Piezoelectric resonant micro-robot based on 3D printing elastic structure

The asymmetric structure microrobot based on PVDF piezoelectric film was fabricated using 3D printing technology, which overcomes the limitations of existing micro piezoelectric resonant robots in terms of high performance and complex structure, and enables flexible control and efficient fabrication of multiple motion modes.

CN121696907APending Publication Date: 2026-03-20UNIV OF ELECTRONICS SCI & TECH OF CHINA
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Patent Information

Application Number
CN202511941654.9
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-12-22
Publication Date
2026-03-20

AI Technical Summary

Technical Problem

Existing technologies have significant limitations in achieving high performance, high reliability, multi-functional integration, and complex three-dimensional structures, especially the shortcomings of micro piezoelectric resonant robots in terms of motion stability and miniaturization.

Method used

Elastic structures based on PVDF piezoelectric films were fabricated using 3D printing technology. Asymmetrical left arm, right arm, left leg, right leg, and torso were designed. The inverse piezoelectric effect of the PVDF piezoelectric film was used to excite the vibration of the elastic matrix, realizing multiple motion modes. This was combined with high-precision molding of PLA material.

Benefits of technology

It achieves a flexible structure, is easy to miniaturize, improves reliability and service life, simplifies the manufacturing process, and enhances motion control flexibility, making it suitable for fields such as narrow space detection, pipeline inspection, and biomedicine.

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Abstract

The invention provides a piezoelectric resonant micro-robot based on a 3D printing elastic structure, and belongs to the technical field of micro-robots. The piezoelectric resonant micro-robot comprises a left leg, a right leg, a left arm, a right arm, a trunk, a PVDF piezoelectric film and a hump. The left leg, the right leg, the left arm, the right arm, the trunk and the hump form an elastic layer structure, the whole elastic layer structure is integrally formed, and the left arm, the right arm, the left leg and the right leg adopt asymmetric structural design. When alternating voltage is applied to the piezoelectric film, micro-deformation generated by the film can excite mechanical vibration of the elastic structure, and under the specific frequency, the asymmetric leg structure can enable the robot to achieve linear motion. Under different frequencies, the vibration difference of the left and right legs can realize steering motion; and the movement speed can be controlled by changing the voltage amplitude. According to the asymmetric structure, the motion control flexibility is enhanced; due to the integrated design, the system structure is simplified, and the reliability is improved; the 3D printing process ensures accurate forming of a complex structure, and miniaturization and batch production are facilitated.
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Description

Technical Field

[0001] This invention belongs to the field of microrobot technology, and in particular relates to a piezoelectric resonant microrobot based on a 3D printed elastic structure. Background Technology

[0002] Miniature resonant robots are characterized by high dynamic efficiency and continuous and stable motion. They are driven by directly converting electrical energy into mechanical vibration energy, eliminating the need for traditional complex transmission mechanisms. They work in fields with extremely high requirements for motion stability, such as precision testing, biomedicine, and micro-assembly, and represent a cutting-edge research direction in the field of high-end equipment.

[0003] The vibration sources of micro-resonant robots mainly include electromagnetic, electrostatic, and piezoelectric actuation methods. Among them, electromagnetic actuation is difficult to miniaturize and is prone to heat generation; electrostatic actuation has low driving force and is easily affected by the environment; while piezoelectric actuation, as a type of intelligent actuation, has advantages such as high output, fast response, high efficiency, and high control precision. Micro-robots based on piezoelectric resonance exhibit outstanding characteristics such as high energy density, fast movement speed, and rich dynamic characteristics. Currently, laser cutting technology is often used for rapid prototyping and flexible structure design of such robots, especially suitable for applications with special shape requirements (such as bendability and wearability) but not requiring extremely high performance. However, this process has significant limitations in achieving high performance, high reliability, multi-functional integration, and complex three-dimensional structures. To address these limitations, this invention proposes a solution based on 3D printing technology, aiming to overcome the above-mentioned technical shortcomings and improve the overall performance of micro-piezoelectric resonant robots. Summary of the Invention

[0004] The purpose of this invention is to provide a piezoelectric resonant microrobot based on a 3D-printed elastic structure. The aim is to solve the technical problems of significant limitations in achieving high performance, high reliability, multifunctional integration, and complex three-dimensional structures in the prior art by driving the deformation of a PVDF (Polyvinylidene Fluoride) piezoelectric film to produce a high-precision and asymmetric structure with different motion modes under different voltage driving.

