Flexible actuator rigidity autonomous calibration method

By constructing the kinematic model and flexibility calibration formula of the flexible actuator, the autonomous calibration of the flexible actuator is achieved, solving the problem that changes in stiffness characteristics during the spacecraft during orbit operation affect the load stability, and improving high frequency Evaluation of disturbance attenuation performance and selection of control parameters.

CN119245976APending Publication Date: 2025-01-03BEIJING INST OF CONTROL ENG
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Patent Information

Application Number
CN202411374399.X
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-09-29
Publication Date
2025-01-03

AI Technical Summary

Technical Problem

During the spacecraft's orbit, changes in the stiffness characteristics of the flexible actuator affect the load stability and high-frequency disturbance attenuation performance, and it is difficult for the prior art to achieve accurate evaluation and autonomous calibration.

Method used

By constructing a kinematic model of the flexible actuator, adjusting the output force into a sine wave form, and performing autonomous calibration according to the preset threshold value and flexibility calibration formula, obtaining the flexibility and stiffness calibration values ​​of the flexible actuator to achieve autonomous Calibration.

Benefits of technology

The accurate calibration of the stiffness characteristics parameters of the flexible actuator during the spacecraft's orbit operation is achieved, and the evaluation of the load high-frequency disturbance attenuation performance and the trusted selection of control parameters is improved.

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Abstract

The invention provides an autonomous calibration method for rigidity of a flexible actuator. The method comprises the steps that the output force of each flexible actuator is adjusted based on a flexible actuator kinematic model obtained through construction, so that the output force is in a sine wave form; whether the output force of the flexible actuator at the current moment is larger than a preset calibration threshold value or not is judged; if yes, calibrating the flexible actuator based on an actuator flexibility calibration formula to obtain a flexibility calibration value of the flexible actuator; if not, taking the next moment as the current moment, and returning to the step of judging the output force of the flexible actuator; whether the difference value between the flexibility calibration value at the current moment and the flexibility calibration value at the previous moment is larger than a calibration end threshold value or not is judged, and if yes, the step of judging the flexibility calibration value is executed again; and if not, calibrating the rigidity of the flexible actuator based on the flexibility calibration value at the current moment. According to the scheme, autonomous calibration of stiffness characteristic parameters of the flexible actuator during on-orbit operation of a spacecraft can be realized.
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Description

Technical Field

[0001] The embodiments of the present invention relate to the technical field of spacecraft attitude control, and in particular to a method for autonomously calibrating the stiffness of a flexible actuator. Background Art

[0002] A two-stage composite control system is formed by a pointing platform composed of a certain configuration and equipped with flexible actuators with active pointing control and passive vibration isolation. This can achieve high-precision pointing and high-stability control of the payload, and will become an essential technology for high-quality control of spacecraft.

[0003] With the long-term operation of spacecraft in orbit, the degradation of the performance parameters of its original components is inevitable. Among them, the stiffness characteristics of the flexible actuator are directly related to the high-frequency disturbance attenuation characteristics, affecting the load stability and the selection of secondary composite control parameters. Therefore, timely and accurate acquisition of its characteristic parameters can accurately evaluate the on-orbit operation status of the spacecraft.

[0004] Therefore, there is an urgent need to provide an autonomous stiffness calibration method for flexible actuators. Summary of the invention

[0005] The embodiment of the present invention provides a method for autonomously calibrating the stiffness of a flexible actuator, which can realize autonomous calibration of the stiffness characteristic parameters of the flexible actuator during the on-orbit operation of the spacecraft, thereby realizing accurate evaluation of the high-frequency disturbance attenuation performance of the spacecraft payload.

[0006] In a first aspect, an embodiment of the present invention provides a method for autonomously calibrating the stiffness of a flexible actuator, wherein a plurality of flexible actuators constitute an active pointing platform to drive a load to move;

[0007] Methods include:

[0008] Step S1, adjusting the output force of each flexible actuator based on the constructed kinematic model of the flexible actuator so that the output force is in the form of a sine wave;

[0009] Step S2, determining whether the output force of the flexible actuator at the current moment is greater than a preset calibration threshold;

[0010] Step S3: if yes, calibrate the flexible actuator based on the actuator compliance calibration formula to obtain a compliance calibration value of the flexible actuator;

[0011] Step S4: if not, take the next moment as the current moment and return to step S2;

[0012] Step S5, determining whether the difference between the current flexibility calibration value and the previous flexibility calibration value is greater than the calibration end threshold, if so, returning to step S3;

[0013] Step S6: if not, calibrate the stiffness of the flexible actuator based on the compliance calibration value at the current moment.

