Multi-point planning based method and device for improving motion trajectory of slip-ringless dual-shaft synchronous alternating dynamo alternator

Abstract

The application discloses a multi-point planning-based improved method and device for a no-slip-ring double-shaft SADA motion trajectory, planning points are selected based on the motion state division of SADA; planning trajectory motion parameters are calculated based on the planning points; and the planning angle, angular velocity and angular acceleration are output according to the planning trajectory motion parameters obtained through calculation. The application can accurately calculate the angle, angular velocity and angular acceleration of the SADA motion planning trajectory, gives accurate trajectory input for SADA planning motion, improves the planning efficiency through simple planning point selection, and effectively solves the discontinuous problem of SADA planning motion.

Description

Technical Field

[0001] This invention relates to the field of aerospace technology, and specifically to a method and apparatus for improving the motion trajectory of a slip-ring-free dual-axis SADA system based on multi-point planning. Background Technology

[0002] The dual-axis slip-ring-free SADA motion planning used in existing engineering projects adopts segmented motion trajectory planning, which has the problem of discontinuity in the angle, angular velocity, and angular acceleration at the connection points between planning segments, making it difficult to make the SADA motion trajectory as smooth as possible. Summary of the Invention

[0003] To address the aforementioned problems, this invention provides a method and apparatus for improving the motion trajectory of a slip-ring-free dual-axis SADA system based on multi-point planning, aiming to effectively solve the problem of discontinuous motion planning in SADA systems.

[0004] According to a first aspect of the present disclosure, a method for improving the motion trajectory of a slip-ring-free dual-axis SADA system based on multi-point planning is provided, the method comprising the following steps:

[0005] Selecting planning points based on motion state division in SADA;

[0006] Calculate the motion parameters of the planned trajectory based on the planning points;

[0007] Based on the calculated motion parameters of the planned trajectory, the planned angle, angular velocity, and angular acceleration are output.

[0008] A further technical solution of the present invention is as follows: Based on the motion state division of SADA, the starting point of the planning cycle is point M, the ending point is point Q, and there are two intermediate points N and P in between. The trajectory is planned in multiple segments. First, a quartic polynomial is used to plan the trajectory between point M and point N. Then, a cubic polynomial is used to plan the trajectory between the two intermediate points N and P. Finally, a quartic polynomial is used to plan the trajectory between point P and the ending point Q.

[0009] A further technical solution of the present invention is: calculating the motion parameters of the planned trajectory based on the planning points, specifically expressed as:

[0010] ,

[0011] ,

[0012] ,

[0013] in, , , Here are the calculation expressions for the planning angles of segments MN, NP, and PQ, respectively, and their corresponding planning durations are respectively... , 、 , 、 、 is the corresponding planning time, , , Let

[0014] ;

[0015] ;

[0016] ;

[0017] , , is the planning trajectory motion coefficient to be solved;

[0018] Based on the known starting motion parameters, end motion parameters and motion rules of intermediate points, the planning trajectory motion coefficient is obtained by solving the planning angle calculation expression , , .

[0019] Further technical solutions of the application are: the planning trajectory motion coefficient is obtained by solving the planning angle calculation expression , , , specifically comprising:

[0020] From the planning 0 time, the initial angle is ,

[0021] (1)

[0022] From the planning 0 time, the initial angular velocity is ,

[0023] (2)

[0024] From the planning 0 time, the initial angular velocity is ,

[0025] (3)

[0026] From the N-point angle The end angle of the MN segment is the same,

[0027] (4)

[0028] From the N-point angle The same as the initial angle of the NP segment at time 0, so

[0029] (5)

[0030] The angular velocity of the N point is kept continuous, so

[0031] (6)

[0032] The angular acceleration of the N point is kept continuous, so

[0033] (7)

[0034] The angle of the P point is kept continuous, so The same as the final angle of the NP segment, so

[0035] (8)

[0036] The angle of the P point is the same as the initial angle of the PQ segment, so

[0037] (9)

[0038] The angular velocity of the P point is kept continuous, so

[0039] (10)

[0040] The angular acceleration of the P point is kept continuous, so

[0041] (11)

[0042] The angle of the Q point is known to be so

[0043] (12)

[0044] The angular velocity of the Q point is known to be so

[0045] (13)

[0046] The angular acceleration of the Q point is known to be

[0047] (14)

[0048] From equations (1) to (14), we can write in matrix form as follows:

[0049] (15)

[0050] ​Equation (15) can be expressed as

[0051] Equation (16)

[0052] From equation (16), we have

[0053] Equation (17)

[0054] From equation (17), we can calculate the coefficients:

[0055] According to a second aspect of the embodiments of the present disclosure, a multi-point planning based no-slip-ring double-shaft SADA motion trajectory improvement device is provided, and the device comprises:

[0056] A planning point selection module is configured to select a planning point based on a motion state of the SADA.