[0005] To solve the above-mentioned technical problems, the specific technical solution of the present invention is as follows:

[0006] A piezoelectric resonant microrobot based on a 3D-printed elastic structure is disclosed. The piezoelectric resonant microrobot includes a left leg, a right leg, a left arm, a right arm, a torso, a PVDF piezoelectric film, and a hump. The left leg, right leg, left arm, right arm, torso, and hump constitute an elastic layer structure, and the entire elastic layer structure is integrally formed.

[0007] There are three legs on the left, and the three legs are connected perpendicularly to the left arm; there are two legs on the right, and the two legs are connected perpendicularly to the right arm; the left and right arms are connected to the upper part of the hump; the lower part of the hump is connected to the torso.

[0008] The torso is used to support the PVDF piezoelectric film. The torso is bonded to the PVDF piezoelectric film and integrated into a complete drive component.

[0009] A silver wire is bonded to the upper and lower surfaces of the PVDF piezoelectric film, serving as electrode leads, namely the high voltage line and the ground line, respectively; the two electrode leads are connected to a voltage amplifier, which is connected to a signal generator;

[0010] Driven by an AC voltage, the PVDF piezoelectric film deforms, causing the torso to vibrate, which in turn causes the hump to vibrate. The hump then causes the left leg, right leg, left arm, and right arm to vibrate, thus realizing the robot's movement.

[0011] Furthermore, the elastic layer structure is modeled using Solidworks and integrally formed using PLA material via 3D printing.

[0012] Furthermore, the left and right arms adopt an asymmetrical structural design, mainly reflected in the difference in length: the left arm is 5 mm long and the right arm is 3 mm long; the width of both the left and right arms is 2 mm and the thickness is 0.5 mm; thus, the left and right arms have different vibration modes under the same voltage drive.

[0013] Furthermore, the left and right legs are asymmetrical structures, with the right leg consisting of two 0.75mm wide legs and the left leg consisting of three 0.50mm wide legs. The length of both the left and right legs is 18mm and the thickness is 0.50mm.

[0014] Furthermore, the tail end of the torso contacts the motion plane, which is the platform on which the entire robot is placed. It contacts the bottom of the left and right legs and the tail end, forming a direct energy transmission path. Vibrational energy is transmitted to the motion plane through the torso, and the reaction force generated by the interaction with the motion plane propels the robot to move.

[0015] Furthermore, the angle between the left and right legs and the plane of motion is 72°, and the angle between the tail and the plane of motion is 30°. This design enables the piezoelectric resonant microrobot to move forward or backward at different frequencies.

[0016] Compared with the prior art, the present invention has the following beneficial technical effects:

[0017] 1) The piezoelectric resonant microrobot based on 3D printed elastic structure proposed in this invention consists of an integrally formed elastic matrix and a PVDF film as the driving element. The structure is flexible and easy to miniaturize. The proposed motion control method excites the overall vibration of the elastic matrix through the inverse piezoelectric effect of PVDF. Thanks to its carefully designed asymmetric structure, the robot will excite vibration modes with directional tendencies under voltage drive at different resonant frequencies, thereby directly generating diverse movements such as forward, backward or turning. This realizes a simplified strategy of controlling the direction of motion by simply adjusting the frequency of the electrical signal.

[0018] 2) This invention abandons traditional manual cutting and laser cutting methods and adopts 3D printing integrated molding technology, which not only significantly improves the structural accuracy and consistency, but also facilitates the rapid iteration and optimization of the model, and the overall process is simpler and more efficient.

[0019] 3) This invention uses PVDF flexible piezoelectric film as the driving element. Although its piezoelectric coefficient is lower than that of traditional piezoelectric ceramics, it has excellent flexibility, impact resistance and fatigue life, and can be reused, which greatly improves the reliability and service life of the robot.

