A Versatile Soft Crawling Robot with Rapid Locomotion

Abstract

This article presents a versatile soft crawling robot capable of rapid and effective locomotion. The robot mainly consists of two vacuum-actuated spring actuators and two electrostatic actuators. By programming the actuation sequences of different actuators, the robot is able to achieve two basic modes of locomotion: linear motion and turning. Subsequently, we have developed analytical models to interpret the static actuation performance of the robot body, including linear and bending motions. Moreover, an empirical dynamic model is also developed to optimize the locomotion speed in terms of frequency and duty cycle of the actuation signal. Furthermore, with the help of the strong electroadhesion force and fast response of the deformable body, the soft robot achieves a turning speed of 15.09°/s, which is one of the fastest among existing soft crawling robots to the best of our knowledge. In addition to the rapid and effective locomotion, the soft crawling robot can also achieve multiple impressive functions, including obstacle navigation in confined spaces, climbing a vertical wall with a speed of 6.67 mm/s (0.049 body length/s), carrying a payload of 69 times its self-weight on a horizontal surface, crossing over a 2 cm (0.15 body length) gap, and kicking a ball.

Introduction

Soft robotics has attracted much interest over the past decade due to their impressive attributes, including inherent compliance, unprecedented agility, and infinite degrees of freedom.^1,2 Built of soft materials, soft robots can withstand external impacts, which enables them to work effectively in unstructured and harsh environments.³ Another benefit of employing soft materials leads to a much simpler robotic structure, as mechanical components such as rigid links and joints that are extensively employed in the traditional robots are not required for soft robots.⁴ In addition, with excellent resilience, soft robots can achieve muscle-like actuation and mimic the behavior of soft biological systems much better compared with traditional rigid-bodied robots.⁵

Many impressive soft robots inspired by soft-bodied animals such as octopus,^6,7 caterpillar,^8–12 and jellyfish^13–15 have been developed in the literature, of which soft crawling robots are particularly interesting due to their potential applications as surveillance robots in complex environments. In the past decade, many kinds of soft crawling robots have been developed with different materials and actuation mechanisms. In particular, as one of the very first soft crawling robots, a quadrupedal soft robot was proposed by Shepherd et al.² By combining crawling and undulation paces, this multigait robot could navigate difficult obstacles. Later, Tolley et al.³ developed an untethered version of this robot, which could work in tough environments. In addition, vacuum-driven pneumatic actuators have been employed in soft crawling robots as well. Robertson and Paik¹⁶ designed a modular soft robot using vacuum-powered soft pneumatic actuators, which can achieve crawling and rolling locomotion. Other smart actuators have also been used to develop soft crawling robots, such as shape memory alloys (SMAs),^10,17,18 ionic polymer metal composites,^19,20 as well as dielectric elastomer actuators (DEAs).^21–23 These soft crawling robots achieve locomotion either through the mechanism of asymmetric friction or the coordination of several soft actuators, both of which are not effective, especially during turning motions.

Recently, the use of electrostatic actuators to generate asymmetric friction forces has become popular for some DEA-based soft crawling robots since they can generate reversible adhesion forces.^21,22 With strong electroadhesion forces, these soft crawling robots are able to achieve effective and steady motion without slippage. However, the small deformation and output force of the robot body greatly limit the locomotion speed and payload ability of the robots. Moreover, Wu et al.²⁴ improved the locomotion efficiency of the quadrupedal soft robot by coupling the electrostatic actuators on the feet. The robot could even walk on a 30° inclined metal surface with the use of the electrostatic actuators. However, the out-of-plane deformation of the robot body induces air gap between the electrostatic actuators and the attached surface, which decreases the efficiency of the electrostatic actuators and makes the locomotion ineffective.

In this article, we have developed a versatile soft crawling robot that consists of two vacuum-actuated spring actuators (VASAs) as the robot body and two electrostatic actuators as the robot feet (Fig. 1A). Compared with the existing soft crawling robots, our robot is superior in terms of locomotion speed and efficiency due to the large deformation and fast response of the VASA. For example, the soft crawling robot achieves a turning speed of 15.09°/s, which is one of the fastest among existing soft crawling robots to the best of our knowledge. Furthermore, the steady locomotion and simple structure of the VASA allow for the development of analytical models, which can be used to interpret and optimize the actuation performance of the robot. Finally, multiple impressive functions, including obstacle navigation in confined spaces, climbing a vertical wall with a speed of 6.67 mm/s (0.049 body length/s), carrying a payload of 69 times its self-weight, crossing over a 2 cm (0.15 body length) gap, and kicking a ball, are demonstrated by this soft crawling robot.

FIG. 1.

Schematic of the soft crawling robot. (A) The robot consists of two VASAs and two electrostatic actuators. Made of compression spring and fabric bladder, the VASAs contract linearly at actuated state. (B) Actuation sequence of electrical or vacuum signals on each actuator for the robot locomotion. The red line indicates that the electrical or vacuum signal is applied to the respective robot foot or body, whereas the blue line indicates no voltage or vacuum is applied. (C) Schematic of the forward locomotion of the soft crawling robot by following the actuation sequence in (B). VASAs, vacuum-actuated spring actuators. Color images are available online.