[0014] In a second aspect, an embodiment of the present invention further provides a flexible actuator stiffness autonomous calibration device, which is composed of a plurality of flexible actuators to form an active pointing platform to drive a load to move;

[0015] The device includes:

[0016] An adjustment unit, used for adjusting the output force of each flexible actuator based on the constructed kinematic model of the flexible actuator, so that the output force is in a sine wave form;

[0017] The first judgment unit is used to judge whether the output force of the flexible actuator at the current moment is greater than a preset calibration threshold; if so, calibrate the flexible actuator based on the actuator flexibility calibration formula to obtain the flexibility calibration value of the flexible actuator; if not, return to the next moment as the current moment to execute the output force judgment step of the flexible actuator;

[0018] The second judgment unit is used to judge whether the difference between the flexibility calibration value at the current moment and the flexibility calibration value at the previous moment is greater than the calibration end threshold. If so, return to the judgment step of executing the flexibility calibration value; if not, calibrate the stiffness of the flexible actuator based on the flexibility calibration value at the current moment. In a third aspect, an embodiment of the present invention further provides a computing device, including a memory and a processor, wherein a computer program is stored in the memory, and when the processor executes the computer program, the method described in any embodiment of this specification is implemented.

[0019] In a fourth aspect, an embodiment of the present invention further provides a computer-readable storage medium having a computer program stored thereon, which, when executed in a computer, enables the computer to execute the method described in any embodiment of this specification.

[0020] On the other hand, an embodiment of the present application further provides a computer program product, which includes a computer program. A processor of a computer device reads the computer program from a computer-readable storage medium, and the processor executes the computer program, so that the computer device executes any of the methods described in the above embodiments.

[0021] On the other hand, an embodiment of the present invention further provides a computer program product, including a computer program, which implements the steps of the above-mentioned method when executed by a processor.

[0022] An embodiment of the present invention provides a method for autonomously calibrating the stiffness of a flexible actuator. The method first constructs a kinematic model of the flexible actuator, and adjusts the output force of the flexible actuator to a sinusoidal wave form based on the kinematic model. Then, the output force of the flexible actuator at each moment is judged based on a preset calibration threshold. When the output force is greater than the preset calibration threshold, the flexible actuator is calibrated. When the output force is less than the preset calibration threshold, it is judged whether the output force of the flexible actuator at the next moment is greater than the preset threshold. Finally, if the difference between the flexibility calibration values ​​at the current moment and the previous moment is less than the calibration structure threshold, the stiffness of the flexible actuator is calibrated with the flexibility calibration value at the current moment. In this way, the autonomous calibration of the stiffness characteristic parameters of the flexible actuator during the on-orbit operation of the spacecraft can be achieved, thereby enabling accurate evaluation of the high-frequency disturbance attenuation performance of the spacecraft payload. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0024] Figure 1 is a flow chart of a method for autonomously calibrating the stiffness of a flexible actuator provided by one embodiment of the present invention;

[0025] Figure 2 It is a structural diagram of the output force form of a flexible actuator provided by one embodiment of the present invention;

[0026] Figure 3 is a diagram of stiffness calibration results of a flexible actuator provided by an embodiment of the present invention; wherein rod1 to rod6 represent stiffness calibration results of the 1st to 6th flexible actuators respectively;

[0027] Figure 4 is a hardware architecture diagram of a computing device provided by an embodiment of the present invention;

[0028] Figure 5 It is a structural diagram of a flexible actuator stiffness autonomous calibration device provided by one embodiment of the present invention. DETAILED DESCRIPTION

[0029] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0030] Please refer to Figure 1 , an embodiment of the present invention provides a method for autonomously calibrating the stiffness of a flexible actuator, wherein a plurality of flexible actuators constitute an active pointing platform to drive a load to move;

[0031] The method includes:

[0032] Step S1, adjusting the output force of each flexible actuator based on the constructed kinematic model of the flexible actuator so that the output force is in the form of a sine wave;

[0033] Step S2, determining whether the output force of the flexible actuator at the current moment is greater than a preset calibration threshold;

[0034] Step S3: if yes, calibrate the flexible actuator based on the actuator compliance calibration formula to obtain a compliance calibration value of the flexible actuator;

[0035] Step S4: if not, take the next moment as the current moment and return to step S2;

[0036] Step S5, determining whether the difference between the current flexibility calibration value and the previous flexibility calibration value is greater than the calibration end threshold, if so, returning to step S3;

[0037] Step S6: if not, calibrate the stiffness of the flexible actuator based on the compliance calibration value at the current moment.

