matrix)

[0229] ;

[0230] Then, in the Rb coordinate system, the coordinates of point b_B are:

[0231] ;

[0232] where L_B is the line Projection in this plane:

[0233] ;

[0234] edge is ;

[0235] So finally, the coordinates of point b in the base coordinate system can be calculated as:

[0236] ;

[0237] Similarly, the coordinates of point c can be calculated.

[0238] Through the above, it is to obtain the values of the intersection points a′, b′, c′ of the upper plane at the end pose in the base coordinate under the assumed value . Then, the value that meets the solution accuracy is obtained by the Newton iteration method. Then, the values of points a′, b′, c′ that meet the accuracy in the base coordinate can be obtained.

[0239] The calculated results need to meet: ; Solve the value. Using the Newton iteration method, let:

[0240] ;

[0241] The equation ;

[0242] ;

[0243] ;

[0244] Until ( is the solution accuracy), then meets the position P; then the fulcrum coordinates of the upper plane at this position are obtained. After obtaining the values of points a′, b′, c′ that meet the accuracy in the base coordinate, the current pose Q of the platform can be obtained through the mechanical structure.

[0245] Then the center point of the upper plane at this position is:

[0246] ;

[0247] The normal vector of the upper plane is:

[0248] ;

[0249] Then it can be obtained that:

[0250] ;

[0251] ;

[0252] ;

[0253] ;

[0254] ;

[0255] ;

[0256] Then the current platform has an attitude:

[0257] .

[0258] By constructing an accurate kinematic model and an efficient calculation method through the above steps, the platform can achieve high-precision displacement and angle change control in three-dimensional space, ensuring its stable and accurate operation in different application scenarios, and improving the quality and efficiency of precision machining and inspection operations.

[0259] The high-precision attitude adjustment of the machine is achieved through inverse kinematic calculation and forward kinematic calculation. It can accurately calculate the movement distance and angle of each motion axis according to the given platform attitude or position information, realizing high-precision adjustment of the platform attitude; in practical applications, the displacement and rotation angle control of the platform in three-dimensional space can reach extremely high precision, meeting the strict requirements of fields such as precision machining and inspection. The flexibility and adaptability of the algorithm are improved. This algorithm is not only applicable to the independent operation of the four-axis attitude adjustment platform, but also can be used in combination with the XY motion axis, greatly enhancing the motion flexibility and adaptability of the platform; in different application scenarios, the appropriate motion mode can be selected according to specific requirements, improving the versatility and practicality of the platform. The motion control precision is improved. During the motion control process, by accurately calculating and controlling the motion of each motion axis, the error during the platform motion is effectively reduced, improving the precision and stability of the motion control; it is of great significance for ensuring the quality of machining and inspection and improving production efficiency.

[0260] The above is only the preferred embodiment of the present invention. It should be understood that the present invention is not limited to the form disclosed herein, should not be regarded as excluding other embodiments, but can be used in various other combinations, modifications and environments, and can be changed within the scope of the concept described herein through the above teachings or the technology or knowledge in related fields. And the changes and modifications made by those skilled in the art without departing from the spirit and scope of the present invention should all be within the protection scope of the appended claims of the present invention.

Claims

1. A motion control method for a four-axis attitude adjustment platform, the platform comprising a stationary platform, a motion axis and a rotational motion axis, characterized in that, The method steps include: Step 1: Coordinate system and structure parameter definition: A coordinate system is constructed around the static platform of the four-axis posture adjustment platform, including the motion axes and the rotational motion axes. Step 2: Inverse solution operation process: Based on the target three-dimensional displacement and the rotation angles around the axes, an initial transformation matrix and a normal vector are constructed to simulate the spatial transformation relationship under the ideal motion state of the platform. Equations are constructed through rotation and translation variables to calculate the key coordinate points after transformation. Based on the static platform, motion axes, and rotational motion axes of the platform, an objective function is constructed and solved using the Newton iteration method. It continuously approaches the solution that meets the accuracy requirements to determine the exact values of the rotation and translation variables, and precisely calculates the motion distances and angle adjustment amounts of each axis for realizing the inverse solution from the target posture to the drive parameters. Step 3: Forward solution operation process: Given the current position information of the platform, calculate the coordinates of the hinge points on the lower platform, set the variable of the key link angle, and obtain the calculation path of the coordinates of the support points on the upper platform. Through projecting points onto a plane, constructing a new coordinate system and a transformation matrix, the conversion and calculation between coordinate systems are realized, and the coordinates of each hinge point in the base coordinate system are precisely solved. Equations are constructed according to the geometric constraint conditions, and the Newton iteration method is used again to solve the link angle to ensure that the calculation results are highly consistent with the known position information. Finally, the accurate posture parameters of the platform are obtained, completing the forward derivation from the position information to the posture.

