3.1. Linear deformation

For linear deformation, both SPAs exhibit identical deformation under the same actuation pressure; hence, only one actuator is considered in this section to analyze the extension length $\Delta L$ upon air pressure $\Delta P$ . Figure 5(a) shows that the SPA is in the initial state before it is actuated by the high-pressure air shown by the dark blue area. The pressure of the low-pressure air shown by the light blue area in the cavity of the SPA is a standard air pressure ( ${P_0} \approx 0.1$ MPa). When the high-pressure air is supplied into the cavity, as shown in the dark blue box in Fig. 5(b), the volume of high-pressure air expands from ${V_1}$ to ${V_2}$ , and its pressure drops from ${P_1}$ to ${P_2}$ . Meanwhile, the expanded high-pressure air does work to the low-pressure air in the cavity, silicone cylinder, and spring. Therefore, as shown by the light blue box in Fig. 5(b), the volume of the low-pressure air is compressed from ${V_0}$ to ${V^{\prime}_2}$ , and its pressure rises from ${P_0}$ to $P^\prime_2 $ . The extension length of SPA is $\Delta L$ . If the energy dissipation in the process of actuating the SPA is ignored, according to the energy conservation law, the following relation can be obtained:

(1) \begin{equation}{W_1} = {W_0} + {W_2} + {W_3}\end{equation}

where ${W_1}$ is the work done by the expansion of the high-pressure air from initial state to extended state of SPA, ${W_0}$ is the energy absorbed by the compression of the low-pressure air from initial state to extended state of SPA, ${W_2}$ is the strain energy of the silicone cavity in the extended state, and ${W_3}$ is the elastic potential energy of the spring.

Figure 5. Schematic of the actuation state of SPA. (a) Initial state: the high-pressure air is not supplied into the cavity of SPA. (b) Actuated state: SPA is actuated by the high-pressure air.

We assume that the high-pressure air and low-pressure air in Fig. 5(a) are ideal gas. The expansion process of the high-pressure air and the compression process of the low-pressure air in Fig. 5(b) are adiabatic and isentropic. Therefore, the high-pressure air in expansion process and the low-pressure air in compression process satisfy the relation in Eqs. (2) and (3), respectively. Equations (2) and (3) are described as follows:

(2) \begin{equation}P{V^r} = {P_1}V_1^r = {P_2}V_2^r\end{equation}

and

(3) \begin{equation}{P^\prime }{V^\prime }^r = {P_0}V_0^r = P_2^\prime V{_2^{\prime r}}\end{equation}

where P and V are the pressure and volume, respectively, of the high-pressure air at any time during the expansion process, ${P_1}$ and ${V_1}$ are the pressure and volume, respectively, of the high-pressure air in the initial state, ${P_2}$ and ${V_2}$ are the pressure and volume, respectively, of the high-pressure air in the extended state, r is the polytropic coefficient which is a constant ( $r = 1.4$ ), ${P^\prime }$ and ${V^\prime }$ are the pressure and volume, respectively, of the low-pressure air at any time during the compression process, ${P_0}$ and ${V_0}$ are the pressure and volume, respectively, of the low-pressure air in the initial state, and $P^\prime_2 $ and $V^\prime_2 $ are the pressure and volume, respectively, of the low-pressure air in the extended state.

In the extended state shown in Fig. 5(b), the expanded high-pressure air and the compressed low-pressure air are in equilibrium in the cavity of SPA. Therefore, the following relation can be obtained:

(4) \begin{equation}{P_2} = P^\prime_2 \end{equation}

Furthermore, the work ${W_1}$ done by the expansion of the high-pressure air and the energy ${W_0}$ absorbed by the compression of the low-pressure air satisfy the relation in Eqs. (5) and (6), respectively. Equations (5) and (6) are described as follows:

(5) \begin{equation}{W_1} = \int_{{V_1}}^{{V_2}} {PdV} \end{equation}

And

(6) \begin{equation}{W_0} = \int_{V^\prime_2 }^{{V_0}} {{P^\prime }d{V^\prime }} \end{equation}

The volume relation between the expanded high-pressure air and compressed low-pressure in Fig. 5(b) is expressed as:

(7) \begin{equation}{V_2} = {V_0} + \frac{{{\pi}\!\Delta L{d^2}}}{4} - V^\prime_2 \end{equation}

where $\Delta L$ is the extension length of SPA in extended state and d is the inner diameter of the silicone cylinder.