Materials and Methods

Mechanical design of the soft crawling robot

As shown in Figure 1A, the soft crawling robot mainly consists of two VASAs as the robot body and two electrostatic actuators as the robot feet. The VASA contains a compression spring enclosed in an airproof bladder made of thermoplastic polyurethane-coated polyester fabric. A thin silicone tube is employed to connect the fabric bladder with a vacuum pump for pneumatic actuation. The use of a fabric-based body and thin silicone tubes makes the robot body susceptible to tears by sharp objects; therefore, the contact with sharp objects should be avoided. When subjected to vacuum pressure, the actuator contracts along the axial direction. Similar vacuum-driven actuators that incorporate different skeletons such as origami structures²⁵ or foams¹⁶ were also reported in the literature. Compared with the origami structures, the use of compression springs as the skeleton enables a quick recovery for the actuator to its original state after vacuum pressure is removed. Moreover, the compression spring also constrains the radial deformation of the actuator and leads to a linear motion, which is challenging to achieve for the foam-based vacuum actuator.

Besides the VASAs, the electrostatic actuators also play an important role in the robot locomotion. As shown in Figure 1A, the electrostatic pad consists of two parallel compliant electrodes (silver nanowire) and a dielectric layer (polyurethane). When subjected to voltage, positive and negative charges accumulate on the two electrodes, respectively. If the actuator approaches a dielectric surface, the electric field generated by the two electrodes induces dielectric polarization to form surface charges. The presence of the dielectric layer prevents the surface charges from neutralizing with those on the electrodes. These opposite charges attract each other, which leads to electroadhesion force between the actuator and the dielectric surface. When the voltage is off, the induced charges disappear quickly, which results in fast and reversible adhesion. Compared with other adhesion technologies such as suction cups,²⁶ microspines,²⁷ and gecko-inspired adhesives,^28–30 electrostatic actuators are lightweight, simple-structured, and robust for various types of surfaces including glass, wood, paper, and metal.^31,32

It is difficult to assemble the robot body and robot feet directly because of the different shaped interfaces. Therefore, two flat foot stands with round caps are employed to link the robot body and feet. The caps and the foot stands are three-dimensional (3D) printed using VeroClear (Object 260). Small bearings are placed in between the caps and the foot stands to allow the round caps to rotate freely. This is because other than axial contraction, the VASA also experiences a twisting motion due to the coil property, which makes the feet rotate and decreases the electroadhesion efficiency.

Locomotion mechanism

The two VASAs are actuated by an external vacuum pump (V-i140SV, Value) that is connected to the robot via flexible tubes at one end near the rear foot. Upon actuation, the VASA contracts to an actuated state that increases with the applied percentage of vacuum (Fig. 1A). Meanwhile, the two electrostatic actuators are charged from an external voltage amplifier (EMCO CA60, XP Power) with maximum voltage rating at 6 kV. Upon actuation, the induced electroadhesion force increases the friction force between the foot and the attached substrate. The four actuators are controlled simultaneously by an external electrical circuit shown in Supplementary Figure S1. By actuating the four actuators with different sequences, we demonstrate two fundamental modes of locomotion: linear and turning motion.

As illustrated in Figure 1B, the linear motion involves three steps: (1) Activation of the rear foot anchors the robot from sliding backward. (2) Activation of the front foot and deactivation of the rear foot simultaneously create an asymmetrical friction force between the front and rear foot of the robot, which leads to forward movement when the robot body contracts at the same time. (3) The third step repeats the first step with the robot body and front foot deactivated and the rear foot activated. The restoring force generated by the compression spring pushes the front foot forward while the rear foot adheres to ground. Repeating the actuation sequence, the soft robot moves to the right continuously. Figure 1C schematically demonstrates the movement of the robot by following this actuation sequence in Figure 1B.

Due to the fast and reversible adhesion force generated by the feet, the soft robot is capable of moving toward another direction by simply reversing the actuation sequence of the front and rear foot. Figure 2A shows a sequence of images when the robot achieves forward and backward movement. The small schematic inset at the bottom right corner of each frame indicates the actuation states of the actuators at the corresponding step. A video showing the bidirectional linear motion of the robot is available in Supplementary Movie S1. The maximum speed the soft robot achieved with optimized actuation signals is around 16.29 mm/s (0.12 body length/s), which is comparable to or even higher than that of some other soft crawling robots based on vacuum actuator (0.08 body length/s),¹⁶ pneumatic actuators (0.2 body length/s),² or SMA (0.018 body length/s).¹⁷

FIG. 2.

Demonstration of the two basic modes of locomotion. (A) A sequence of images of the soft robot crawling in two directions. The arrows indicate the direction of motion. (B) A sequence of images of the soft robot turning in two directions. The arrows indicate the direction of motion. The red rectangles on the insets (at the bottom right corner) indicate which actuators are currently actuated; gray rectangles represent deactivation of the actuators. Color images are available online.