[0038] In an embodiment of the present invention, a kinematic model of the flexible actuator is first constructed, and the output force of the flexible actuator is adjusted to a sinusoidal wave form based on the kinematic model. Then, the output force of the flexible actuator at each moment is judged based on a preset calibration threshold. When the output force is greater than the preset calibration threshold, the flexible actuator is calibrated. When the output force is less than the preset calibration threshold, it is judged whether the output force of the flexible actuator at the next moment is greater than the preset threshold. Finally, if the difference between the flexibility calibration value at the current moment and the previous moment is less than the calibration structure threshold, the stiffness of the flexible actuator is calibrated with the flexibility calibration value at the current moment. In the above manner, the autonomous calibration of the stiffness characteristic parameters of the flexible actuator during the on-orbit operation of the spacecraft can be achieved, thereby enabling accurate evaluation of the high-frequency disturbance attenuation performance of the spacecraft payload.

[0039] In the embodiment of the present invention, the active pointing platform is composed of several flexible actuators in a certain configuration, wherein the flexible actuator includes a passive damping mechanism, an active driving mechanism and a linear displacement sensor installed in sequence; the passive damping mechanism is used to provide passive damping force for the movement of the flexible actuator to attenuate external high-frequency disturbance force and torque, the active driving mechanism is used to provide active driving force for the movement of the flexible actuator, and the linear displacement sensor is used to measure the translational displacement of the flexible actuator. In this way, the active pointing platform has active pointing control and passive vibration isolation functions, and can achieve high-precision pointing and high-stability control of the load.

[0040] For step S1:

[0041] In some embodiments, the kinematic model of the flexible actuator is as follows:

[0042]

[0043] Wherein, m is the load mass (for example, it can be 10 kg), c is the damping coefficient of the passive damping mechanism (for example, it can be 0.04 N / (mm / s), k is the stiffness coefficient of the active driving mechanism (for example, it can be [13,14,15,16,17,18] N / mm), x is the output displacement of the linear displacement sensor, and F is the output force of the flexible actuator.

[0044] In some embodiments, the output force of the flexible actuator is in the form of:

[0045] F=Asin(2*π*f*t)

[0046] Wherein, A is the driving force amplitude, f is the driving force period (for example, may be 0.1 Hz), and t is the driving force output time.

[0047] In the embodiment of the present invention, a kinematic model of the flexible actuator is first constructed based on the structure of each flexible actuator, and then the output force in the flexible actuator is adjusted using the constructed kinematic model, so that the output force of the active driving mechanism in each flexible actuator is in the form of a sine wave (such as Figure 2 This type of output force is relatively smooth and can minimize damage to the flexible actuator structure.

[0048] For steps S2 to S4:

[0049] In some embodiments, the actuator compliance calibration formula is as follows:

[0050] τ i (k) = τ i (k-1)+λ i ·xi (F i (k)-τ i (k-1))

[0051] In the formula, x i is the output displacement of the linear displacement sensor of the i-th flexible actuator, λ i is the compliance calibration coefficient of the i-th flexible actuator, τ i (k) is the compliance calibration value of the i-th flexible actuator at the current moment, τ i (k-1) is the compliance calibration value of the i-th flexible actuator at the previous moment, and Fi(k) is the output force of the i-th flexible actuator.

[0052] In the embodiment of the present invention, the output force of each flexible actuator is judged and compared with the preset calibration threshold to determine whether the flexible actuator needs to be calibrated at the current time k. For example, if at the current time k, the output force F of the i-th (i=1, 2, ..., N) flexible actuator is i (k)>F i_th (preset calibration threshold), the flexible actuator is calibrated according to the above calibration formula. During the calibration process, the flexibility calibration coefficient of the flexible actuator is appropriately adjusted (for example, it can be 0.001), so that the flexible actuator calibration can be adjusted with high efficiency and high precision. Furthermore, considering that the output force of the flexible actuator is in the form of a sine wave, when the output force is small, the calibration will introduce errors. Therefore, if the output force F of the i-th flexible actuator is i (k)<F i_th (preset calibration threshold) is not calibrated until the output force of its flexible actuator is greater than the preset calibration threshold.