Substituting Eqs. (2), (4), and (7) into Eq. (5), the work ${W_1}$ done by the expansion of the high-pressure air is expressed as:

(8) \begin{equation}{W_1} = \frac{{\left( {{P_2} - P_2^{\frac{1}{r}}P_1^{\frac{{r - 1}}{r}} - \left( {P_2^{\frac{{r - 1}}{r}} - P_1^{\frac{{r - 1}}{r}}} \right)\!P_0^{\frac{1}{r}}} \right)\!{V_0} + \dfrac{{{\pi}\!\Delta L{d^2}}}{4}\left( {{P_2} - P_2^{\frac{1}{r}}P_1^{\frac{{r - 1}}{r}}} \right)}}{{1 - r}}\end{equation}

Furthermore, substituting Eqs. (3) and (4) into Eq. (6), the energy ${W_0}$ absorbed by the compression of the low-pressure air is described as:

(9) \begin{equation}{W_0} = \frac{{\left( {{P_0} - P_0^{\frac{1}{r}}P_2^{\frac{{r - 1}}{r}}} \right)\!{V_0}}}{{1 - r}}\end{equation}

Because ${P_2}$ is the absolute pressure in the cavity of SPA in extended state, the relation between the relative pressure $\Delta P$ and the absolute pressure ${P_2}$ in the cavity is ${P_2} = \Delta P + {P_0}$ . Substituting this relation into Eqs. (8) and (9), respectively, ${W_1}$ and ${W_0}$ can be expressed as:

(10) \begin{align}{W_1} & = \frac{{\left( {\left( {\Delta P + {P_0}} \right) - {{\left( {\Delta P + {P_0}} \right)}^{\frac{1}{r}}}P_1^{\frac{{r - 1}}{r}} - \left( {{{\left( {\Delta P + {P_0}} \right)}^{\frac{{r - 1}}{r}}} - P_1^{\frac{{r - 1}}{r}}} \right)\!P_0^{\frac{1}{r}}} \right)\!{V_0}}}{{1 - r}}\nonumber\\[4pt] & \quad + \frac{{\dfrac{{{\pi}\Delta L{d^2}}}{4}\left( {\left( {\Delta P + {P_0}} \right) - {{\left( {\Delta P + {P_0}} \right)}^{\frac{1}{r}}}P_1^{\frac{{r - 1}}{r}}} \right)}}{{1 - r}}\end{align}

and

(11) \begin{equation}{W_0} = \frac{{\left( {{P_0} - {{\left( {\Delta P + {P_0}} \right)}^{\frac{{r - 1}}{r}}}P_0^{\frac{1}{r}}} \right)\!{V_0}}}{{1 - r}}\end{equation}

In addition to compressing the low-pressure air, the expansion of the high-pressure air also drives SPA to extend in Fig. 5(b). Therefore, part of the work done by the expansion of the high-pressure air is converted into the strain energy ${W_2}$ of the cylindrical silicone wall and the elastic potential energy ${W_3}$ of the spring. The strain energy ${W_2}$ of the silicone wall satisfies the following relation:

(12) \begin{equation}{W_2} = W{V_s}\end{equation}

where W is the volumetric energy density of the silicone rubber and ${V_s}$ is the volume of the silicone wall which can be expressed as:

(13) \begin{equation}{V_s} = \frac{{\pi \!\left( {{D^2} - {d^2}} \right)\!l}}{4}\end{equation}

where D and d are the outer diameter and inner diameter, respectively, of the silicone cylinder and l is the length of the cavity of SPA.