[0057] A planning trajectory motion parameter calculation module is configured to calculate a planning trajectory motion parameter based on the planning point.

[0058] A planning trajectory motion output module is configured to output a planned angle, angular velocity, and angular acceleration according to the planning trajectory motion parameter obtained by calculation.

[0059] In a further technical solution of the present disclosure, the device is based on a motion state division of the SADA, the start point of a planning period is the M point, the end point is the Q point, there are two intermediate points N and P, the trajectory is planned in multiple segments, a quartic polynomial is used to plan the trajectory between the M point and the N point, a cubic polynomial is used to plan the trajectory between the two intermediate points N and P, and finally a quartic polynomial is used to plan the trajectory between the P point and the end point Q.

[0060] Compared with the prior art, the multi-point planning algorithm of the present disclosure can accurately calculate the angle, angular velocity, and angular acceleration of the SADA motion planning trajectory, provides an accurate trajectory input for SADA planning motion, improves the planning efficiency by simplifying the selection of the planning point, and effectively solves the discontinuity problem of SADA planning motion.

[0061] It should be understood that the foregoing general description and the following detailed description are only exemplary and explanatory, and cannot limit the present disclosure. BRIEF DESCRIPTION OF DRAWINGS

[0062] The accompanying drawings, which are incorporated into and form part of the specification, illustrate embodiments consistent with the present disclosure and, together with the specification, serve to explain the principles of the present disclosure.

[0063] ​​​Figure 1 This is a schematic diagram of the improved motion trajectory method for slip-ring-free dual-axis SADA based on multi-point planning in an embodiment of the present invention;

[0064] Figure 2 This is a schematic diagram of multi-point planning trajectory division in an embodiment of the present invention;

[0065] Figure 3 This is a structural diagram of the slip-ring-free dual-axis SADA motion trajectory improvement device based on multi-point planning in an embodiment of the present invention;

[0066] Figure 4 This is the A-axis planning angle curve in this embodiment of the invention;

[0067] Figure 5 It is the expected approximate angle of axis A minus the planning angle error in the embodiment of the present invention;

[0068] Figure 6 This is the A-axis angular velocity curve in an embodiment of the present invention;

[0069] Figure 7 This is the A-axis angular acceleration curve in an embodiment of the present invention;

[0070] Figure 8 This is the B-axis planning angle curve in this embodiment of the invention;

[0071] Figure 9 It is the expected approximate angle of the B-axis minus the planning angle error in the embodiment of the present invention;

[0072] Figure 10 This is the B-axis angular velocity curve in this embodiment of the invention;

[0073] Figure 11 This is the B-axis angular acceleration curve in this embodiment of the invention. Detailed Implementation

[0074] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be noted that, for ease of description, only the parts relevant to the present invention are shown in the drawings, not the entire structure.

[0075] Before discussing the exemplary embodiments in more detail, it should be noted that some exemplary embodiments are described as processes or methods depicted as flowcharts. Although the flowcharts describe the steps as sequential processes, many of these steps can be performed in parallel, concurrently, or simultaneously. Furthermore, the order of the steps can be rearranged. The process can be terminated when its operation is complete, but may also have additional steps not included in the figures. The process can correspond to a method, function, procedure, subroutine, subroutine, etc.

[0076] This invention aims to achieve solar array tracking under dual-axis slip-ring-free SADA planning motion, and utilizes a multi-point planning method to improve the motion trajectory of slip-ring-free dual-axis SADA, which can be applied to the field of satellite dual-axis slip-ring-free SADA motion planning and control.