[0020] 4) This invention relies solely on a single PVDF piezoelectric film as the driving source. By flexibly adjusting the excitation voltage frequency, it can stimulate multiple vibration modes of the robot, thereby achieving six degrees of freedom motion, including forward, backward, left turn, right turn, and other directions.

[0021] 5) The asymmetric structure enhances the flexibility of motion control; the integrated design simplifies the system structure and improves reliability; 3D printing technology ensures the precise molding of complex structures, facilitating miniaturization and mass production; the overall structure is compact and lightweight, with low power consumption and no electromagnetic interference. This robot is suitable for applications such as narrow space exploration, pipeline inspection, biomedicine, and micromanipulation. Its innovative asymmetric structural design provides a new solution for the motion control of microrobots. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 This is a schematic diagram of the piezoelectric resonant microrobot structure based on a 3D-printed elastic structure according to the present invention.

[0024] Figure 2This is a schematic diagram of the forearm and foreleg of the piezoelectric resonant microrobot based on a 3D-printed elastic structure according to the present invention.

[0025] Figure 3 This is a top view of the simulation results of the forward motion mode of the piezoelectric resonant microrobot based on the 3D printed elastic structure of the present invention.

[0026] Figure 4 This is a side view of the simulation results of the forward motion mode of the piezoelectric resonant microrobot based on the 3D printed elastic structure of the present invention.

[0027] Figure 5 This is a top view of the simulation results of the backward motion mode of the piezoelectric resonant microrobot based on the 3D printed elastic structure of the present invention.

[0028] Figure 6 This is a side view of the simulation results of the backward motion mode of the piezoelectric resonant microrobot based on the 3D printed elastic structure of the present invention.

[0029] The markings in the diagram are as follows: 1-Left leg; 2-Right leg; 3-Left arm; 4-Right arm; 5-Tortoise; 6-PVDF piezoelectric film; 7-Tail end; 8-Hump; 9-High voltage line; 10-Ground wire. Detailed Implementation

[0030] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0031] This invention proposes a piezoelectric resonant microrobot based on a 3D-printed elastic structure, such as... Figure 1-2 As shown, the piezoelectric resonant microrobot includes a left leg 1, a right leg 2, a left arm 3, a right arm 4, a torso 5, a PVDF piezoelectric film 6, and a hump 8. The left leg 1, right leg 2, left arm 3, right arm 4, torso 5, and hump 8 constitute an elastic layer structure, and the entire elastic layer structure is integrally formed.

[0032] There are three left legs 1, which are perpendicularly connected to the left arm 3; there are two right legs 2, which are perpendicularly connected to the right arm 4. The left arm 3 and the right arm 4 are connected to the upper part of the hump 8. The lower part of the hump 8 is connected to the torso 5.

[0033] The torso 5 is a flat plate structure with dimensions of 20*10*0.3mm, similar to a cantilever beam, used to support the PVDF piezoelectric film. The torso 5 and the PVDF piezoelectric film 6 are firmly bonded together with double-sided tape with a thickness of 0.05mm, forming a complete drive component.

[0034] The PVDF piezoelectric film 6 is a flexible film with dimensions of 20*10*0.022mm. Both sides are coated with a layer of silver less than a micrometer thick, used as electrodes. A silver wire with a diameter of 0.05mm is bonded to the top and bottom surfaces of the PVDF piezoelectric film, serving as electrode leads: a high-voltage wire 9 and a ground wire 10, respectively. The specific positions of the electrode leads are not critical, as both sides of the PVDF piezoelectric film serve as electrodes; it is sufficient that the two wires are bonded to different surfaces. The two electrode leads are connected to a voltage amplifier, which is connected to a signal generator. The PVDF piezoelectric film must be thin enough to generate deformation sufficient to drive robot movement under a limited voltage amplitude.

[0035] Driven by AC voltage, the PVDF piezoelectric film 6 deforms, causing the torso 5 to vibrate, which in turn causes the hump 8 to vibrate. Then, the hump 8 causes the left leg 1, right leg 2, left arm 3, and right arm 4 to vibrate, thus realizing the robot's movement.