Mooney–Rivilin model is often used to predict the nonlinear and large deformation of the silicone rubber. [Reference Marechal, Balland, Lindenroth, Petrou, Kontovounisios and Bello35] Here, we used this model to calculate the volumetric energy density W of the silicone rubber. The Mooney–Rivilin model is given as:

(14) \begin{equation}W = {C_{10}}\!\left( {{I_1} - 3} \right) + {C_{01}}\!\left( {{I_2} - 3} \right)\end{equation}

where ${C_{10}}$ and ${C_{01}}$ are the material constants with the value of 0.1064 and 0.0019 MPa, respectively, which were measured by a tensile test (ZQ-1000, China). ${I_1}$ and ${I_2}$ are the first and second principal invariants of the Cauchy–Green strain tensor, which can be expressed as:

(15) \begin{align}\left\{ \begin{array}{l}{I_1} = \lambda _r^2 + \lambda _\theta ^2 + \lambda _a^2\\[4pt]{I_2} = \lambda _r^2\lambda _\theta ^2 + \lambda _\theta ^2\lambda _a^2 + \lambda _a^2\lambda _r^2\end{array} \right.\end{align}

where ${\lambda _r}$ , ${\lambda _\theta }$ , and ${\lambda _a}$ are the radial elongation ratio, circumferential elongation ratio and axial elongation ratio, respectively, of the silicone wall.

While SPA is actuated by the high-pressure air, the spring wound on the outer wall of the silicone cylinder restrains its radial expansion. Therefore, the outer diameter D of the silicone cylinder remains unchanged. However, the inner diameter of the silicone cylinder increases with the increase of the extension length.

As shown in Fig. 5(a) and (b), when the length of the cylindrical silicone wall is extended from l to $l + \Delta L$ , the inner diameter of the silicone cylinder increases from d to ${d^\prime }$ . The red dash circles shown in the section views of Fig. 5(a) and (b) represent the middle layer of the silicone wall in the initial state and extended state, respectively. Because the thickness (t=2 mm) of the silicone wall in the initial state is much smaller than the outer diameter (D=20 mm) of the silicone cylinder, we regard the circumferential elongation ratio of the middle layer as the circumferential elongation ratio of the silicone wall during the extension of SPA. Then, the thickness change ratio and length change ratio of the silicone wall can be considered as the radial elongation ratio and axial elongation ratio of the silicone wall, respectively. Therefore, the radial elongation ratio ${\lambda _r}$ , circumferential elongation ratio ${\lambda _\theta }$ , and axial elongation ratio ${\lambda _a}$ of the silicone wall in the extended state shown in Fig. 5(b) can be expressed as:

(16) \begin{align}\left\{ \begin{array}{l}{\lambda _r} = \dfrac{{D - {d^\prime }}}{{D - d}}\\[11pt]{\lambda _\theta } = \dfrac{{\pi d^\prime_m }}{{\pi {d_m}}} = \dfrac{{D + {d^\prime }}}{{D + d}}\\[13pt]{\lambda _a} = \dfrac{{{l_1}}}{l} = \dfrac{{l + \Delta L}}{l}\end{array} \right.\end{align}

where ${d_m}$ and $d^\prime_m $ are the diameters of the middle layer in the initial state and extended state, respectively. According to the incompressibility of the silicone rubber, we have the following relation:

(17) \begin{equation}{\lambda _r}{\lambda _\theta }{\lambda _a} = 1\end{equation}

Substituting Eqs. (13), (14), (15), (16), and (17) into Eq. (12), the strain energy ${W_2}$ of the silicone wall in the extended state can be obtained:

(18) \begin{equation}{W_2} = \frac{{\pi {C_{10}}\!\left( {{D^2} - {d^2}} \right)}}{4}\left( {\frac{{2{l^2}}}{{l + \Delta L}} + \frac{{{{\left( {l + \Delta L} \right)}^2}}}{l} - 3} \right) + \frac{{\pi {C_{01}}\!\left( {{D^2} - {d^2}} \right)}}{4}\left( {\frac{{{l^3}}}{{{{\left( {l + \Delta L} \right)}^2}}} + 2\!\left( {l + \Delta L} \right) - 3} \right)\end{equation}

Furthermore, the elastic potential energy ${W_3}$ of the spring under the extension length $\Delta L$ can be expressed as:

(19) \begin{equation}{W_3} = \frac{{k\Delta {L^2}}}{2}\end{equation}

where k is the stiffness coefficient of the metal spring with a value of 50 N/m, which was measured by a tensile test (ZQ-100, China).