In addition to linear movement, this soft robot can also achieve turning motion. When both VASAs are actuated with vacuum, the robot can achieve linear motion, as discussed earlier. However, when only one of the VASAs is actuated, the robot turns due to the constraint imposed by the other VASA. The detailed turning performance will be discussed later. The actuation sequences for the turning motion are similar to those of the linear motion in Figure 1B except that only one VASA is actuated and follows the rear foot signal. For example, by following the actuation sequences in the insets of Figure 2B, the robot turns clockwise when only the right VASA is activated. Similarly, the robot turns anticlockwise by actuating the left VASA only while keeping the actuation signals unchanged for the front and rear foot. Supplementary Movie S2 demonstrates the turning motion of the robot. Figure 2B shows the captured images of the robot from this turning motion. The robot first makes a clockwise turn and then reserves the turning direction. The two basic modes of locomotion generated through a simple sequence of binary actuations greatly improve the mobility of the soft robot, which builds the foundation for more complex movement and further enhances its potential for practical applications especially as a surveillance robot.

Theoretical Modeling of the Robot Body

Static modeling of the VASA

As mentioned earlier, the robot body can achieve both linear and bending motion when subjected to vacuum pressure. The deformation of the body depends on the vacuum pressure as well as the property of the spring. In this section, static analysis is established to understand the relation between the input vacuum pressure and the corresponding deformation.

Linear deformation

For linear deformation, both VASAs exhibit identical deformation under the same actuation pressure, hence only one actuator is considered in this section to analyze the linear deformation Δx upon vacuum pressure ΔP. Figure 3 shows the simplified schematic of the VASA with its initial geometrical parameters: the original length L₀, the wire diameter d, and the outer diameter of the spring D. We define the distance between two adjacent coils as \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\;{P_0} = \left( {{L_0} - {L_{SH}}} \right) / n$$ \end{document} , where n is the number of active coils and L_SH is the solid height. After compression, the distance becomes \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${ \rm{ \;}}{P_d} = \left( {{L_0} - {L_{SH}} - \Delta x} \right) / n$$ \end{document} . We assume that the fabric is nonstretchable, hence it sags between the coils and forms an arc with a depth of h as illustrated in Figure 3. This arc reduces the equivalent area that the vacuum pressure exerts on. Therefore, the force equilibrium between the applied vacuum pressure and the spring force gives the governing equation as: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} \Delta P \pi { \left( { \frac { D } { 2 } - h } \right) ^2 } = k \Delta x , \tag { 1 } \end{align*} \end{document}

FIG. 3.

Section view of the simplified schematic of the VASA with geometrical parameters. The dark curve in the enlarged section represents the fabric bladder.

where k is the spring constant.

Now P₀ becomes the length of this arc as we assume that the fabric is not stretchable and P_d is the respective chord length. The radius and angle of the arc are defined as R and θ as shown in Figure 3. Based on the geometrical relationship, the distance between two adjacent coils can be rewritten as: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${P_0} = 2R \theta$$ \end{document} and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${P_d} = 2R \sin \theta$$ \end{document} . The depth of the arc can be calculated as \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$h = R - R \cos \theta = {P_0} ( 1 - \cos \theta ) / \left( {2 \theta } \right)$$ \end{document} .

Hence the deformation can be derived as \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} \Delta x = n{P_0} - 2nR \sin \theta. \tag{2} \end{align*} \end{document}

Substituting Equation (2) into the governing equation, it becomes \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} \Delta P \pi \left({D \over 2} - {{{P_0}} \over {2 \theta }}{ \left( 1 - \cos \theta \right) } \right) ^2 = k \left( {n{P_0} - {{n{P_0}} \over \theta } \sin \theta } \right). \tag{3} \end{align*} \end{document}

Therefore, the relation between ΔP and θ can be obtained by solving Equation (3) numerically. We can further derive the deformation of the spring upon vacuum pressure based on Equation (2).

To verify the analytical model and identify the most suitable spring for the soft crawling robot, we conducted experiments on four VASAs with different compression springs. These springs have the same outer dimensions (L₀ and D) but differ in spring constant, wire diameter, and number of active coils. The properties of the springs are detailed in Supplementary Table S1. The robot body was first placed on the table with one end fixed to the ground. A vacuum pump with maximum 87% vacuum was used as the power source. The output vacuum pressure was controlled by a vacuum regulator (IRV10 Series, SMC) and a digital sensor (ZSE30A Series, SMC). Upon actuation, the deformation of the robot body was measured with a laser sensor (ILD 1700, MicroEpsilon), and the data were collected with a sampling frequency of 100 Hz through a data acquisition device (USB-6363, National Instrument). Vacuum pressure was slowly applied to the body from 0 to 85 kPa at a step of 5 kPa. The data were recorded when the deformation of the robot body was stable. Three trials were conducted for each VASA, and the results are plotted in Figure 4.

FIG. 4.

Linear deformation of the robot body as a function of the applied vacuum pressure. Four different VASAs with an increasing spring constant (from Spring A to Spring D) are employed to measure the vacuum-induced deformation. The square markers represent the experimental data, and the solid curve represents the theoretical result.

