Reprogrammable Flexible Piezoelectric Actuator Arrays with a High Degree of Freedom for Shape Morphing and Locomotion

Abstract

The high degree of freedom (DoF) shape morphing widely exists in biology for mimicry, camouflage, and locomotion. Currently, a lot of bionic soft/flexible actuators and robots with shape-morphing functions have been developed to realize conformity, grasp, and movement. Among these solutions, two-dimensional responsive materials and structures that can shape morph into different three-dimensional configurations are valuable for creating reversible high DoF shape morphing. However, most existing methods are predetermined through the fabrication process and cannot reprogram their shape, facing limitations on multifunction. Besides, the achievable geometries are very limited due to the device’s low integrated level of actuator elements. Here, we develop a polyvinylidene fluoride flexible piezoelectric actuator array based on a row/column addressing (RCA) scheme for reprogrammable high DoF shape morphing and locomotion. The specially designed row/column electrodes form a 6 × 6 array, which contains 36 actuator elements. By developing a high-voltage RCA control system, we can individually control all the elements in the array, leading to a highly reprogrammable array with various sophisticated high DoF shape morphing. We also demonstrate that the array is capable of propelling a robotic fish with various locomotions. This research provides a new method and approach for biomimetic robotics with better mimicry, aero/hydrodynamic efficiency, and maneuverability, as well as haptic display and object manipulation.

Introduction

The rigid actuation units, such as motors and cylinders, are widely integrated with traditional robotics. However, the bulky and complex structure, the high power consumption, and the rigid contact conditions limit miniaturization, high-level integration, and environmental adaptation. Compliant actuators exist extensively in plants and animals, such as the folding of the leaf, mimicry of insect bodies, and grasping of the octopus arms,^1,2 with a range of significant advantages of higher efficiency, higher strength-to-weight ratio, better flexibility, and more complex functions.^3,4 Inspired by these biological organisms, soft/flexible actuators have been developed for a variety of applications that are not possible using traditional rigid robots and actuators, including bionic robots, artificial muscles, soft grippers, wearable haptic devices, and medical devices.^5,6

Mimicry is a very common and defensive method for biologies. Animals change their appearance to confuse the predators.^1,7 For example, by inflating the mantle and trailing the arms behind the body, the mimic-octopus can mimic a jellyfish.⁸ These tasks need high degree of freedom (DoF) organs to transform into several on-demand shapes. Besides mimicry, a lot of animals kinematically adjust their motor organs, including arms, wings, fins, and bodies, to obtain the most optimized geometry for aero/hydrodynamics. For example, the propulsive efficiency of a ship propeller is 50% based on good design,⁹ but, by active deflection control of fluke, a fin whale can yield a propulsive efficiency of about 86%.¹⁰ For an average ship, the turning radius is 3–10 body length (BL),¹¹ but for a dolphin, the turning radius is as low as 0.11–0.17 BL.¹² These tasks need high DoF organs to continuously morph shape, which inspires the highly efficient locomotion and high maneuverability of flying and swimming bionic robots.^13,14 Therefore, imitating these abilities of high DoF shape morphing is valuable to achieve the same level of simplicity, efficiency, and multifunction.^15–17