Substituting Eqs. (10), (11), (18), and (19) into Eq. (1), the relation between the extension length $\Delta L$ of SPA and the pressure $\Delta P$ in the cavity of the silicone cylinder can be obtained:

(20) \begin{align}& \frac{{\left( {\Delta P + \left( {P_0^{\frac{1}{r}} - {{\left( {\Delta P + {P_0}} \right)}^{\frac{1}{r}}}} \right)\!P_1^{\frac{{r - 1}}{r}}} \right)\!{V_0} + \dfrac{{\pi\!\Delta L{d^2}}}{4}\!\left( {\left( {\Delta P + {P_0}} \right) - {{\left( {\Delta P + {P_0}} \right)}^{\frac{1}{r}}}P_1^{\frac{{r - 1}}{r}}} \right)}}{{1 - r}} - \frac{1}{2}k\Delta {L^2} \nonumber\\& \!\!\!\!\!\quad - \frac{{\pi {C_{10}}\!\left( {{D^2} - {d^2}} \right)}}{4}\!\left( {\frac{{2{l^2}}}{{l + \Delta L}} + \frac{{{{\left( {l + \Delta L} \right)}^2}}}{l} - 3} \right) + \frac{{\pi {C_{01}}\!\left( {{D^2} - {d^2}} \right)}}{4}\left( {\frac{{{l^3}}}{{{{\left( {l + \Delta L} \right)}^2}}} + 2\left( {l + \Delta L} \right) - 3} \right) = 0\end{align}

To verify the analytical model of the linear deformation of SPA, we conducted experiments to measure the extension length $\Delta L$ at different pressures $\Delta P$ . The experimental setup is shown in Fig. 6(a). SPA was fixed on the optical platform by a support frame fabricated by 3D printing. The extension length $\Delta L$ of SPA was measured by a digital laser displacement sensor (BL-100N, BOJKE) located on the left side of SPA. The pressure $\Delta P$ of the compressed air supplied by an air compressor was adjusted by a digital pressure reducing valve (IR2000, Atuosi). To prevent the burst of SPA, a pretest has been carried out to determine that the maximum pressure supplied to SPA is 0.2 MPa. The pressure was supplied to SPA from 0 to 0.2 MPa with a step size of 0.01 MPa. Ten trials were conducted under the same conditions to confirm the repeatability. The average measurement results are plotted in Fig. 6(b).

Figure 6. Measurement of the extension length of SPA under different pressures. (a) Experimental apparatus used in the measurement. (b) Comparison between the theoretical and experimental results for the extension length of SPA under different pressures.

Figure 6(b) shows the comparison between the theoretical (black line) and experimental (red circles) results for the extension length at different pressures. The error bar represents the standard deviation of 10 measurements of the extension length at each pressure. With the increase of pressure, the theoretical extension length and experimental extension length both show a nonlinear increasing trend because of the nonlinear deformation of the silicone rubber. It is clear that the maximum extension length of SPA is 19.74 mm at the pressure of 0.2 MPa. The theoretical results agree well with the experimental results. However, the discrepancy between the theoretical result and the experimental result increases with the increase of the pressure. There are two main reasons: (1) there is energy dissipation during the extension of SPA actuated by the high-pressure air, which increases with the increase of the pressure, and (2) the thickness of the silicone wall casting in the lab is not completely uniform, which leads to slight bending deformation during the extension of SPA, and the bending deformation of SPA increases with the increase of the pressure.

3.2. Bending deformation

As described in Section 2.2, when only one SPA is actuated, this SPA will bend due to the constraint of another SPA, which drives SRWCR to turn. As shown in Fig. 7(a), the actuated left SPA bends an angle $\alpha $ to the right due to the constraint of the right SPA. Meanwhile, the right SPA is forced to bend the same angle to the right by the left SPA. Because the right SPA is only forced to bend and is not actuated by the high-pressure air, we consider the length of the centerline of the right SPA remains unchanged. The length of the centerline of the left SPA is ${L_1}$ . From Fig. 7(a), the following geometric relation can be obtained:

