Development of a miniature quadrupedal piezoelectric robot combining fast speed and nano-resolution
Graphical abstract
Introduction
Miniature ambulatory robots have been a popular research direction in the field of robotics in recent years [1], [2], [3], [4], [5], [6]. Benefiting from their small sizes, flexible motions and lower power cost compared to middle or large robots [7], [8], [9], they have been widely developed for applications in fault inspection, search and rescue, micro-manipulation, micro-manufacturing and so on [10], [11], [12], [13]. Traditional miniature ambulatory robots are usually actuated by electromagnetic motors [14], [15], [16], [17]. For example, Su et al. [18] proposed a quadruped robot with a size of 72 × 76 × 35 mm3, which were driven by vibrations of its cantilever legs, and could trot at speeds up to 206 mm/s. Besides, Birkmeyer et al. [19] designed a dynamic autonomous sprawled hexapod (DASH) with a length of 100 mm; the DASH, actuated by a single motor, realized a maximum speed of 1500 mm/s. The miniature ambulatory robots driven by electromagnetic motors exhibited impressive performances, especially for high speed. However, with the rapid development in the field of biology, nano-manufacturing, etc., the miniature robots are required to exhibit superior performances, such as nano-resolution, large working range, multi-DOF flexible motions and further miniaturization [20], [21], [22]. The robots, driven by electromagnetic motors, cannot satisfy above strict requirements duo to the restrictions of their driving principle and transmission mechanism.
For further improving the performance of the miniature ambulatory robots, much of the interest in new driving methods has been motivated. Recent advances include the miniature robots actuated by shape memory alloys [23], [24], [25], dielectric elastomers [26], [27], [28], magnetostrictive materials [29], [30], [31], artificial muscles [32], [33], [34], piezoelectric ceramics [35], [36], [37] and so on. Among them, the miniature piezoelectric robots, developed by the inverse piezoelectric effect of piezoelectric ceramics, exhibit many advantages such as fast response, high resolution, compact structure and immunity to electromagnetic interference [38], [39], [40], [41], [42], and have been favored by many researchers in recent years. Wu et al. [43] proposed an insect-scale piezoelectric robot with a size of 30 × 10 × 5 mm3 and a weight of 0.024 g, the robot was actuated by a PVDF (Polyvinylidene difluoride film) and achieved a high speed of 200 mm/s and a load of 0.406 g. Zhong et al. [44] designed a cubic centimeter robot based on inertial stick-slip driving, the robot was limited in 10 × 10 × 10 mm3, the realized maximum speed and resolution were 13.1 mm/s and 4.8 μm, respectively. Some other miniature piezoelectric robots with impressive performances are successfully developed, such as LPMRs [45], [46], [47], HAMRs [48], [49], [50] Miniwalkers [51], [52], [53], Min-RARs [54,55].
The miniature piezoelectric robots can be divided into the resonant piezoelectric robots [56], [57], [58] and the non-resonant piezoelectric robots [59], [60], [61] according to whether the piezoelectric actuators vibrate at their resonant frequencies. The resonant ones, usually actuated by unimorph or bimorph actuators, are easier to realize high speed (hundreds of mm/s) due to their high working frequency and relative larger vibration amplitudes [62], [63], [64]. For instance, Oldham et al. [65] presented a six-legged resonant piezoelectric robot with a size of 21 × 31.8 × 3 mm3, it could operate with a high speed of 170 mm/s and a jumping height of 1 mm, through the vibrations of their cantilever-like legs. Peng et al. [66] proposed a miniature four-legged resonant piezoelectric robot, which was limited in a size of 35 × 30 × 9 mm3 and a weight of 9 g; the robot could trot at a high speed of 330 mm/s and carry a load of 55 g. To improve the resolution of the resonant piezoelectric robot, Liu et al. [67] designed an exciting signal in pulse mode to help their resonant robot achieve a resolution of 0.44 μm; meanwhile, the robot was limited in 58 × 44 × 12 mm3, and could trot at a speed of 516 mm/s. Although the resonant piezoelectric robots can realize resolutions of submicron level, reaching the nanometer resolution is very difficult for them.
On the other hand, the non-resonant piezoelectric robots, usually driven by piezoelectric stacks, can achieve nano-resolution by the direct deformation of piezoelectric stacks, and realize large range motion by accumulating tiny steps [68], [69], [70], [71]. For example, Ma et al. [72] presented a pole-climbing non-resonant piezoelectric robot with a size of 50 × 54 × 86 mm3, which exhibited a resolution of 85 nm and a maximum speed of 100.9 μm/s. Fuchiwaki et al. [73] designed an inchworm-actuated non-resonant piezoelectric robot with a size of 32 × 32 × 20 mm3 and a weight of 35 g, the robot realized a high resolution of 25 nm and a maximum speed of about 1.4 mm/s. To increase the speed of the non-resonant piezoelectric robot, Deng et al. [74] proposed a fast impact mechanism, which made their non-resonant piezoelectric robot realize a speed of 3.65 mm/s. In addition, the robot was limited in 200 × 200 × 40 mm3, and achieved a high resolution of 16 nm, however, the fast impact made the robot be unstable during its motions.