[0036] The elastic layer structure was modeled using Solidworks and integrally formed using PLA material through 3D printing. PLA material possesses excellent stiffness and dimensional stability, enabling the elastic layer structure to combine good structural rigidity, high manufacturing precision, and excellent microstructure forming capabilities. The integral 3D printing process not only ensures the overall structural stability of the robot during movement but also provides a crucial foundation for precisely controlling its motion modes.

[0037] The left arm 3 and right arm 4 are designed with an asymmetrical structure, mainly in terms of their length difference: the left arm 3 is 5 mm long, and the right arm 4 is 3 mm long. Both are 2 mm wide and 0.5 mm thick. Thus, the left arm 3 and right arm 4 have different vibration modes under the same voltage drive.

[0038] The left leg 1 and right leg 2 are asymmetrical structures. The right leg 2 consists of two legs, each 0.75 mm wide, while the left leg consists of three legs, each 0.50 mm wide. Both the left leg 1 and right leg 2 are 18 mm long and 0.50 mm thick. This structure aims to utilize the differences in stiffness and distribution between the left and right legs to amplify the differences in their vibration modes under the same voltage drive.

[0039] The asymmetrical structure of the left and right arms, and the left and right legs, enables the piezoelectric resonant microrobot to exhibit different motion modes at different voltage frequencies. The legs employ an asymmetrical design, with significant differences in width and position between the left and right legs. This asymmetrical structure allows the robot to generate differentiated vibration responses under piezoelectric actuation, providing a structural basis for achieving multiple motion modes.

[0040] To achieve effective displacement, the torso 5 is designed as a thin structure to generate a sufficiently large amplitude under the drive of the PVDF piezoelectric film. The tail end 7 of the torso 5 contacts the motion plane, which is the platform on which the entire robot is placed. It contacts the bottom ends of the left leg 1 and the right leg 2, as well as the tail end 7, forming a direct energy transmission path. Vibrational energy is transmitted to the motion plane through the torso, and the reaction force generated by the interaction with the motion plane propels the robot to move.

[0041] The elastic layer structure is in complete contact with the motion plane. The angle between the left leg 1, the right leg 2 and the motion plane is 72°, and the angle between the tail end 7 and the motion plane is 30°. This design enables the piezoelectric resonant microrobot to move forward or backward at different frequencies.

[0042] The driving principle of this invention utilizes the inverse piezoelectric effect of a PVDF piezoelectric film. When an alternating voltage is applied to the piezoelectric film, the resulting micro-deformation excites mechanical vibrations in the elastic structure. By adjusting the frequency of the input voltage, different resonant modes of the robot body can be excited. At a specific frequency, the asymmetrical leg structure enables the robot to achieve linear motion; at different frequencies, the vibration difference between the left and right legs enables steering motion; and by changing the voltage amplitude, the movement speed can be controlled. This control strategy allows for flexible switching between multiple motion modes with only a single driving element.

[0043] This invention also provides a driving method for a piezoelectric resonant microrobot based on a 3D-printed elastic structure, the method comprising:

[0044] By applying an AC voltage and a grounding signal to the upper and lower surfaces of the PVDF piezoelectric film 6 respectively, the PVDF piezoelectric film deforms under the inverse piezoelectric effect, thereby causing forced vibrations in the torso and foreleg structures. Under voltage excitation at different frequencies, the robot exhibits significantly different motion modes.

[0045] Experiments show that when the voltage amplitude is 400V, the robot responds to sinusoidal excitation above 100Hz, and its behavior exhibits regularity with frequency variation, as detailed below:

[0046] 100–500Hz: The left and right legs vibrate significantly, with the amplitude of the right leg being greater than that of the left leg. The robot as a whole exhibits a forward and clockwise movement trend.

[0047] 500–600Hz: The vibration intensity of the left and right legs tends to be consistent, and the robot mainly exhibits forward linear motion.

[0048] 600–750Hz: The system enters a clear resonant state. Although the amplitude of a single left leg is still slightly smaller than that of the right leg, since there are three left legs and two right legs, the overall vibration intensity of the left legs is dominant, and the robot behaves as if it is moving forward and turning counterclockwise.