(21) \begin{equation}\frac{{{L_1} - L}}{\alpha } = \Delta s\end{equation}

where $\Delta s$ is the distance between the centerlines of the two SPAs. In addition, we assume that the previous relation for linear deformation still holds during bending motion. Then, we know that ${L_1} = L + \Delta L$ , where $\Delta L$ is the extension length of the centerline of the left SPA under the pressure of $\Delta P$ . By substituting this relation into Eq. (21), we have

(22) \begin{equation}\Delta L = \alpha \Delta s\end{equation}

Figure 7. Measurement of the bending deformation of SPA. (a) Schematic of the bending deformation of SPA. (b) Comparison between the theoretical and experimental results for the bending angle of SPA under different pressures.

Substituting Eq. (22) into Eq. (20), the relation between the bending angle $\alpha $ and the input pressure $\Delta P$ can be expressed as:

(23) \begin{align}& \frac{{\left( {\Delta P + \left( {P_0^{\frac{1}{r}} - {{\left( {\Delta P + {P_0}} \right)}^{\frac{1}{r}}}} \right)\!P_1^{\frac{{r - 1}}{r}}} \right)\!{V_0} + \dfrac{{\pi\! \Delta L{d^2}}}{4}\!\left( {\left( {\Delta P + {P_0}} \right) - {{\left( {\Delta P + {P_0}} \right)}^{\frac{1}{r}}}P_1^{\frac{{r - 1}}{r}}} \right)}}{{1 - r}} - \frac{1}{2}k{\alpha ^2}\Delta {s^2} \nonumber\\& - \frac{{\pi {C_{10}}\!\left( {{D^2} - {d^2}} \right)}}{4}\left( {\frac{{2{l^2}}}{{l + \alpha \Delta s}} + \frac{{{{\left( {l + \alpha \Delta s} \right)}^2}}}{l} - 3} \right) + \frac{{\pi {C_{01}}\!\left( {{D^2} - {d^2}} \right)}}{4}\left( {\frac{{{l^3}}}{{{{\left( {l + \alpha \Delta s} \right)}^2}}} + 2\left( {l + \alpha \Delta s} \right) - 3} \right) = 0\end{align}

Experiment on bending angles at different pressures was conducted to validate the bending model. The two rear wheels were braked by the two rear ASBs, and the left SPA was actuated. The pressure was applied from 0 to 0.2 MPa with a step size of 0.01 MPa. At each pressure, the bending angle was obtained using image analysis software (Image J, National Institute of Health, MD). Ten trials were conducted under the same conditions to confirm the repeatability. The average results are shown in Fig. 7(b).

Figure 7(b) shows the comparison between the theoretical (black line) and experimental (red circles) results for the bending angle at different pressures. The error bar represents the standard deviation of 10 measurements of the bending angle at each pressure. It is obvious that the maximum bending angle of SPA is 33.79° at the pressure of 0.2 MPa. In addition, with the increase of the pressure, the increasing trend of the theoretical bending angle is consistent with that of the experimental bending angle. However, the discrepancy between the theoretical result and the experimental result increases with the increase of the pressure. The main reason is that because of the constraint of the unactuated SPA, the extension length of the centerline of the actuated SPA in the experiment is less than the theoretical value, and the discrepancy between them increases with the increase of the pressure.

4.1. Measurement of the actuation period

We take the linear motion of SRWCR as an example to analyze the actuation period of SRWCR. Because the actuation sequence of the linear motion involves four steps shown in Fig. 3(a), the actuation period is equal to the total time taken to achieve the four steps. As shown in Fig. 8, the actuation period T of the linear motion can be obtained:

(24) \begin{equation}T = 2{T_1} + {T_2} + {T_3}\end{equation}

where ${T_1}$ is the braking time taken by ASB to brake the wheel, and ${T_2}$ and ${T_3}$ are the extension time and contraction time of SPA, respectively.

Figure 8. Schematic of the actuation period for the linear motion of SRWCR. The actuation period includes the braking time of the two front wheels and the two rear wheels, as well as the extension time and contraction time of the two SPAs.