Figure 4 shows the comparison between the theoretical and experimental results for the four VASAs under different vacuum pressures. The deformation scales with the applied vacuum pressure and exhibits some nonlinearity especially when the spring constant is small. This nonlinearity mainly comes from the distortion of the fabric. As vacuum pressure increases, the fabric sags deeper into the springs, thus the effective area of the vacuum pressure is reduced, leading to a decreasing gradient. This nonlinearity decreases as the spring constant increases (from Spring A to Spring D). The reason is that the distance between two coils P₀ becomes smaller, leading to a smaller sag depth h even under high vacuum pressure, thus the effective area does not change much throughout the applied vacuum pressure range. In addition, we can also conclude from Figure 4 that the robot body with smaller spring constant generates larger deformation under the same vacuum pressure. Hence, Spring A is employed in our soft robot in the following sections to achieve fast locomotion. The theoretical results agree well with the experimental results. The small discrepancy mainly comes from the inaccurate assumption of the circular sagging. In practice, the fabric has some creases between two adjacent coils because the overall length of the fabric along the perimeter does not change (Supplementary Movie S1). Hence, the actual effective area for the vacuum pressure is slightly larger than our assumptions.

Bending deformation

We build an analytical model for the bending motion of the robot body. Figure 5 shows the simplified schematic of the robot body and the free body diagram of the top 3D printed component during the bending motion. When only VASA 1 is actuated, the contraction of the actuator exerts a force F₁ to the 3D printed component; meanwhile VASA 2 generates a force F₂ to the 3D printed component as well. Besides, there is a bending moment M generated from the bending of the two springs. From the force and moment equilibrium, we can conclude that \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${F_1} = {F_2}$$ \end{document} and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${ \rm{ \;}}M = {F_1} \Delta s$$ \end{document} , where Δs is the distance between the centerlines of the two VASAs as shown in Figure 5. In addition, the lateral bending moment of a spring can also be calculated using the following equation³³: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} { M_s } = { \frac { E { d^4 } } { 32n \left( { 2 + \nu } \right) D } } \alpha = { k_2 } \alpha , \tag { 4 } \end{align*} \end{document}

FIG. 5.

The simplified schematic of the robot body and the free body diagram of the top three-dimensional printed component during the bending motion. The right VASA is named as VASA 1 and the left one is VASA 2.

where E, d, n, ν, and D are the inherent properties of the spring and can be grouped as a spring bending coefficient k₂. The bending angle α shown in Figure 5 is defined as the angle between the top and bottom 3D printed surfaces. Thus, the bending moment M can be rewritten as \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$M = 2{k_2} \alpha$$ \end{document} , and subsequently, the relationship between the force and the bending angle can be written as: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} { F_1 } = { F_2 } = { \frac { 2 { k_2 } \alpha } { \Delta s } } . \tag { 5 } \end{align*} \end{document}

From the geometrical relationship, we have \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} \frac { { { L_0 } - \Delta { x_2 } } } { \alpha } - \frac { { { L_0 } - \Delta { x_1 } } } { \alpha } = \Delta s , \tag { 6 } \end{align*} \end{document}

where \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\Delta {x_1}$$ \end{document} and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\Delta {x_2}$$ \end{document} are the deformation of the two VASAs, respectively. We assume that Hook's law still holds for the two springs. Substituting \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\Delta {x_2} = {F_2} / k$$ \end{document} and Equation (5) into Equation (6), we can derive the bending angle α as: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} \alpha = { \frac { k \Delta { x_1 } \Delta s } { k \Delta { s^2 } + 2 { k_2 } } } . \tag { 7 } \end{align*} \end{document}

We further assume that the previous relation for linear deformation still holds during the bending motion, then the governing equation for VASA 1 can be written as: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} \Delta P \pi { \left( { \frac { D } { 2 } - h } \right) ^2 } = k \Delta { x_1 } + { F_1 } . \tag { 8 } \end{align*} \end{document}

Substituting Equations (5) and (7) into the governing Equation (8), we have \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} \Delta P \pi { \left( { \frac { D } { 2 } - h } \right) ^2 } = k \Delta { x_1 } + { \frac { 2 { k_2 } k } { k \Delta { s^2 } + 2 { k_2 } } } \Delta { x_1 } . \tag { 9 } \end{align*} \end{document}

By solving this equation numerically, we can get the relation between the input vacuum pressure ΔP and the bending angle α.

Experiments on bending angles at different pressures were conducted to validate the bending model. As before, four robots with different springs were employed in our experiment. The rear foot of the robot was fixed on the table, and only one VASA was actuated. The vacuum pressure was applied from 0 to 85 kPa, and pictures were taken at each 5 kPa step using a high-resolution camera (6D Mark II, Canon) after the bending angle was stabilized. The images were processed through software (Tracker, Open Source Physics) to output the bending angles. Three trials were performed for each robot. The results are shown in Figure 6.

FIG. 6.

Bending angle of the robot body as a function of the applied vacuum pressure. Four different VASAs of increasing spring constants (from Spring A to Spring D) are employed to measure the bending angles under different vacuum pressures. The square markers represent the experimental data, and the curve represents the theoretical result.