[0049] 750–950Hz: At the critical state of motion transition, the robot exhibits a "struggling" phenomenon, with a weak overall displacement trend.

[0050] 950–1160Hz: The amplitude of the left and right legs is significantly reduced. The driving force mainly comes from the direct interaction between the torso vibration and the ground. The robot moves backward as a whole. At the same time, because the amplitude of the right leg is greater than that of the left leg, it turns clockwise backward.

[0051] 1160–1260Hz: Continue moving backward, with the left and right legs vibrating at roughly the same amplitude, and the robot moving backward in a straight line as a whole.

[0052] 1260–1360Hz: The vibration intensity of the right leg is higher than that of the left leg, and the robot behaves as if it is turning backward and counterclockwise.

[0053] In addition, other motion modes were observed in the higher frequency range, which will not be described in detail here.

[0054] This embodiment selects typical forward and backward motion frequencies and performs kinematic simulation analysis using COMSOL Multiphysics software. To elucidate the complete motion mechanism, one motion cycle is divided into four phases in the simulation, and observations are conducted from both top-down and side-down perspectives. The simulation conditions are set as follows: contact constraints between the robot and the motion plane are set, with the contact angles between the left leg 1, right leg 2, and the motion plane being 72°, and the contact angle between the tail end 7 and the motion plane being 30°; a frictional force with a coefficient of friction of 0.5 is introduced to simulate a real environment. Under a voltage excitation of 400V, transient analysis is used to study the motion modes corresponding to different frequencies. It is worth noting that all transient deformations are amplified by 100 times.

[0055] Driven by a sinusoidal voltage of 600Hz and an amplitude of 800 Vp-p, the robot's motion sequence is as follows: Figure 3 and Figure 4 As shown:

[0056] Initial stage (corresponding to) Figure 3 a in Figure 4 (a) The instantaneous voltage corresponding to the driving voltage is 0, the PVDF piezoelectric film has not yet started to vibrate, and the system is in a static state.

[0057] Oscillation start-up stage (corresponding to) Figure 3 b in Figure 4 (b) When the instantaneous voltage corresponding to the driving voltage is 100 V, the PVDF piezoelectric film begins to vibrate and drives the torso structure to vibrate together, with the forelegs vibrating slightly. At this time, the amplitude is small, and the driving force generated has not yet overcome the static friction of the system, so the robot does not undergo macroscopic displacement.

[0058] Drive phase (corresponding) Figure 3 c in Figure 4 (c) The instantaneous voltage corresponding to the driving voltage is 300 V, which further enhances the vibration of the elastic layer, and the energy is transferred from the torso to the forelegs. The forelegs show a clear tendency to swing backward, thereby generating an effective driving force that propels the robot forward as a whole.

[0059] Turning phase (corresponding) Figure 3 d in Figure 4 In d): the instantaneous voltage corresponding to the driving voltage is 400 V, and the overall vibration elastic layer and the front leg vibration of the robot both reach their peak values. Since the overall vibration intensity of the left leg is greater than that of the right leg, an asymmetrical driving torque is formed during the continuous backward movement, which ultimately causes the robot to exhibit a composite motion of forward movement and counterclockwise rotation.

[0060] Accordingly, this embodiment also provides a detailed analysis of the robot's backward motion mode under a sinusoidal voltage drive of 1200Hz and an amplitude of 800 Vp-p, and the results are as follows. Figure 5 and Figure 6 As shown:

[0061] Initial stage (corresponding to) Figure 5 a in Figure 6 (a) The instantaneous voltage corresponding to the driving voltage is 0, the PVDF piezoelectric film has not yet started to vibrate, and the robot as a whole is in a static state.

[0062] Oscillation start-up stage (corresponding to) Figure 5 b in Figure 6 (b) At the instantaneous voltage of 100 V corresponding to the driving voltage, the PVDF piezoelectric film begins to vibrate and drives the torso structure to vibrate together. At this time, the amplitude is small, and the generated driving force has not yet overcome the static friction of the system, so the robot does not undergo macroscopic displacement. Compared with low-frequency excitation, the vibration response of the forelegs is significantly weakened in this stage.