An experiment has been conducted to measure the extension time ${T_2}$ and contraction time ${T_3}$ of SPA. The experimental setup is shown in Fig. 9(a). The SPA was fixed on the optical platform by a support frame fabricated by 3D printing. The extension length $\Delta L$ of the SPA was measured by a digital laser displacement sensor (BL-100N, BOJKE), and the data were collected with a sampling frequency of 100 Hz through a data acquisition device (USB-6002, National Instrument). The compressed air was supplied into SPA by connecting a digital pressure reducing valve and a solenoid valve in turn through flexible air tubes. The solenoid valve used as the actuation switch of SPA was controlled by an Arduino controller (Arduino Nano). Before the experiment, the pressure of the compressed air was adjusted to 0.2 MPa by the digital pressure reducing valve. Then, the solenoid valve was opened under the control of the Arduino controller, and SPA began to extend. After the solenoid valve was opened for 1.5 s which is much longer than the extension time of SPA, the solenoid valve was closed, and SPA began to contract. The extension length of SPA during the extension and contraction processes were recorded by the data acquisition device. Three trials were conducted under the same conditions to confirm the repeatability. The average measurement results are plotted in Fig. 9(b). The full extension phase (rising) between the two blue dash line takes about 0.4 s to reach the maximum extension length, and the contraction phase (dropping) between the two red dash line takes about 0.5 s. Therefore, the extension time ${T_2}$ and contraction time ${T_3}$ of SPA are 0.4 and 0.5 s, respectively.

Figure 9. Measurement of the extension time and contraction time of SRWCR. (a) Measuring device for the extension time and contraction time of SRWCR. (b) The deformation curve of SPA actuated by the pressure of 0.2 MPa. The extension phase between the two blue dash line takes about 0.4 s. The contraction phase between the two red dash line takes about 0.5 s.

Before measuring the braking time of ASB, to prevent ASB from bursting due to the excessive pressure, the safety pressure supplied to ASB has been measured which is 0.08 MPa. Then, the same experimental setup shown in Fig. 2 was employed to determine the braking time of ASB. The pressures supplied to ASB and SPAs were adjusted to 0.08 and 0.2 MPa, respectively. The two rear wheels were braked by the corresponding ASBs. Then, after a delay, the two SPAs were extended simultaneously. If the two rear wheels could not move backward during the extension of SPAs, we considered that they were fully braked. The experimental result indicates that when the delay time is $ \ge 0.15$ s, the two rear wheels can be fully braked. Therefore, the braking time of ASB is 0.15 s. Substituting the braking time ${T_1}$ , extension time ${T_2}$ , and contraction time ${T_3}$ into Eq. (24), the actuation period of SRWCR (T=1.2 s) can be obtained.

4.2. Measurement of the linear speed

The same experimental setup shown in Fig. 2 was employed to measure the linear speed of SRWCR crawling on the flat ground. The pressures supplied to SPAs and ASBs were adjusted to 0.2 and 0.08 Mpa, respectively, by the two digital pressure reducing valves. The braking time of ASB and the extension time and contraction time of SPA were set to 0.15, 0.4, and 0.5 s, respectively, to ensure that the actuation period of SRWCR is 1.2 s. SRWCR crawled from the green start line to the red finish line with a crawling distance of 500 mm. The linear crawling process shown in Supplementary Movie S3 was recorded by a camera. Figure 10(a) shows the snapshots of the linear crawling process. Three trials were conducted under the same conditions to calculate the average crawling speed. The experimental results show that the average linear speed of SRWCR is 14.97 mm/s.

Figure 10. Measurement of the motion speed of SRWCR. (a) The image snapshots of the linear speed measurement of SRWCR. (b) The image snapshots of the underwater locomotion process of SRWCR. (c) The image snapshots of the turning speed measurement of SRWCR.

In addition to moving in the air, the intrinsic waterproof of SPAs and ASBs allows SRWCR to move underwater. Except for moving at the bottom of a glass water tank, the measurement experiments of the linear speed of SRWCR moving underwater and in the air have the same experimental configuration. The underwater crawling process of SRWCR shown in Supplementary Movie S4 was recorded by a camera. Figure 10(b) shows the snapshots of the underwater crawling process. Three trials were conducted under the same conditions to calculate the average underwater crawling speed. The experimental results show that the average underwater linear speed of SRWCR is 13 mm/s, which is smaller than the linear speed in the air due to the resistance of water.