An approach to achieve shape morphing is to transform a flat two-dimensional (2D) surface into three-dimensional (3D) geometries,¹⁸ by programming the active materials.^15–17 Besides, a morphology of a 2D-pixelated actuator array would be potentially applied in high DoF shape morphing, haptic display, and object manipulation.^16,19–23 Various materials and mechanisms are capable, such as dielectric elastomers (DEs),^22,24 shape memory alloys (SMAs) and polymers (SMPs),^25,26 phase transition of liquid crystal elastomers (LCEs),^27,28 magnetic responsive polymers,^29,30 soft pneumatic and hydraulic actuators,^31,32 and photoresponsive materials.^33,34 However, one of their current major limitations is the nonreprogrammability or limited reprogrammability, which means, after fabrication, the device can only transform into one type or a few types of shapes.^35–37 For example, a deformable magnetic membrane is predetermined by the process of magnetization, and different types of morphing can only be realized by the process of demagnetization and remagnetization.^38,39 Another limitation is the low DoF. Due to the bulky structure and complex control method, the number of individually controlled soft actuators is very low, such as hydraulic and pneumatic actuators.^40,41 For the magnetic membranes, a huge external magnetic field control system is also a barrier.^29,30,38,39 The third limitation is the slow response, which means the deformation time ranges from several seconds to tens of seconds. This problem hinders the application of kinematics. For some thermally responsive materials, such as SMAs, SMPs, and LCEs, the phase change has to wait for the slow temperature shift.^25–28,42 For some electrochemical polymers, the deformation happened due to the ionic migration under the external electric field so the response is also slow, although the applied voltage is low and the circuit system can be simply designed.^17,43 Besides, DE is quick response, lightweight, and promising for shape morphing. But it can only extend itself due to the electrostatic attraction, no matter whether a positive or a negative voltage is applied.⁴⁴ Therefore, a DE actuator can only bend in one direction, which limits the DoF. Polyvinylidene fluoride (PVDF) is a mature and reliable flexible piezoelectric material.⁴⁵ Compared with the abovementioned materials and mechanisms, based on the inverse piezoelectric effect, the PVDF film can rapidly generate extension and compression in d₃₁ mode, and this feature has been made use of fast-moving insect robots.^46,47 Furthermore, the technology of a matrix of piezoelectric units, such as 2D ultrasonic transducers,^48,49 will prove the feasibility of a matrix of PVDF actuator elements.

In this article, we propose a concept of a pixelated biological locomotive organ and a reprogrammable high DoF shape morphing mechanism and design a PVDF/polyethylene terephthalate (PET) flexible piezoelectric actuator array (Fig. 1). To mimic the high DoF shape morphing of locomotive organs, such as the patagium of flying squirrel and the body of oarfish, the pixelated actuator array can morph the dynamic geometry and adapt itself to the external aero/hydrodynamic conditions (Fig. 1A). As shown in Fig. 1B, generally, a unimorph piezoelectric actuator has three statuses: flat status without applied voltage, down status with positive voltage, and up status with negative voltage. The flat, down, and up statuses are defined as 0, 1, and −1 logic values in the control circuit and program, respectively. So by individually defining the logic value of each element, all the elements can form a combination of logic values, and the whole array can perform different types of high DoF shape morphing with reprogramming based on the corresponding array configurations. The structure of the actuator array is a stack of very thin polymer sheets bonded by the laminating process. It contains 1 PVDF piezoelectric active layer, 1 silicone adhesion layer, 1 PET elastic layer, 12 row/column electrodes, 5 insulators, and 5 jumpers (Fig. 1C). The design of the row/column electrodes allows n² independent actuator elements using 2n control inputs, which is much lower than n² inputs of the parallel method. Two sets of connection pins are placed at the edge of the PVDF on both sides. To connect the row electrodes (rows 2–6) to their corresponding pins, five copper jumpers with 3 μm thickness are adopted. The definition of elements by the index of rows and columns is illustrated in Supplementary Fig. S1. A thin layer of the insulator is placed between the jumper and the PVDF to avoid short circuits and electric discharge. Due to the additional bending stiffness applied to the actuator array, the location of the jumper/insulator pairs is determined by their lengths, so the stiffness distribution of the whole array can be as uniform as possible. A prototype 6 × 6 array is pictured in Fig. 1D. A cross-sectional scanning electron microscopy image shows the unimorph structure made of a 25 μm thick PVDF layer, two 400 nm thick chromium (Cr)/copper (Cu) layers on the top and bottom sides of the PVDF layer, a 25 μm thick silicone layer, and a 25 μm thick PET layer at the bottom. Exploiting this high DoF reprogrammable actuator array, we also exhibit a bionic robotic fish with better maneuverability and functions. As compared with other actuation methods in Supplementary Table S1, we can see that our actuator array system has more individual elements and actuator statuses with reprogramming and fast response benefits from piezoelectric material and row/column addressing (RCA) scheme.

FIG. 1.