[0077] The following embodiments are provided for a proposed method and device for improving the motion trajectory of a slip-ring-free biaxial SADA system based on multi-point planning:

[0078] like Figure 1 As shown, a method for improving the motion trajectory of a slip-ring-free dual-axis SADA system based on multi-point planning includes the following steps:

[0079] S1. Select planning points based on motion state division of SADA;

[0080] S2. Calculate the motion parameters of the planned trajectory based on the planning points;

[0081] S3. Based on the calculated motion parameters of the planned trajectory, output the planned angle, angular velocity, and angular acceleration.

[0082] In the specific implementation process, such as Figure 2 As shown, the trajectory planning within the complete orbital cycle starts from point M, and sequentially enters tracking motion segment 1: MN segment, with a planning duration of tf1; turning motion segment 1: NP segment, with a planning duration of tf2; tracking motion segment 2: PQ segment, with a planning duration of tf3; tracking motion segment 3: M*N* segment, with a planning duration of tf1; turning motion segment 2: N*P* segment, with a planning duration of tf2; and tracking motion segment 4: P*Q* segment, with a planning duration of tf3.

[0083] The selection criteria for point P are:

[0084] ,

[0085] ,

[0086] when When, select this point as point P, where This represents the solar vector in the orbital frame. For the representation of his solar vector in an inertial frame, To set a conditional angle threshold, This represents the attitude quaternion of the orbital coordinate system relative to the inertial coordinate system.

[0087] Based on the SADA-based motion state division, the starting point of the planning period is M point, the ending point is Q point, and there are N and P two intermediate points in the middle. The trajectory planning is divided into multiple segments, and 4-3-4 trajectory can be used. First, use the quartic polynomial to plan the trajectory between M point and N point, then use the cubic polynomial to plan the trajectory between N point and P point, and finally use the quartic polynomial to plan the trajectory between P point and Q point.

[0088] Based on the planning point calculation planning trajectory motion parameters, the specific expression is:

[0089] ,

[0090] ,

[0091] , (1)

[0092] Among them, , , MN, NP, PQ segment planning angle calculation expression respectively, its corresponding planning time length is , , , , , Corresponding planning time, , , Let

[0093] ;

[0094] ;

[0095] ;

[0096] , , Planning trajectory motion coefficient needs to be solved;

[0097] Based on the known starting point motion parameters, ending point motion parameters and intermediate point motion rules, the planning trajectory motion coefficient is obtained by solving the planning angle calculation expression , , .

[0098] , , Unknown coefficient matrix needs to be solved, which can be solved by the following conditions:

[0099] 1) The initial angle of M point is known ;

[0100] 2) Known initial angular velocity of M point ;

[0101] 3) Known initial angular acceleration of M point ;

[0102] 4) Known angle of N point , which is also the end position of the MN segment quartic polynomial;

[0103] 5) The angle of N point is the same as the initial angle of NP segment, ensuring motion continuity;

[0104] 6) The angular velocity of N point remains continuous;

[0105] 7) The angular acceleration of N point remains continuous;

[0106] 8) Known angle of P point , which is the same as the end angle of NP segment;

[0107] 9) The angle of P point is the same as the initial angle of PQ segment;

[0108] 10) The angular velocity of P point remains continuous;

[0109] 11) The angular acceleration of P point remains continuous;

[0110] 12) Known angle of Q point at the end ;

[0111] 13) Given angular velocity of Q at the end ;

[0112] 14) Given angular acceleration of Q at the end ;

[0113] The following is the process of solving unknown coefficients:

[0114] 1) From the planning 0 time, the initial angle is , then

[0115] (2)

[0116] 2) From the planning 0 time, the initial angular velocity is , then

[0117] (3)

[0118] 3) From the planning 0 time, the initial angular velocity is , then

[0119] (4)

[0120] 4) Angle from point N If the angle at the end of segment MN is the same, then

[0121] (5)

[0122] 5) Angle from point N The initial angle is the same as that at time 0 of segment NP, thus we have

[0123] (6)

[0124] 6) Since the angular velocity at point N remains continuous, therefore we have

[0125] (7)

[0126] 7) Since the angular acceleration at point N remains continuous, therefore we have

[0127] (8)

[0128] 8) Angle from point P The angle at the end of segment NP is the same, therefore we have

[0129] (9)

[0130] 9) Since the angle at point P is the same as the initial angle of segment PQ, therefore we have

[0131] (10)

[0132] 10) Since the angular velocity at point P remains continuous, therefore...