As shown in Figure 6, when subjected to vacuum pressure, the bending angle follows a similar trend as the linear deformation. It can be observed that VASA with smaller spring constant experiences larger bending angle under the same vacuum pressure due to the small restoring force generated by the spring. In addition, the gradient of bending angle for the same VASA also decreases when the vacuum pressure becomes higher due to fabric sagging effect. The maximum bending angle is around 61° when spring A is actuated with 85% vacuum. The large bending angle ensures the robot to achieve fast turning speed, which will be discussed later. The good agreement between the experimental and theoretical results demonstrates that the analytical model can accurately predict the bending performance of the robot body.

Speed optimization

There are many parameters that can affect the speed of the robot, for example, the input vacuum pressure, the properties of compression springs, and the actuation signals. As discussed earlier in Figure 4, larger vacuum pressure leads to larger deformation for VASA with smaller spring constant. Therefore, we adopt two Spring A and 87% vacuum for the soft robot to achieve larger linear speed. In this section, we mainly focus on optimizing the square actuation signal for larger linear speed. The square actuation signal contains two input variables, namely frequency and duty cycle. The frequency of the linear locomotion is the inverse of the period, which decides the actuation time in each cycle. Each period comprises two phases: loading and unloading phases. In the loading phase, the vacuum pressure is applied to actuate the body; the vacuum pressure is released for the body to elongate during the unloading phase. Duty cycle is defined as the percentage of the loading time in one period.

Step response

To find the optimized actuation frequency and duty cycle, it is important to know the step response of the robot body when subjected to a step signal. The same experimental setup for the static linear deformation was employed to study the step response of the robot body. Figure 7A shows the actuation signal used for the test. Ten trials were conducted for the robot body. The averaged step response curve of the body is plotted in Figure 7B. Since the error is very small, error bar is not shown here.

FIG. 7.

The step response of the robot body. (A) The step input signal starts at t = 2 s and ends at t = 12 s. (B) The deformation curve of the robot body under the actuation signal in (A). The two dashed lines represent the two equilibrium deformation states when the robot achieves steady locomotion.

As shown in Figure 7B, the full loading phase (rising) takes about 5 s to reach the maximum deformation and the unloading phase (dropping) takes about 8 s. Since most of the rising and dropping are accomplished within 2 s, it is not efficient for the robot to achieve fast speed if the actuation frequency is too small. Given a fixed frequency and duty cycle, the deformation of the robot body in the loading and unloading phases should be the same if steady locomotion is achieved, as denoted by the two dashed lines in Figure 7B. The intersection points between the two dashed lines and the step response curve represent the equilibrium deformation states in the loading and unloading phases. We define the maximum and minimum deformation of the robot during the steady locomotion to be y₁ and y₂, and the starting and ending time of the loading and unloading phases are t₁, t₂ and t₃, t₄, respectively. We further assume that the robot body follows the same loading/unloading curve in the step response during steady locomotion. Therefore, the loading (t_l) and unloading (t_u) time can be calculated as \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${t_2} - {t_1}$$ \end{document} and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${t_4} - {t_3}$$ \end{document} , respectively. The distance (L) traveled by the robot in one cycle is \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\;{y_2} - {y_1}$$ \end{document} . The frequency and duty cycle of the locomotion can then be represented as \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$f = 1 / \left( {{t_l} + {t_u}} \right)$$ \end{document} and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$DC = {t_l} / \left( {{t_l} + {t_u}} \right) = {t_l}*f$$ \end{document} , respectively. Finally, the average speed (v) of the robot can be calculated as \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${ \rm{ \;}}v = L*f$$ \end{document} . Therefore, we can derive the speed of the robot at a specific frequency and duty cycle if we know the maximum and minimum deformation y₁ and y₂ in steady locomotion.

To get y₁ and y₂, we first need to obtain empirical equations for the loading and unloading curves. By fitting the experimental data, the fitting functions for the loading and unloading curves can be obtained as shown in Supplementary Figure S2. Hence, the following equality needs to be satisfied in order for the robot to achieve steady locomotion. \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} {Y_l} \left( {{t_1}} \right) = {Y_u} \left( {{t_4}} \right) \tag{10} \end{align*} \end{document} \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} {Y_l} \left( {{t_2}} \right) = {Y_u} \left( {{t_3}} \right). \tag{11} \end{align*} \end{document}

Equations (10) and (11) can be solved numerically to obtain the speed of the robot. In our numerical solution, the frequency is limited from 0.1 to 2.0 Hz and the duty cycle ranges from 0% to 100%.

Two sets of experiments were conducted to verify the model. The first set of experiments fixed the actuation frequency to be 1 Hz and varied the duty cycle from 0% to 100%. The second set fixed the duty cycle to be 50% while changing the frequency from 0.1 to 2 Hz. In the experiments, the soft robot crawled on a flat wooden surface. Laser sensor was used to capture the crawling distance of the robot. The average speed of the robot was calculated over three steady continuous cycles during the locomotion. Figure 8 shows the speed of the robot at 1 Hz frequency and 50% duty cycle. It can be observed that the theoretical model can accurately predict the experimental results.

FIG. 8.