2. The motion control method of a four-axis attitude adjustment platform according to claim 1, characterized in that The platform posture is: ； Among them, move_x, move_y, and move_z are the displacement amounts in the X, Y, and Z axis directions respectively, and angle_x, angle_y, and angle_z are the rotation angles around the X, Y, and Z axes respectively. The mechanical structure obtains the transformation matrix: ； The normal vector is: ； Among them: ax = angle_x, ay = angle_y, az = angle_z.

3. A motion control method for a four-axis attitude adjustment platform according to claim 2, characterized in that, Assume that after transformation, when rotating θ angle upward at the outer angle and translating by the amount of offset(XO, YO, ZO), the posture Q is satisfied. Then the constructed equation is: ； Among them: ； ； According to the mechanical structure characteristics: ； The calculated transformed coordinate points and : ； 。 4. The motion control method of a four-axis attitude adjustment platform according to claim 3, characterized in that, According to the mechanical structure characteristics: ； Among them, is the normal vector of the moving plane of the Z2 connecting rod, is the normal vector of the moving plane of the Z3 connecting rod; obtain the equation of, and solve this equation, and use the Newton iteration method to solve the approximate solution of the equation: ； ； ； ； Among them, , is a very small quantity until , is the solution accuracy, then Satisfying the attitude Q, the transformed coordinate points can be obtained: ； ； 。 5. A motion control method for a four-axis attitude adjustment platform according to claim 4, characterized in that, The center position also shifts after transformation. The current center position is: ； If there is a distance difference h_thickness between the actual upper plane and the calculated upper plane, then the offsets of the center point in the X, Y, and Z directions after deflection are respectively: ； ； ； The translation amount of the coordinates of the upper platform after transformation is: ； Among them, h_0 is the platform height at the zero position: 。 6. The motion control method of a four-axis attitude adjustment platform according to claim 5, characterized in that, Finally, the coordinates of the hinge points on the upper platform are obtained as: ； ； ； Then the coordinates of the hinge points on the lower plane: ； ； ； Then calculate the motion distance: ； ； ； Match the displacement stage moving in the X and Y directions to move the zero point of the upper plane back to the original 0 position, plus the required displacement amounts in the X and Y directions: ； ； ； The output quantity , is the position where the X-axis moves to.

7. A motion control method for a four-axis attitude adjustment platform according to claim 6, characterized in that The calculation of the correct solution in motion control refers to the process of calculating the platform attitude Q when the current position of the motion platform is known : According to the geometric structure of the platform, the coordinates of the hinge points on the lower platform can be obtained as: ； ； ； Let the angle between the Z1 connecting rod and the horizontal plane at this time , it can be obtained according to the mechanical relationship that: 。 8. A motion control method for a four-axis attitude adjustment platform according to claim 7, characterized in that, According to the fact that the connecting rod only moves in a plane, project point a onto the motion plane of the connecting rod Z2 for calculation. From and , it can be obtained that point is: ； ； Draw the projection plane and establish a new coordinate system Rb at point B. Take as the X'-axis; as the Z'-axis; the Y'-axis is perpendicular to the plane spanned by X' and Z', and the origin is point B: ； ； Then the transformation matrix of the Rb coordinate system is: ； The homogeneous form is: ； First, transform the coordinates from the base coordinate system to the Rb coordinate system. The homogeneous form of the inverse transformation matrix is: ； The inverse matrix of the identity matrix is its transpose matrix: ； In the Rb coordinate system, the coordinates of point b_B are: ； Among them, the projection of L_B on the line in this plane is: ； edge is ; The coordinates of point b in the base coordinate system can be calculated as: ； Based on this, the coordinates of point c are calculated.

9. The motion control method of a four-axis attitude adjustment platform according to claim 8, characterized in that, The calculated result should satisfy: ; Solve value. Using the Newton-Raphson method, let: ； Derive the equation ; ； ； Until (( For solution accuracy), then Satisfy position P; then obtain the fulcrum coordinates of the upper plane at this position; then the center point of the upper plane at this position is: ； The normal vector of the upper plane is: ； Obtain: ； ； ； ； ； ； Obtain the current platform posture as: 。

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