[0133] (11)

[0134] 11) Since the angular acceleration at point P remains continuous, therefore...

[0135] (12)

[0136] 12) Given that the angle of point Q is... Therefore, there is

[0137] (13)

[0138] 13) Given that the angular velocity of point Q is... Therefore, there is

[0139] (14)

[0140] 14) Given that the angular acceleration at point Q is... ,

[0141] (15)

[0142] The formula (2) to formula (15) can be written in the following matrix form:

[0143] (16)

[0144] The formula (16) can be expressed as

[0145] (17)

[0146] From the formula (17), the following can be obtained

[0147] (18)

[0148] Through (18), the coefficient can be calculated:

[0149] Another embodiment is used to illustrate a multi-point planning based no slip ring double-shaft SADA motion trajectory improvement device, as shown in Figure 3 The device 300 includes:

[0150] A planning point selection module 310, configured to select a planning point based on a motion state of the SADA;

[0151] A planning trajectory motion parameter calculation module 320, configured to calculate a planning trajectory motion parameter based on the planning point;

[0152] A planning trajectory motion output module 330, configured to output a planned angle, angular velocity and angular acceleration according to the planning trajectory motion parameter obtained by calculation.

[0153] The device 300 is based on the motion state division of the SADA, and the starting point of the planning period is the M point, the ending point is the Q point, and there are two intermediate points N and P in the middle. The trajectory is planned in multiple segments. First, a quartic polynomial is used to plan the trajectory between the M point and the N point, then a cubic polynomial is used to plan the trajectory between the two intermediate points N and P, and finally a quartic polynomial is used to plan the trajectory between the P point and the ending point Q.

[0154] In addition to the above modules, the device 300 can also include other components, however, since these components are irrelevant to the content of the embodiments of the present disclosure, their illustrations and descriptions are omitted here.

[0155] The other specific working processes of the multi-point planning based no slip ring double-shaft SADA motion trajectory improvement device 300 refer to the description of the above multi-point planning based no slip ring double-shaft SADA motion trajectory improvement method embodiments, and will not be repeated here.​​​

[0156] To verify the effectiveness of the method and apparatus of this invention, a simulation example is used to illustrate the beneficial effects of the invention. The angle, angular velocity, and angular acceleration curves planned along axes A and B show that the angle, angular velocity, and angular acceleration are all smooth throughout the entire orbital cycle. Furthermore, the angular velocity and angular acceleration are zero at the beginning and end of the planned cycle, exhibiting a regular periodic motion. The algorithm's implementation logic and computational complexity are simple, facilitating engineering implementation. Table 1 in the verification example shows the simulation conditions for the planned cycle.

[0157] Table 1

[0158]

[0159] like Figure 4 The figure shows the angle curve for the A-axis planning. Figure 5 The approximate angle of axis A is the difference between the planned angle error and the expected angle. Figure 6 Plan the angular velocity curve for axis A. Figure 7 Plan the angular acceleration curve for axis A. Figure 8 Plan the angle curve for the B-axis. Figure 9 The approximate angle of the B-axis is the expected angle minus the planning angle error. Figure 10 Plan the angular velocity curve for the B-axis. Figure 11 An angular acceleration curve is planned for the B-axis. These curves show that the transition from the tracking motion segment to the turning motion segment, or vice versa, is continuous and smooth, demonstrating the effectiveness of the method and apparatus of this invention.

[0160] In this document, the terms “comprising,” “including,” or any other variations thereof are intended to cover non-exclusive inclusion, such that a step or method that comprises a list of elements includes not only those elements but also other elements not expressly listed or inherent to such a step or method.