(A) The speed of the robot as a function of the duty cycle when the actuation frequency is fixed to be 1 Hz. (B) The speed of the robot as a function of the actuation frequency when the duty cycle is fixed to be 50%. The blue points represent the experimental data, and the black curve represents the theoretical result. (C) The speed of the robot as a function of the actuation frequency and duty cycle. Color images are available online.

As shown in Figure 8A, when frequency is fixed at 1 Hz, the speed first increases with the increasing duty cycle and then decreases to zero. In our experiment, the maximum speed achieved is 16.29 mm/s, and it happens when duty cycle equals 70%. The model predicts that the maximum speed at 1 Hz occurs when the duty cycle equals 66%, which is very close to the experimental observation. Figure 8B shows that when duty cycle is fixed at 50%, the speed increases as the frequency increases. The speed of the robot increases fairly rapidly when the frequency is below 1 Hz. After 1 Hz, the speed increases with a much slower pace. The reason is that when the frequency is small, the deformation of the body tends to cover a larger deformation range, which may include the small gradient region in Figure 7B, thus leading to a smaller gradient.

Despite the good prediction, the theoretical results are still slightly larger than the experimental results. The inaccuracy of the model mainly comes from two aspects. First, in our model, we assume that the adhesion feet can adhere to the surface instantly once activated. While in practice, the robot foot needs a very short time to establish the adhesion force due to the charging/discharging process.²² As a result, slight slippage occurs in the locomotion, which leads to a smaller speed compared with the theoretical result. Another aspect lies in that the deflation/inflation conversion process is ignored in the model, whereas in practice there is conversion time between deflation and inflation due to the air inertia.

Figure 8C is the color map of all frequency and duty cycle combinations within the specified ranges. From this color map, we can observe that when the duty cycle approaches to 0% or 100%, the robot speed approaches to zero no matter what the frequency is. This is because the extreme duty cycle limits the loading or unloading time to an extreme small value, which inevitably decreases the deformation of the body. In addition, the color map of the speed is not symmetrical about the 50% duty cycle line and larger speed concentrates in the region between 60% and 70% duty cycle. This can be attributed to the different loading and unloading characteristics of the robot body. As shown in Figure 7B, the absolute gradient of the unloading curve is slightly larger at higher actuation frequency compared with the loading curve, thus requiring less time to achieve the same deformation for the unloading process.

The analytical models developed in this section further enhanced our understanding on the working mechanism of the VASA. As derived from the model, compression springs with smaller spring constant could generate large actuation deformation, leading to fast linear and turning motion of the robot. In addition, the models also helped us to visualize the counterintuitive asymmetrical effects of the actuation signals on the locomotion speed. The good agreement of the predicted results with the experimental data also allows us to apply the models to design the actuation signals given the desired locomotion speed.

Capabilities of the Soft Crawling Robot

As discussed earlier, the soft robot is capable of both linear and turning locomotion, thus has the potential to navigate through obstacles in confined spaces. In addition, the use of electrostatic actuators not only ensures steady locomotion but also helps the robot to move on inclined surfaces. In this section, we will discuss the capabilities of the soft robot in terms of the fast turning, obstacle navigation, wall climbing, payload capability, and so on.

Turning

To characterize the turning performance, a turning signal with a frequency of 0.5 Hz and 87% vacuum was applied to the robot. The turning motion was then recorded with a high-resolution camera at 50 frames per second. The turning angle is defined as the angle between the edge of the front foot and the horizontal line as shown in the insets of Figure 9. By processing the video frames using Tracker, we extracted the turning angle of the robot with respect to time as shown in Figure 9. This experiment was conducted with four different actuation frequencies, and the results can be found in Supplementary Figure S3. It can be calculated that the maximum turning speed is around 15.09°/s when the actuation frequency is 0.5 Hz. In addition, the rotation center almost remains in the same place, which can be observed from Supplementary Movie S2. The small turning radius together with the fast turning speed empowers the soft crawling robot to work in confined spaces.

FIG. 9.

The experimental results of the turning angle as a function of time. The insets show representative images of the soft robot during the turning motion.

The overall turning speed of a soft crawling robot is the product of the effective turning angle in one cycle and the actuation frequency. For some crawling robots,^3,10,34,35 the turning angle generated in one cycle is quite large but can be adversely affected by slippage, which decreases the effective turning angle in one cycle. Moreover, the actuation frequency for these robots is also limited due to the slow cooling rate of SMA or the long response time of the pneumatic actuators. As a result, the turning speed is quite slow for these robots. While other crawling robots^21–23 have a higher actuation frequency, the small effective turning angle still limits their turning speed. In contrast, our soft crawling robot is one of the fastest in terms of turning speed (Table 1), owing to the use of electroadhesion to enhance the effective turning angle and the use of compression springs for the robot body to recover from deformation quickly.

Table 1.