4.3. Measurement of the turning speed

In addition to measuring the linear speed, we have conducted an experiment to measure the turning speed of SRWCR. The experimental setup is the same as the experimental setup shown in Fig. 2. Similar to the linear speed measurement experiment, the pressures supplied to SPAs and ASBs were adjusted to 0.2 and 0.08 MPa, respectively, and the actuation period of SRWCR was set to 1.2 s. SRWCR started from the green start line and turned clockwise to return to the green start line. The turning process of SRWCR shown in Supplementary Movie S5 was recorded by a camera. Figure 10(c) shows the snapshots of the turning process. Three trials were conducted under the same conditions to calculate the average crawling time. The experimental results show that the average crawling time is 64 s, and the turning speed of the SRWCR is 5.63°/s. In addition, the rotation center almost remains in the same place, which can be observed from Supplementary Movie S5, and the turning diameter of SRWCR is about 150 mm.

Table II shows a comparison of the performance of our robot with existing soft crawling robots. Among the crawling robots in Table II, only the robot developed by Qin et al. [Reference Qin, Liang, Huang, Chui, Yeow and Zhu19] has a larger linear speed and turning speed than our robot, which demonstrates that our robot has excellent locomotion performance. In addition, only our robot has the underwater locomotion capability. This capability mainly lies in the waterproof of SPAs and ASBs of our robot. The underwater locomotion capability also indicates the potential advantage of our robot in the design of highly efficient underwater robots, such as underwater sampling robots, underwater monitoring robots, and underwater archaeological robots.

Table II. Comparison of the performance of our robot with existing soft crawling robots.

5.1. 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, a large payload is necessary for the robot in practical applications.

We conducted experiments to study the payload capability of the robot. The same experimental setup in Fig. 2 was employed here to measure the speed of the robot under different payloads. The pressures supplied to SPAs and ASBs were adjusted to 0.2 and 0.08 MPa, respectively. The actuation period of SRWCR was set to 1.2 s. The customized lead blocks with a mass of 100 g as a payload were evenly placed in the rigid head and tail of SRWCR, as shown in the inset of Fig. 11. The payload was increased at a step of 200 g. At each payload, SRWCR crawled from the green start line to the red finish line with a distance of 500 mm. Three trials were conducted under the same conditions to calculate the average crawling speed of SRWCR to reduce the measurement error. When the payload increased to 2 kg, because there was no extra space in the rigid head and tail to place more lead blocks, the payload could not continue to increase. Supplementary Movie S6 shows the crawling process at the payload of 2 kg. The experimental results are shown in Fig. 11.

As shown in Fig. 11, the crawling speed of SRWCR decreases with the increase of the payload. There are two main reasons: (1) the friction forces between the wheels and the ground increase as the payload increases, which limits the deformation of the two SPAs, and (2) because the centers of gravity of the rigid head and tail are not in the same plane as the axes of the two SPAs, after SPAs are extended, the rigid head and tail turn around the corresponding wheel shafts to bend SPAs, which reduces the extension length of SPAs and can be observed in Supplementary Movie S6. The bending angle of SPAs increases with the increase of the payload. In addition, when the payload increases to 2 kg, the crawling speed decreases to 11.18 mm/s, which indicates that the payload of SRWCR is far from the maximum. The great payload capability reveals the potential for the development of an untethered crawling robot, which can achieve autonomous operations in practical applications.

Figure 11. The speed of SRWCR under different payloads.

Table III compared the payload capability of our robot with existing soft crawling robots. It is shown that only the soft crawling robots developed by Qin et al. [Reference Qin, Liang, Huang, Chui, Yeow and Zhu19] can reach the payload of 2 kg. However, our robot has a higher crawling speed under this payload. In addition, compared with other soft crawling robots shown in Table III, our robot not only has the largest payload but also has the largest crawling speed under the corresponding payload, which demonstrates the large payload capability of our robot. The large payload capability of our robot mainly lies in the use of the soft-rigid body. Compared with the purely soft crawling robots, the soft-rigid body of our robot can carry a larger weight without deformation which may cause the robot to fail.