The pixelated PVDF/PET flexible piezoelectric actuator array, the high DoF shape morphing mechanism, and the bionic applications. (A) Schematic flying squirrel and oarfish with pixelated morphing patagium and body. (B) The individually defined elements can form different combinations of logic values and different types of shape morphing. A reprogrammable high DoF shape morphing can be realized based on the corresponding configurations. (C) A multilayered structure of flexible piezoelectric actuator array with a stack of polymer films. (D) The optical photo shows a 6 × 6 array connected with 12 pins to the row and column electrodes. Scale bar, 1 cm. The SEM image shows the cross-sectional view of the prototype array with different layers of materials. Scale bar, 25 μm. DoF, degree of freedom; PVDF, polyvinylidene fluoride; SEM, scanning electron microscopy.

Results

We demonstrate the concept of reprogrammable high DoF shape morphing by fabricating a 6 × 6 array (Fig. 1D). The RCA electrodes are prepared by a microfabrication process (Supplementary Fig. S2). The electrode patterns are formed by a sputtering process. The copper film is cut into strips to form the jumpers. The insulators are prepared from PET films and pressure-sensitive adhesion (Supplementary Fig. S3). At last, we assemble the PVDF film, PET film, copper jumpers, and insulators. More details about the fabrication and assembly of our array can be found in Supplementary Notes S1 and S2.

Actuation of the PVDF flexible piezoelectric actuator

The proposed actuator array adopts the typical unimorph structure. As schematically shown in Fig. 2A, in the unimorph actuator, a piezoelectric layer and an elastic layer are bonded together. When the piezoelectric layer is driven by the applied driving voltage to expand or contract, the elastic layer resists this dimension change, leading to bending deformation. We measure the electrical characteristics of PVDF film to get the dielectric and voltage-current characteristics (Supplementary Fig. S4). In the traditional mechanical model, the actuator can be modeled as a cantilever (Fig. 2A; see Supplementary Note S3 for details).^50,51 The tip displacement (δ₀) is expressed as Eq. (1) and based on the small deflection with geometric linearity, which means δ₀ is much smaller compared with actuator length (L). $δ_{0} = \frac{3 L^{2}}{t_{p}^{2}} \frac{A B (1 + B)}{A^{2} B^{4} + 2 A (2 B + 3 B^{2} + 2 B^{3}) + 1} d_{31} V_{0}$ (1)where t_p denotes the thickness of the piezoelectric layer, d₃₁ denotes the transverse piezoelectric coefficient of the piezoelectric layer, V₀ denotes the driving voltage, A denotes Young’s modulus ratio of the elastic and piezoelectric layers, and B denotes the thickness ratio of the elastic and piezoelectric layers. For the actuators with high Young’s modulus piezoelectric and elastic layers, such as piezoelectric ceramic and metal, this assumption is applicable since the tip displacement is always relatively small.

For the actuators with large tip displacements, the assumption of geometric linearity in Eq. (1) will be inapplicable with a big error. For the proposed flexible piezoelectric actuator, we derive a modified mechanical model (see Supplementary Note S3 for details). For a large deflection with geometric nonlinearity, we divide the beam into n segments and assume each segment as a beam with a small deflection (Fig. 2B). So for the whole beam, δ₀ can be calculated from the superposition of each segment’s deflection with geometric linearity. Different from small deflection, δ_i can be decomposed into δ_xi and δ_yi. So δ₀ (δ_n) can be expressed by δ_x (δ_xn) and δ_y (δ_yn) as $δ_{0} = \sqrt{δ_{x}^{2} + δ_{y}^{2}}$ (2)

FIG. 2.

Mechanical analysis of the unimorph piezoelectric actuator. (A) In the traditional model of small deflection with geometric linearity, the tip displacement δ₀ is much smaller than the length of the actuator L, with the rotation angle α. (B) In the modified model of large deflection with geometric nonlinearity, the beam has a large δ₀ compared with L and can be divided into a series of segments with geometric linearity. (C) Deformed beam shapes are calculated by the FEA simulation (solid), traditional model (dash), and modified model (dot). (D) δ₀ of the modified model, FEA simulation, and experiment against V₀. (E) δ₀ against t_p under different d₃₁. (F) δ₀ against t_m and E_m, a stiffer but thinner elastic layer can generate a larger δ₀. FEA, finite element analysis.