A Comparison of the Average Turning Speed and Turning Radius of Different Soft Crawling Robots

Soft climbing robot	Tethered	Actuation method	BL (mm)	Turning speed (°/s)	Turning radius/BL
Our robot	Yes	Pneumatic	135	15.09	∼0.50
Tolley et al.³	No	Pneumatic	650	∼0.2	∼2.20
Zou et al.⁹	Yes	Pneumatic	154	∼1.63	∼0.42
Umedachi et al.¹⁰	Yes	SMA	85	2.9	∼2.10
Seok et al.³⁴	Yes	SMA	200	∼0.33	∼4.03
Cheng et al.³⁵	Yes	Cable	250	∼0.9	∼1.63
Kandhari et al.³⁶	Yes	Cable	∼1190	∼0.70	∼0.96
Qin et al.²¹	Yes	Dielectric elastomer	115	0.58	∼1.13
Cao et al.²²	Yes	Dielectric elastomer	100	∼0.3	∼1.6
Li et al.²³	Yes	Dielectric elastomer	40	∼11	4

BL, body length; SMA, shape memory alloy.

In addition to the turning speed, the turning radius to the body length ratio is also a good metric to quantify the turning performance of soft robots as smaller turning radius helps the robot to achieve obstacle avoidance even in confined spaces. Therefore, the smaller the ratio is, the better the turning performance of the robot has. As shown in Table 1, our soft robot has a turning radius to body length ratio of about 0.5, which is one of the best among other soft crawling robots. The main reason is that most of the soft crawling robots^{3,10,21–23,34–36} have the turning motion and the linear motion coupled together. Hence, the robot moves forward during turning motion, which leads to a large turning radius. Whereas the omnidirectional soft robot⁹ and our soft robot decouple the linear and turning motion and achieve a high turning radius to body length ratio. This extraordinary turning performance empowers our soft robot to avoid obstacles even in confined spaces.

Obstacle navigation

To demonstrate the mobility of the robot in confined spaces, we drove the robot to navigate through three obstacles by following a figure-of-eight path. The gap distance between two adjacent obstacles is 13.5 cm, which equals to the body length of the robot. Figure 10 shows the captured images of the robot at different time steps. The robot first rotates around the first obstacle anticlockwise and then changes its direction to rotate around the second obstacle clockwise. Finally, the robot returned to the starting position by rotating around the first obstacle anticlockwise again. Due to the fast locomotion speed, the robot managed to complete this task in 90 s. A video of this obstacle navigation is available in Supplementary Movie S3.

FIG. 10.

The soft robot navigates through three obstacles by following a figure-of-eight path. Color images are available online.

Wall climbing

Integrating electroadhesion with the VASAs not only enhances the locomotion efficiency but also endows the robot with the ability to move on inclined surfaces. The strong adhesion force helps the robot to overcome its self-weight and adhere to the inclined surface without falling. In addition, the design of the VASA is another crucial factor in the climbing motion. First, made of springs and fabric, the VASAs that account for most of the robot weight only weigh 21.2 g as shown in Supplementary Table S2. Second, the height of the VASA is limited to the outer diameter of the compression springs, which ensures that the robot height is <30 mm (Supplementary Table S2). Therefore, the center of gravity of the robot is close to the wall, which reduces the risk of falling during climbing. Experiments were conducted to study the relationship between the speed of the robot and the inclined angle. Due to the strong adhesion force, the speed of the robot drops slightly as the inclined angle increases as illustrated in Supplementary Figure S4.

We further challenged the robot with a vertical wall. With the same actuation signal in Figure 1C, the robot failed the vertical climbing task due to the lack of stable adhesion force during the signal transition process. To solve this problem, we programmed a small overlapping time between the actuation of the front and rear foot so that the feet can have enough time to establish stable adhesion force during the signal transition process. The overlapping time was set as 0.3 s through trial and error. Figure 11 shows the progression of the climbing robot on a wooden surface. The speed was measured to be 6.67 mm/s or 0.049 body length per second, which is 3.6 times faster than that of soft wall-climbing robot based on vacuum actuators.¹⁶ A video of this wall-climbing motion is available in Supplementary Movie S4.

FIG. 11.

The soft robot climbs on a vertical wall. The white dashed line indicates the starting position. Color images are available online.

Despite the fast climbing speed, the climbing performance of the current soft robot is still far behind some of the wall-climbing robots driven by motors, such as the flipping robot,³⁷ the Geckobot,²⁹ and the Mini-Whegs robot.³⁰ Therefore, our future plan is to improve the mobility of our robot from the aspects of structure design and enhancement of adhesion force. For example, inspired by the Mini-Whegs soft tape feet, we will try to reduce the thickness of our electrostatic actuators so that it can conform to inhomogeneous substrate geometries.

Payload

Robots are usually designed to perform some functions such as surveillance, search, and rescue, which inevitably require the robot to carry some equipment. Therefore, large payload is necessary for the robot in practical applications. We conducted experiments to study the payload capability of the robot. In this test, 87% vacuum pressure and 3 kV voltage were applied to the robot body and feet, respectively. Yellow weights were placed on the two feet evenly as shown in the inset of Figure 12. The same experimental setup in the speed optimization section was employed here to measure the speed of the robot under different payloads. We calculated the average speed of the robot over three continuous cycles to reduce the measurement error. Figure 12 shows the experimental results with an increasing payload at a step of 200 g. The corresponding locomotion speed drops as the payload increases (Fig. 12; Supplementary Movie S5). The decrease of the speed can be attributed to the increase of the friction force on the feet as the payload increases, which in turn limits the deformation of the robot body. The maximum payload achieved before the speed drops significantly is 3 kg, which is about 69 times its self-weight. The great payload capability reveals the potential for development of an untethered soft robot, which can achieve autonomous operations in practical applications.