[0161] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for improving the motion trajectory of a slip-ring-free biaxial SADA system based on multi-point programming, characterized in that, Includes the following steps: Selecting planning points based on motion state division in SADA; Calculate the motion parameters of the planned trajectory based on the planning points; Based on the calculated motion parameters of the planned trajectory, output the planned angle, angular velocity, and angular acceleration; Based on the motion state division of SADA, let the starting point of the planning cycle be point M, the ending point be point Q, and there are two intermediate points N and P in between. The trajectory planning is divided into multiple segments. First, the trajectory between point M and point N is planned using a quartic polynomial. Then, the trajectory between the two intermediate points N and P is planned using a cubic polynomial. Finally, the trajectory between point P and the ending point Q is planned using a quartic polynomial. The motion parameters of the planned trajectory are calculated based on the planning points, and the specific expression is as follows: , , , in, , , Here are the calculation expressions for the planning angles of segments MN, NP, and PQ, respectively, and their corresponding planning durations are respectively... , , , , , For the corresponding planning time, , , ,make ； ； ； , , The motion coefficients of the planned trajectory that need to be solved; Based on the known motion parameters of the starting point, the ending point, and the motion rules of the intermediate points, the motion coefficients of the planned trajectory are obtained by solving the planning angle calculation expression. , , ; The motion coefficients of the planned trajectory are obtained by solving the expression for the planning angle. , , Specifically, it includes: From the planning at time 0, the initial angle is ,but （1） From the planning at time 0, the initial angular velocity is ,but （2） From the planning at time 0, the initial angular velocity is ,but （3） From N points angle If the angle at the end of segment MN is the same, then （4） Angle from point N The initial angle is the same as that at time 0 of segment NP, thus we have （5） Since the angular velocity at point N remains continuous, therefore we have （6） Since the angular acceleration at point N remains continuous, therefore we have （7） Angle from point P The angle at the end of segment NP is the same, therefore we have （8） Since the angle at point P is the same as the initial angle of segment PQ, therefore we have （9） Since the angular velocity at point P remains continuous, we have （10） Since the angular acceleration at point P remains continuous, we have （11） Given that the angle of point Q is Therefore, there is （12） Given that the angular velocity of point Q is Therefore, there is （13) Given that the angular acceleration at point Q is , （14） Equations (1) to (14) can be written in the following matrix form: （15） Equation (15) can be expressed as （16） From equation (16), we can obtain （17） The coefficient can be calculated using (17): , , .

2. A slip-ring-free dual-axis SADA motion trajectory improvement device based on multi-point planning, characterized in that, The device includes: The planning point selection module is used to select planning points based on the motion state division of SADA. The planning trajectory motion parameter calculation module is used to calculate the planning trajectory motion parameters based on the planning points; The planned trajectory motion output module is used to output the planned angle, angular velocity, and angular acceleration based on the calculated planned trajectory motion parameters. The device is based on the motion state division of SADA, with the starting point of the planning cycle being point M, the ending point being point Q, and two intermediate points N and P in between. The trajectory is planned in multiple segments. First, a quartic polynomial is used to plan the trajectory between point M and point N, then a cubic polynomial is used to plan the trajectory between the two intermediate points N and P, and finally a quartic polynomial is used to plan the trajectory between point P and the ending point Q. The motion parameters of the planned trajectory are calculated based on the planning points, and the specific expression is as follows: , , , in, , , Here are the calculation expressions for the planning angles of segments MN, NP, and PQ, respectively, and their corresponding planning durations are respectively... , , , , , For the corresponding planning time, , , ,make ； ； ； , , The motion coefficients of the planned trajectory that need to be solved; Based on the known motion parameters of the starting point, the ending point, and the motion rules of the intermediate points, the motion coefficients of the planned trajectory are obtained by solving the planning angle calculation expression. , , ; The motion coefficients of the planned trajectory are obtained by solving the expression for the planning angle. , , Specifically, it includes: From the planning at time 0, the initial angle is ,but （1） From the planning at time 0, the initial angular velocity is ,but （2） From the planning at time 0, the initial angular velocity is ,but （3） From N points angle If the angle at the end of segment MN is the same, then （4） Angle from point N The initial angle is the same as that at time 0 of segment NP, thus we have （5） Since the angular velocity at point N remains continuous, therefore we have （6） Since the angular acceleration at point N remains continuous, therefore we have （7） Angle from point P The angle at the end of segment NP is the same, therefore we have （8） Since the angle at point P is the same as the initial angle of segment PQ, therefore we have （9） Since the angular velocity at point P remains continuous, we have （10） Since the angular acceleration at point P remains continuous, we have （11） Given that the angle of point Q is Therefore, there is （12） Given that the angular velocity of point Q is Therefore, there is （13) Given that the angular acceleration at point Q is , （14） Equations (1) to (14) can be written in the following matrix form: （15） Equation (15) can be expressed as （16） From equation (16), we can obtain （17） The coefficient can be calculated using (17): , , .

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