We use the finite element analysis (FEA) method to simulate the deformation of the actuator by COMSOL 5.6 software. Fig. 2C compares the normalized deformed beam with different lengths by using the traditional model, modified model, and FEA simulation when V₀ is 1500 V. When the length of the actuator is short, the traditional model is close to the FEA simulation due to the small deflection. When the length gets longer, the traditional model gets a higher error than the modified model. Fig. 2D shows δ₀ of the modified model, FEA simulation, and experiment under different V₀, and it can be found that the modified model describes the actuator very well. Fig. 2E shows the impact of d₃₁ on δ₀, when d₃₁ is lower than 25 pC/N, δ₀ decreases as the increase of t_p, and when d₃₁ is higher than 25 pC/N, there will be a peak on the curve and this peak will move right when d₃₁ increases. Fig. 2F illustrates the impact of elastic layer thickness (t_m) and Young’s modulus (E_m) on δ₀, and it can be found that there is a peak on the surface. To show the data more clearly, Supplementary Fig. S5A and Supplementary S5B have generated the side views of Fig. 2F. An elastic layer with a high Young’s modulus and a small thickness is preferred to achieve larger deflection.

High-voltage-RCA control system and demonstration of a 6 × 6 actuator array

Although the current traditional RCA scheme has been applied to control soft actuators, the controllable voltage is still very low.^17,22 The reprogrammability of our actuator array relies on the topology of row/column electrodes and the high-voltage RCA (HV-RCA) control system. Fig. 3 schematically shows an HV-RCA circuit of an n × n array. In this circuit, the Arduino Mega 2560 (digikey.cn) controls all the other modules (±HV source, row control, and column control) as the core unit. The ±HV source contains a positive and a negative HV source. The output ±HVs are pulse-width modulation wave controlled, and the characterization is shown in Supplementary Fig. S6A. The row control contains a ±HV switch and a row switch module. The ±HV switch receives the ±HV and selects the polarity. Then, the row switch will finally determine the output (±HV or 0V) and apply the voltage to the row electrode in the array. In the meantime, the column control modules, which contain column switches, are connected to the column electrodes and will determine the status of grounded (GND) or float to the column electrodes. When a column is enabled (GND), the other columns will be unselected (float). During this period, the logic values (±1 and 0) can be defined for each row, and the corresponding actuator elements in the enabled column can be controlled, while the elements in the unselected columns will not work. This mechanism is shown in Supplementary Movie S1 by two actuators with floating and grounded bottom electrodes. By column scanning, all the elements in the array can be individually controlled, so the array can realize shape morphing. A detailed control program flow is shown in Supplementary Fig. S6B and described in Supplementary Note S4. Taking the control process of the 1 × 2 array as an example, Fig. 3B (i) shows the voltage applied on the row electrodes with an enlarged view (Fig. 3B (ii)) for continuous morphing, which means the whole array can vibrate with a specific rhythm. The upper two curves in Fig. 3B (i) show the frequency controls, and elements (1, 1) and (1, 2) are working under 1 and 2 Hz, respectively. The other two curves show the phase control; both elements are working under 1 Hz with a 180-degree phase difference. Since the PVDF film acts as a capacitor, the charging and discharging process is clear. Although the applied voltages are not continuous as shown in Fig. 3B (ii), due to the fast scanning, the morphing of the array will be finally formed under a specific geometry by all the defined elements. More detailed circuit characterizations of the 1 × 2 array are shown in Supplementary Fi. S6C and Supplementary S6D, and the corresponding static and continuous morphing are shown in Supplementary Fig. S7 and Fig. S8 and Supplementary Movie S2. The logic value of each actuator element can be determined from the synthesis of the switches in the circuit.

FIG. 3.