[0063] Drive phase (corresponding) Figure 5 c in Figure 6(c) The instantaneous voltage corresponding to the driving voltage is 300 V, further enhancing the vibration of the elastic layer. Although the amplitude of the forelegs has increased compared to the previous stage, it is still relatively weak overall; the vibration energy is mainly concentrated in the torso. The direct friction between the torso and the plane generates the dominant backward thrust, driving the robot to move backward as a whole.

[0064] Turning phase (corresponding) Figure 5 d in Figure 6 (d) The instantaneous voltage corresponding to the driving voltage is 400 V, and the vibration of the elastic layer reaches its peak. Since the overall vibration intensity of the left and right front legs is similar, no significant steering torque is formed. At the same time, the torso continuously provides a backward frictional driving force, which ultimately causes the robot to exhibit a straight backward motion mode.

[0065] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A piezoelectric resonant microrobot based on a 3D-printed elastic structure, characterized in that, The piezoelectric resonant microrobot includes a left leg (1), a right leg (2), a left arm (3), a right arm (4), a torso (5), a PVDF piezoelectric film (6), and a hump (8); the left leg (1), right leg (2), left arm (3), right arm (4), torso (5), and hump (8) constitute an elastic layer structure, and the entire elastic layer structure is integrally formed. There are three left legs (1), and the three left legs (1) are connected vertically to the left arm (3); there are two right legs (2), and the two right legs (2) are connected vertically to the right arm (4); the left arm (3) and the right arm (4) are connected to the upper end of the hump (8); the lower end of the hump (8) is connected to the torso (5); The torso (5) is used to support the PVDF piezoelectric film (6). The torso (5) is bonded to the PVDF piezoelectric film (6) to form a complete drive component. A silver wire is bonded to the upper and lower surfaces of the PVDF piezoelectric film, respectively, serving as electrode leads, namely a high voltage line (9) and a ground line (10); the two electrode leads are connected to a voltage amplifier, which is connected to a signal generator; The PVDF piezoelectric film (6) deforms under the drive of AC voltage, causing the torso (5) to vibrate, which in turn causes the hump (8) to vibrate. Then the hump (8) causes the left leg (1), right leg (2), left arm (3), and right arm (4) to vibrate, thus realizing the robot's movement.

2. The piezoelectric resonant microrobot based on a 3D-printed elastic structure according to claim 1, characterized in that, The elastic layer structure was modeled using Solidworks and 3D printed in one piece using PLA material.

3. The piezoelectric resonant microrobot based on a 3D-printed elastic structure according to claim 1, characterized in that, The left arm (3) and right arm (4) are designed with an asymmetrical structure, mainly reflected in the difference in length: the left arm (3) is 5 mm long and the right arm (4) is 3 mm long; the width of the left arm (3) and the right arm (4) is 2 mm and the thickness is 0.5 mm; so that the left arm (3) and the right arm (4) have different vibration modes under the same voltage drive.

4. The piezoelectric resonant microrobot based on a 3D-printed elastic structure according to claim 1, characterized in that, The left leg (1) and right leg (2) are asymmetrical structures. The right leg (2) consists of two legs 0.75mm wide, and the left leg (1) consists of three legs 0.50mm wide. The length of the left leg (1) and the right leg (2) is 18mm, and the thickness is 0.50mm.

5. The piezoelectric resonant microrobot based on a 3D-printed elastic structure according to claim 1, characterized in that, The tail end (7) of the torso (5) is in contact with the motion plane, which is the platform on which the entire robot is placed. It is in contact with the bottom of the left leg (1), the right leg (2) and the tail end (7), forming a direct energy transmission path. Vibration energy is transmitted to the motion plane through the torso, and the reaction force generated by the interaction with the motion plane is used to propel the robot to move.

6. The piezoelectric resonant microrobot based on a 3D-printed elastic structure according to claim 5, characterized in that, The angle between the left leg (1) and the right leg (2) and the plane of motion is 72°, and the angle between the tail end (7) and the plane of motion is 30°. This design enables the piezoelectric resonant microrobot to move forward or backward at different frequencies.