[0053] For steps S5 to S6:

[0054] In some embodiments, the stiffness of the flexible actuator is calibrated by the following formula:

[0055] k cabi =1 / τ i (k)

[0056] In the formula, k cabi is the stiffness calibration value of the i-th flexible actuator, τ i (k) is the compliance calibration value of the i-th flexible actuator at the current moment.

[0057] In the embodiment of the present invention, if the output force of the flexible actuator is greater than the preset calibration threshold value, when the flexible actuator is calibrated, k is greater than 1, that is, the flexible actuator needs to be calibrated at least twice, and then the flexibility calibration value τ at the current k moment is i(k) and the flexibility calibration value τ at the previous k-1 moment i (k-1) and compare the difference with the calibration end threshold. If τ i (k)-τ i (k-1)<τ min (calibration end threshold), then the calibration of the flexible actuator is ended, with the current flexibility calibration value τ i (k) Calibrate the stiffness of the flexible actuator; if τ i (k)-τ i (k-1)>τ min (calibration end threshold), the flexibility calibration formula is used to repeatedly calibrate it until the above conditions are met. In this way, the above method can be used to calibrate the stiffness of each flexible actuator (such as Figure 3 shown).

[0058] It should be noted that in the embodiment of the present invention, the preset calibration threshold and the end calibration threshold can be determined according to the experience of those skilled in the art. For example, the preset calibration threshold can be F i_th It can be 16Nm, ending the calibration threshold τ min It can be 0.01.

[0059] In summary, in the embodiment of the present invention, the above method can realize the accurate and autonomous calibration of the stiffness of each flexible actuator in the active pointing platform of the spacecraft, thereby realizing the accurate on-orbit evaluation of the high-frequency disturbance attenuation and vibration isolation performance of the spacecraft payload, and providing a reliable selection for the closed-loop control parameters of the secondary composite control.

[0060] like Figure 4 , Figure 5 As shown, an embodiment of the present invention provides a flexible actuator stiffness autonomous calibration device. The device embodiment can be implemented by software, or by hardware or a combination of software and hardware. From the hardware level, Figure 4 As shown, it is a hardware architecture diagram of a computing device where a flexible actuator stiffness autonomous calibration device provided by an embodiment of the present invention is located, except Figure 4 In addition to the processor, memory, network interface, and non-volatile memory shown in the figure, the computing device in which the device is located in the embodiment may also generally include other hardware, such as a forwarding chip responsible for processing messages, etc. Taking software implementation as an example, Figure 5 As shown, as a device in a logical sense, it is formed by the CPU of the computing device in which it is located reading the corresponding computer program in the non-volatile memory into the memory and running it. This embodiment provides a flexible actuator stiffness autonomous calibration device, which is composed of a plurality of flexible actuators to form an active pointing platform to drive the load to move;

[0061] The device includes:

[0062] An adjustment unit 501, configured to adjust the output force of each flexible actuator based on the constructed kinematic model of the flexible actuator, so that the output force is in a sinusoidal wave form;

[0063] The first judgment unit 502 is used to judge whether the output force of the flexible actuator at the current moment is greater than a preset calibration threshold; if so, calibrate the flexible actuator based on the actuator flexibility calibration formula to obtain the flexibility calibration value of the flexible actuator; if not, return to the next moment as the current moment to execute the output force judgment step of the flexible actuator;

[0064] The second judgment unit 503 is used to judge whether the difference between the flexibility calibration value at the current moment and the flexibility calibration value at the previous moment is greater than the calibration end threshold. If so, it returns to the judgment step of executing the flexibility calibration value; if not, the stiffness of the flexible actuator is calibrated based on the flexibility calibration value at the current moment.

[0065] In an embodiment of the present invention, the adjustment unit 501 can be used to execute step S1 in the above method embodiment, the first judgment unit 502 can be used to execute steps S2 to S4 in the above method embodiment, and the second judgment unit 503 can be used to execute steps S5 to S6 in the above method embodiment.