FIG. 12.

The speed of the robot under different payloads.

Table 2 compared the payload capability of our robot with existing soft crawling robots. Two indicators, namely the payload to self-weight ratio and the locomotion speed under payload, are employed to quantify the payload capability. It is important to note that the self-weight of the robot only counts the weight of the robot, and the weight of the power source and control units are excluded in the calculation. As mentioned in the earlier discussion, the locomotion speed of the robot decreases as the payload increases, as shown in Figure 12. Hence, two payload-speed points of our soft robot are chosen for the comparison. As illustrated in Table 2, our soft robot has the largest payload to self-weight ratio compared with other soft crawling robots. Although the soft robot developed by Li et al.²³ has a higher locomotion speed than that of our robot under maximum payload, our soft robot is capable of even higher locomotion speed when the payload to self-weight ratio is at a similar level. The large payload to self-weight ratio of our robot mainly lies in the use of the VASA. Compared with other soft crawling robots based on electrical actuated polymers,^20–22 the VASA can generate much larger output force, leading to large payload.

Table 2.

A Comparison of the Payload and Speed Under Payload of Different Soft Crawling Robots

Soft climbing robot	Tethered	Actuation method	Payload (g)	Self-weight (g)	Payload/weight	Speed under payload (BL/s)
Our robot with 1 kg weight	Yes	Pneumatic	1000	43	2300%	0.0713
Our robot with 3 kg weight	Yes	Pneumatic	3000	43	6900%	0.0432
Tolley et al.³	No	Pneumatic	1200	3800	32%	0.0077
Li et al.²³	Yes	Dielectric elastomer	∼15	5	300%	∼0.05
Cao et al.²²	No	Dielectric elastomer	181	71.6	253%	0.02
Must et al.²⁰	No	IEAP	1.499	0.221	678%	0.015

IEAP, ionic electromechanically active polymer.

In addition to the investigation of the payload on flat surfaces, experiments are also performed to measure the payload capability of the soft robot on inclined surfaces. As shown in Supplementary Movie S6, the robot can carry a 20 g weight and climb on a 45° inclined surface. It should be noted that the payload capability of the robot on inclined surfaces is much smaller compared with that on the flat surface. The reason is that the payload on the inclined surfaces depends on the electrostatic force, which is much smaller than the output force of the robot body. Increasing the voltage could increase the adhesion force but at the cost of potential electrical breakdown. Therefore, increasing the adhesion force will be one of our key future research directions as it not only helps increase the mobility of the robot on the wall but also enhances the payload capability on the inclined surfaces.

In addition to the above mentioned capabilities, the robot could also cross a gap and kick a ball due to the fast recovery ability of its body (See Supplementary Data). More details can be found in Supplementary Fig. S5 and Supplementary Movies S7 and S8.

Conclusion and Future Work

In this article, we have demonstrated a versatile soft crawling robot capable of rapid and effective locomotion. The robot body, made of two VASAs, contracts in response to vacuum pressure and recovers to the original state quickly upon deactivation, which ensures a large deformation per actuation cycle. Meanwhile, the robot feet, made of two electrostatic actuators, can anchor on the attached surface without slippage to improve the locomotion efficiency. Therefore, the robot is able to achieve rapid linear motion and records one of the fastest turning speed to date among existing soft crawling robots. Moreover, our soft crawling robot also has five distinctive advantages compared with the existing soft crawling robots. (1) The robot works well in confined spaces with undesirable obstacles because of its small turning radius. (2) It can move in inclined even vertical surfaces due to the use of electroadhesion technology. (3) The robot is able to carry a payload of 69 times its self-weight on a horizontal surface, which reveals the potential of developing a fully autonomous soft robot. (4) The robot can function in more complex environments with gaps because of its deformable body and electrostatic feet. (5) The simple robotic structure facilitates the modeling of the robot locomotion, consequently reducing the difficulty in developing a control strategy for the robot. Therefore, this novel soft crawling robot can serve as a test bed for developing fully untethered and autonomous soft robots to perform effectively in unstructured environments.

Despite these impressive functionalities, the current soft robot still has many aspects that can be improved on. First, our current soft robot requires external wires and power source, which greatly limits its functionalities especially in practical applications. Hence, we plan to develop a fully untethered soft robot with the power source and control circuits on board. Second, the speed optimization for the robot is based on an empirical model developed by a data-driven method. To increase the generalizability of the modeling, we intend to develop an analytical model which takes the change in the air pressure of the robot body into account for analysis of the step response. Third, we plan to enhance the adhesion force and improve the mobility of our robot from the aspects of structure design.

Footnotes

Acknowledgments

This work is supported by MOE academic research grant (R-397-000-301-114) awarded to R.C.-H.Y, and MOE Tier 1 Singapore (R-265-000-609-114) and ASTAR Singapore (R-265-000-629-305) awarded to Z.J.

Author Disclosure Statement

No competing financial interests exist.

Supplementary Material

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Supplementary Material

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