HV-RCA circuit and the demonstration of a 6 × 6 array with static and continuous morphing. (A) HV-RCA circuit scheme of an n × n array. (B) The voltage applied on the row electrodes for continuous morphing of the 1 × 2 array. (i) For the upper two curves, element (1, 1) will bend under 1 Hz and element (1, 2) will bend under 2 Hz. For the bottom two curves, element (1, 1) will bend under 1 Hz at 0°, and element (1, 2) will bend under 1 Hz at 180°. (ii) The enlarged view of the applied voltages, which are not continuous. (C) Static morphing is demonstrated by defining elements in columns 1, 2, 3, 4, 5, and 6 as logic values of (i) −1, −1, −1, 1, 1, and 1, and elements in rows 1, 2, 3, 4, 5, and 6 as logic values of (ii) 1, 1, 1, −1, −1, and −1; (iii) 1, 1, −1, −1, 1, and 1; (iv) 1, −1, 1, −1, 1, and −1. (D) Continuous morphing of phase mixing is demonstrated by defining elements in rows 1, 2, 3, 4, 5, and 6 as phases of 0°, 72°, 144°, 216°, 288°, and 360° (wavy motion) when the frequency is 1 Hz. (E) Continuous morphing of phase mixing is demonstrated by defining elements in columns 1, 2, 3, 4, 5, and 6 as phases of 0°, 72°, 144°, 216°, 288°, and 360° (twist motion) when the frequency is 1 Hz. Scale bars, 1 cm. Orange dash line, original shape. Yellow dash line, morphed shape. The curvature and twist angle are also listed. HV-RCA, high-voltage row/column addressing.

For the preliminary verification of the n × n HV-RCA system, we fabricate a 2 × 2 array and do the test by static (Supplementary Fig. S9A) and continuous morphing (Supplementary Fig. S9B–S9D). We demonstrate the static morphing of different combinations of bending down (1), keeping flat (0), and bending up (−1) (Supplementary Fig. S9A (i) and (ii)). The continuous morphing of different combinations of frequencies (frequency mixing) is demonstrated and listed in Supplementary Fig. S9B (i) and (ii). The continuous morphing of different combinations of 0° and 180° phases when the frequency is 1 Hz (phase mixing) is demonstrated and listed in Supplementary Fig. S9C (wavy motion) to S9D (twist motion). Several other types of static morphing, frequency mixing, and phase mixing have been programmed and demonstrated in Supplementary Movie S3.

For a higher DoF of shape morphing, a surface should be divided into more elements. We develop our array system into 6 × 6, so the 36 individually controllable elements will perform more types of sophisticated shape morphing. We first demonstrate static morphing. As listed in Fig. 3C (i)–(iv), we apply the logic values of ±1 to the rows and columns according to different combinations. It is clear that the array performs several similar wavy shapes, but the peak and valley, including number and location, can be configurated. Any combination of logic values can be applied to the array by reprogramming. Several other types of static morphing have been programmed similarly and demonstrated in Supplementary Movie S4. After the static morphing, we program the array to demonstrate reversible, spatiotemporal control of the surface deformation and show continuous and smooth shape morphing. We also do different types of frequency mixing on this 6 × 6 array and showed them in Supplementary Movie S4 to ease the presentation. In Fig. 3B and Supplementary Movie S4, we apply 0°, 72°, 144°, 216°, 288°, and 360° to rows 1–6 when the frequency is 1 Hz, so all the rows will bend rhythmically, and a more delicate wavy motion can be performed compared with the aforementioned 2 × 2 array. Based on the time series plots in Fig. 3D and Supplementary Movie S4, the wave peak and valley move gradually from the anchor to the tip. Different from the wavy motion in which we apply phases equably to rows, we also try to define columns 1–6 as 0°–360°. As shown in Fig. 3E and Supplementary Movie S4, all the columns will bend rhythmically, and we perform a more delicate twist motion compared with the aforementioned 2 × 2 array. Based on the time series plots in Fig. 3E and Supplementary Movie S4, compared with the initial shape, the tip of the array twisted back and forth gradually. We also performed several other types of phase mixing based on different configurations of phase in Supplementary Movie S4.