[0066] In one embodiment of the present invention, the flexible actuator includes a passive damping mechanism, an active driving mechanism and a linear displacement sensor installed in sequence; wherein the passive damping mechanism is used to provide a passive damping force for the movement of the flexible actuator, the active driving mechanism is used to provide an active driving force for the movement of the flexible actuator, and the linear displacement sensor is used to measure the translational displacement of the flexible actuator.

[0067] In one embodiment of the present invention, in the adjustment unit 501, the kinematic model of the flexible actuator is as follows:

[0068]

[0069] Where m is the load mass, c is the damping coefficient of the passive damping mechanism, k is the stiffness coefficient of the active driving mechanism, x is the output displacement of the linear displacement sensor, and F is the output force of the flexible actuator.

[0070] In one embodiment of the present invention, in the adjustment unit 501, the output force of the flexible actuator is in the following form:

[0071] F=Asin(2*π*f*t)

[0072] Where A is the driving force amplitude, f is the driving force period, and t is the driving force output time.

[0073] In one embodiment of the present invention, in the first determination unit 502, the actuator compliance calibration formula is as follows:

[0074] τ i (k) = τ i (k-1)+λ i ·x i (F i (k)-τ i (k-1))

[0075] In the formula, x i is the output displacement of the linear displacement sensor of the i-th flexible actuator, λ i is the compliance calibration coefficient of the i-th flexible actuator, τ i (k) is the compliance calibration value of the i-th flexible actuator at the current moment, τ i (k-1) is the compliance calibration value of the i-th flexible actuator at the previous moment, and Fi(k) is the output force of the i-th flexible actuator.

[0076] In one embodiment of the present invention, in the second determination unit 503, the stiffness of the flexible actuator is calibrated by the following formula:

[0077] k cabi =1 / τ i (k)

[0078] In the formula, k cabi is the stiffness calibration value of the i-th flexible actuator, τ i (k) is the compliance calibration value of the i-th flexible actuator at the current moment.

[0079] It is understood that the structure illustrated in the embodiment of the present invention does not constitute a specific limitation on a flexible actuator stiffness autonomous calibration device. In other embodiments of the present invention, a flexible actuator stiffness autonomous calibration device may include more or fewer components than shown in the figure, or combine some components, or split some components, or arrange the components differently. The components shown in the figure may be implemented in hardware, software, or a combination of software and hardware.

[0080] The information interaction, execution process and other contents between the modules in the above-mentioned device are based on the same concept as the embodiment of the method of the present invention. For the specific contents, please refer to the description in the embodiment of the method of the present invention, and no further description is given here.

[0081] An embodiment of the present invention further provides a computing device, including a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, a method for autonomously calibrating the stiffness of a flexible actuator in any embodiment of the present invention is implemented.

[0082] An embodiment of the present invention further provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the processor executes a method for autonomously calibrating the stiffness of a flexible actuator in any embodiment of the present invention.

[0083] Specifically, a system or device equipped with a storage medium can be provided, on which software program code that implements the functions of any of the above-mentioned embodiments is stored, and a computer (or CPU or MPU) of the system or device can be enabled to read and execute the program code stored in the storage medium.

[0084] In this case, the program code itself read from the storage medium can realize the function of any one of the above-mentioned embodiments, and thus the program code and the storage medium storing the program code constitute a part of the present invention.

[0085] The storage medium embodiments for providing the program code include a floppy disk, a hard disk, a magneto-optical disk, an optical disk (such as CD-ROM, CD-R, CD-RW, DVD-ROM, DVD-RAM, DVD-RW, DVD+RW), a magnetic tape, a non-volatile memory card, and a ROM. Alternatively, the program code can be downloaded from a server computer by a communication network.

[0086] In addition, it should be clear that the functions of any of the above embodiments can be implemented not only by executing the program code read by the computer, but also by enabling an operating system operating on the computer to complete part or all of the actual operations based on instructions from the program code.

[0087] In addition, it can be understood that the program code read from the storage medium is written to a memory provided in an expansion board inserted into the computer or to a memory provided in an expansion module connected to the computer, and then based on the instructions of the program code, a CPU installed on the expansion board or expansion module is enabled to perform part or all of the actual operations, thereby realizing the functions of any of the above-mentioned embodiments.

[0088] An embodiment of the present application also provides a computer-readable storage medium, on which is stored at least one instruction, at least one program, code set or instruction set, and the at least one instruction, at least one program, code set or instruction set is loaded and executed by a processor to implement a method for autonomously calibrating the stiffness of a flexible actuator provided in the above-mentioned method embodiments.