To sum up, there is an intractable contradiction between the nano-resolution and high speed of the miniature piezoelectric robots, which limit their efficient applications. In other words, although the nano-resolution is enough for the applications in large scale precision detection, nano-manufacturing, etc., the slow speed could hinder the working efficiency. A common strategy is to combine different actuators in one robot. For example, Sun et al. [75] proposed a miniature robot integrating two driving methods (brushless DC motor and piezoelectric driver) to achieve a speed of 50 mm/s and a resolution of 17.4 μrad, respectively, but combining multiple driving methods caused the complex structure and control system. Therefore, a solution integrating the nano-resolution and high speed without increasing combining other actuators is valuable to the applications of the miniature piezoelectric robots, and even has much potential to revolutionize current technologies of miniature robots.
Contribution of this work: Interestingly, we noticed that the quadrupeds, such as dogs, can not only swing freely in place, but also trot fast in a wide range by their legs. Inspired by the multi-mode motions of quadrupeds, a miniature quadruped piezoelectric robot (MQPR) with quasi-static motion and resonant motion was proposed, which can not only operate in place with nano-resolution, but also move fast in large range. These performances give the MQPR great potential to efficiently perform precision manipulations at multiple target locations over a large area, such as detection of circuit board in large integrated circuit or wafers. Specifically, the MQPR achieves several key advancements as follows:
- 1)
The proposed MQPR, with size of 35 × 44 × 12 mm3 and weight of 21.0 g, could operate in quasi-static motion and resonant motion to combine the nano-resolution and fast speed.
- 2)
With the quasi-static motion, the MQPR could realize multi-DOF motions with resolution of higher than 8.8 nm and range of about 2 μm.
- 3)
With the resonant motion, the proposed robot could achieve a linear speed of 393.5 mm/s (11.2 BL/s) and a rotational speed of 246.5 °/s.
- 4)
In order to the effective cooperation of the above two motion mechanisms, the resonant motion in pulse mode was designed and a resolution of 0.31 μm was obtained.
- 5)
The robot could trot smoothly carrying a load of 100 g, which is about 5 times its own weight.
The structure of the proposed MQPR and the two motion mechanisms are indicated in Section 2. Then, Section 3 establishes the theoretical models of the piezo-leg and determines its parameters. The experimental set-ups are established in Section 4, and the characteristics of the piezo-leg and the prototype MQPR are tested in Section 5, and a conclusion is followed in Section 6.
Section snippets
Structure and working principle of the MQPR
In this section, we introduce the overall structure and the structural components of the proposed MQPR and the working principles of the two motion in sequence.
The main structure of the MQPR shown in Fig. 1(a) is illustrated firstly. The MQPR only consists of a pair of connection clamps, two piezo-legs and a sheet. The two piezo-legs are assembled together by the connection clamps with bolts and nuts. Each piezo-leg is composed by eight PZT (Lead Zirconate Titanate) elements and a base leg.
Modeling and parameter determination
The purpose of this work is to combine the quasi-static motion and the resonant motion into the MQPR to achieve both the performances of nano-resolution and fast speed. However, it is difficult to directly establish the numerical relationship between the robot speed and the structure parameters, because that there are very complex friction and impact interactions with high frequency between the driving feet and the ground. Therefore, we analyze the realization conditions of combining the two
Experimental setups and measuring methods
In order to verify the feasibility and reasonability of the abovementioned structure design, working principle analyses and the theoretical models, several experimental setups were built to test the mechanical performances of the piezo-leg and the motion performances of the MQPR, respectively.
Fig. 6 shows the experimental setups used to evaluate the mechanical performances of the piezo-leg. For the non-resonant deformation of the piezo-leg, two capacitive displacement sensors (D-E20.050, Physik
Experiments and discussions
With the abovementioned experimental set-ups, a series experiments were carried out to investigate the performances of the piezo-leg and the MQPR in this section. The mechanical performances of the piezo-leg (non-resonant deformation, resonant frequency and vibration trajectory), the quasi-static motion performances of the MQPR (motion range and coupling, displacement resolution and trajectory synthesis), the resonant motion performances of the MQPR (linear motion speed, in-situ steering speed
Conclusion
In this work, a miniature piezoelectric robot MQPR inspired by the quadrupeds was proposed, designed and tested. The MQPR was not driven by unimorph/bimorph actuators of the common resonant robots or piezoelectric stacks of general non-resonant robots, but the distinctive piezo-leg used to realize nano-resolution and fast speed. The non-resonant motion used to obtain nano-resolution and the resonant motion used to achieve fast speed were integrated into the MQPR. The prototypes of the piezo-leg
CRediT authorship contribution statement
Jing Li: Conceptualization, Formal analysis, Validation, Writing – original draft, Visualization. Jie Deng: Data curation, Validation, Writing – review & editing. Shijing Zhang: Data curation, Validation, Writing – review & editing. Yingxiang Liu: Conceptualization, Methodology, Writing – review & editing, Supervision, Funding acquisition.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was supported in part by the National Natural Science Foundation of China under Grant U1913215 and Grant 5210051275 and in part by the Interdisciplinary Research Foundation of HIT under Grant IR2021233.
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