Table III. Comparison of the payload capability of our robot with existing soft crawling robots.

5.2. Passing capability

In addition to moving on flat ground discussed earlier, functional robots such as inspection robots, rescue robots, and search robots often need to pass through some complex grounds such as grass ground, sand ground, mud ground, speed bump, and inclined surface. Therefore, the robot should have a high passing capability to achieve different functions.

To demonstrate the capability of SRWCR to pass through the complex grounds, a variety of complex grounds were built in Fig. 12. As shown in Fig. 12(a)–(c), the turf, sand, and mud were spread on the rectangular planks to build grass ground, sand ground, and mud ground, respectively. Two speed bumps fabricated by 3D printing were glued on the planks in Fig. 12(d). Besides, a 30° inclined surface was fixed on the planks in Fig. 12(e). Then, we conducted experiments to verify that SRWCR could crawl through the complex grounds shown in Fig. 12. The experimental setup is the same as the experimental setup shown in Fig. 2. The pressures supplied to SPAs and ASBs were adjusted to 0.2 and 0.08 MPa, respectively. The actuation period of SRWCR was set to 1.2 s. The crawling processes of SRWCR on the complex ground were recorded by a camera (Supplementary Movies S7 and S8). The snapshots of the crawling processes on the complex ground are shown in Fig. 13. The experimental results show that SRWCR can crawl through not only the flat ground but also the grass ground, sand ground, mud ground, and speed bump, as shown in Fig. 13(a)–(d). In addition, SRWCR can crawl on a 30° inclined surface, as shown in Fig. 13(e).

Figure 12. Construction of a variety of complex grounds, including (a) grass ground, (b) sand ground, (c) mud ground, (d) speed bump, and (e) inclined surface.

Figure 13. The image snapshots of SRWCR crawling through a variety of complex grounds, including (a) grass ground, (b) sand ground, (c) mud ground, (d) speed bump, and (e) inclined surface.

In addition to crawling through the single complex ground, another experiment has been carried out to verify that SRWCR can crawl through various complex ground simultaneously. As shown in Fig. 14, a mixed complex ground has been built by connecting grass ground, sand ground, mud ground, and speed bump in sequence. Supplementary Movie S9 shows the crawling processes of SRWCR on the mixed complex ground. The snapshots of the crawling processes on the mixed complex ground are shown in Fig. 15. The experimental result shows that SRWCR can easily crawl through the mixed complex ground. The crawling test of SRWCR on the single complex grounds and mixed complex ground proves the high passing capability of SRWCR.

Figure 14. Connecting the grass ground, sand ground, mud ground, and speed bump to construct a mixed complex ground.

Figure 15. The image snapshots of SRWCR crawling through the mix complex ground.

Table IV shows a comparison of the passing capability of soft crawling robots. As shown in Table IV, only our robot is able to crawl through a variety of complex ground such as the grass ground, sand ground, mud ground, speed bump, and inclined surface. Also, only our robot can crawl through the mixed complex ground described earlier. Compared with the soft crawling robot in Table IV, the use of wheels as the feet of our robot greatly improves the passing capability of our robot. Benefit from the high passing capability, our robot also has high environmental adaptability, which makes it have high potential to be used as the functional robots such as the search and rescue robot.

Table IV. Comparison of the passing capability of our robot with existing soft crawling robots.

5.3. Obstacle navigation

To demonstrate the mobility of the robot in confined spaces, we drove SRWCR to navigate through three obstacles by following a figure-of-eight path. The gap distance between two adjacent obstacles is 150 mm, which equals the turning diameter of SRWCR. Figure 16 shows the captured images of the robot at different time steps. SRWCR first rotates around the first obstacle anticlockwise and then changes its direction to rotate around the second obstacle clockwise. Finally, SRWCR returned to the starting position by rotating around the first obstacle anticlockwise again. Due to the fast movement speed, SRWCR managed to complete this task in 129 s. A video of this obstacle navigation is available in Supplementary Movie S10.

Figure 16. SRWCR navigates through two obstacles by following a figure-of-eight path.