[0089] It should be noted that, in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device.

[0090] A person of ordinary skill in the art can understand that all or part of the steps of implementing the above method embodiments can be completed by hardware related to program instructions, and the aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it executes the steps of the above method embodiments; and the aforementioned storage medium includes: ROM, RAM, magnetic disk or optical disk, etc., various media that can store program codes.

[0091] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for autonomously calibrating the stiffness of a flexible actuator, characterized in that: An active pointing platform is formed by a number of flexible actuators to drive the load to move; Methods include: Step S1, adjusting the output force of each flexible actuator based on the constructed kinematic model of the flexible actuator so that the output force is in the form of a sine wave; Step S2, determining whether the output force of the flexible actuator at the current moment is greater than a preset calibration threshold; Step S3: if yes, calibrate the flexible actuator based on the actuator compliance calibration formula to obtain a compliance calibration value of the flexible actuator; Step S4: if not, take the next moment as the current moment and return to step S2; Step S5, determining whether the difference between the current flexibility calibration value and the previous flexibility calibration value is greater than the calibration end threshold, if so, returning to step S3; Step S6: if not, calibrate the stiffness of the flexible actuator based on the compliance calibration value at the current moment.

2. The method according to claim 1, characterized in that The flexible actuator includes a passive damping mechanism, an active driving mechanism and a linear displacement sensor which are installed in sequence; wherein the passive damping mechanism is used to provide a passive damping force for the movement of the flexible actuator, the active driving mechanism is used to provide an active driving force for the movement of the flexible actuator, and the linear displacement sensor is used to measure the translational displacement of the flexible actuator.

3. The method according to claim 1 or 2, characterized in that: The kinematic model of the flexible actuator is as follows: In the formula, m is the load mass, c is the damping coefficient of the passive damping mechanism, k is the stiffness coefficient of the active drive mechanism, and x is the output displacement of the linear displacement sensor. and are the first and second derivatives of the output displacement, respectively, and F is the output force of the flexible actuator.

4. The method according to claim 1, characterized in that The output force of the flexible actuator is in the form of: F=Asin(2*π*f*t) Where A is the driving force amplitude, f is the driving force period, and t is the driving force output time.

5. The method according to claim 1, characterized in that The flexibility calibration formula of the flexible actuator is as follows: t i (k)=τ i (k-1)+λ i ·x i (F i (k)-t i (k-1)) In the formula, x i is the output displacement of the linear displacement sensor of the i-th flexible actuator, λ i is the compliance calibration coefficient of the i-th flexible actuator, τ i (k) is the compliance calibration value of the i-th flexible actuator at the current moment, τ i (k-1) is the compliance calibration value of the i-th flexible actuator at the previous moment, and Fi(k) is the output force of the i-th flexible actuator.

6. The method according to any one of claims 1 to 5, characterized in that The stiffness of the flexible actuator is calibrated by the following formula: k cabi =1 / t i (k) In the formula, k cabi is the stiffness calibration value of the i-th flexible actuator, τ i (k) is the compliance calibration value of the i-th flexible actuator at the current moment.

7. A flexible actuator stiffness autonomous calibration device, characterized in that: An active pointing platform is formed by a number of flexible actuators to drive the load to move; The device includes: An adjustment unit, used for adjusting the output force of each flexible actuator based on the constructed kinematic model of the flexible actuator, so that the output force is in a sine wave form; The first judgment unit is used to judge whether the output force of the flexible actuator at the current moment is greater than a preset calibration threshold; if so, calibrate the flexible actuator based on the actuator flexibility calibration formula to obtain the flexibility calibration value of the flexible actuator; if not, return to the next moment as the current moment to execute the output force judgment step of the flexible actuator; The second judgment unit is used to judge whether the difference between the flexibility calibration value at the current moment and the flexibility calibration value at the previous moment is greater than the calibration end threshold. If so, return to the judgment step of executing the flexibility calibration value; if not, calibrate the stiffness of the flexible actuator based on the flexibility calibration value at the current moment.

8. A computing device, comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the method according to any one of claims 1 to 6 is implemented.

9. A computer-readable storage medium having a computer program stored thereon, which, when executed in a computer, causes the computer to execute the method according to any one of claims 1 to 6.

10. A computer program product, characterized in that The method comprises a computer program, wherein when the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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