Robotic fish with a high DoF shape morphing and locomotion

Finally, we design a robotic fish with a 9 × 4 array as a pixelated body, imitating a fish wriggling its body to swim forward and turn (Fig. 4A). We fabricate the fish body by a similar process to the aforementioned arrays, and then we connect the fish body to the PET head and tail. We change the sputtered electrodes to aluminum to make the robot more like a fish, and we spin-coat a thin layer of polydimethylsiloxane (PDMS) to the column electrodes to avoid short circuits (Supplementary Fig. S10). More details about the fabrication and assembly of our robotic fish can be found in Supplementary Note S5. The definition of elements by the index of rows and columns is shown in Supplementary Fig. S11, and different types of locomotion can be realized by the corresponding configurations. We characterize the propulsion velocity of the robotic fish based on the configurations of wavy motion 1 (Fig. 4B (i)) and wavy motion 3 (Fig. 4B (ii)). It is clear that wavy motion 3 can propel the robot faster than wavy motion 1 because the movement of the wave peak and the valley of wavy motion 3 is faster. We also program the robot that shows the locomotion in Fig. 4C. The array is configured to morph the wavy motion 1 (Fig. 4C (i) and Supplementary Movie S5) and wavy motion 3 (Fig. 4V (ii) and Supplementary Movie S6) with a 1 Hz driving frequency. The fish body is morphing rhythmically to propel the robot forward at different velocities. Besides swimming forward, we also programmed the robot to turn left, as shown in Fig. 4D (i)–(iii). We define rows 4–9 as 1 to keep bending and rows 1–3 as a 2 Hz swing to propel the robot. Since the front part of the robot is facing left and the rear part is producing thrust, the robot can gradually turn left (see Supplementary Movie S7). By expanding the driving time, we also control the robot to realize a U turn in Supplementary Movie S8.

FIG. 4.

Robotic fish with a high DoF shape morphing and locomotion. (A) Photograph of the fabricated robotic fish with a pixelated body of a 9 × 4 array (36 individually controlled elements). (B) Characterization of propulsion velocity of the robotic fish. (i) The fish body is configured to morph under wavy motion 1 (the phases of rows 1–9 are from 0° to 180°) and (ii) wavy motion 3 (the phases of rows 1–9 are from 0° to 360°). (C) Forward of the fish robot. The images show frames from Supplementary Movies S5 and Movie S6, visualizing the morphing of the fish body with (i) wavy motion 1 and (ii) wavy motion 3. (D) Turning left of the fish robot. The (i) top view and (ii) side view images show frames from Supplementary Movie S7. (iii) Rows 4–9 are defined as 1 to keep bending, and rows 1–3 are defined as a 2 Hz swing to propel the robot. Scale bars, 4.5 cm. Yellow dash line, morphed shape.

Conclusions

This article demonstrates a flexible, high DoF actuator array capable of performing reprogrammable shape morphing and locomotion. The proposed actuator array and the corresponding HV-RCA control system overcome the drawbacks of low DoF and low reprogrammability of rigid and soft actuators and benefit from the fast response of PVDF. Our actuator array makes the imitation of high DoF shape morphing and motion in animals possible. The demonstration of our robotic fish, which adopts a customized array, shows locomotion by swimming forward and turning with controllable modes. However, the current solution leaves room for improvement. The required driving voltage is still too high (≤1500 V), preventing the miniaturization of the circuit system and the untethering of the robots.^47,52 So the development of low-voltage flexible piezoelectric material is necessary to further improve the integration of our system. Last, since the current actuator array is thin but large with low stiffness, the output force cannot be high enough for application scenarios of high load with a high frequency, such as small- and medium-sized flying robots. To achieve it, the bimorph actuator structure and the corresponding array control system would be desirable.⁵¹ Finally, although we have already preliminarily verified the proposed robotic fish, some more complicated locomotion with higher DoF and more flow conditions should be further demonstrated. An effective approach to studying the locomotion of an underwater robot is digital particle image velocimetry, which allows direct visualization of water flow around the swimming fish robot by providing different flow conditions.^53,54 This is one of our future works as well.

Footnotes

Author Disclosure Statement

No competing financial interests exist.

Funding Information

This study was financially supported by the University-Enterprise Cooperation Project of Visiting Engineers (FG2023160) in Zhejiang Province and the Project “Teaching Exploration of Solidworks Assembly and Engineering Example Course in the Background of Modern Apprenticeship” (JG3202010) at Shaoxing Vocational and Technical College.

Supplementary Material

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