The robot feet are inspired by the physical and behavioral attributes of an inchworm’s legs. An inchworm performs locomotion in highly complex terrains using its legs and flexible body (Wang et al., 2014). Inchworm locomotion is based on anchoring to a surface using its legs to grip, and then looping the body as it crawls. Legs on both ends of the body grip the surface while the body elongates to move in a certain direction. An overview of the inchworm movement is shown in Figure 1, where it crawls from one end of the round plant-branch by developing tension-based contraction and elongation of the body. While this movement looks relatively simple, it raises various questions, requiring a thorough understanding of the underlying morphological complexity during the crawling behavior of the inchworm. For clarity, this can be divided into two parts:

a) The morphology and movement-behavior of the flexible inchworm body.

The flexible body of an inchworm is composed of soft muscle fibers. Once these longitudinal muscle fibers contract, the inchworm deforms by bending and shortening in length (Han et al., 2017; Zhang et al., 2019; Jiang et al., 2020). The inchworm-legs are foot-like adaptive organs, helping the inchworm to anchor onto a surface. Accordingly, the robot-foot design is inspired from the flexible structure and movement of the inchworm-legs and shows similar adaptation to various curved surfaces (hence, different diameter industrial metal pipes). Overall, we apply the following insights to further develop the robot feet.

1. An inchworm relies heavily on its legs to grip a surface, exerting continuous surface-compliance due to the flexible nature of the worm-body. Thus, the robot design must include a strong surface-adhesion mechanism as well as adaptive characteristics.

We considered the above two aspects when developing an inchworm leg-inspired robot foot. The different elements of robot development are presented in the following section.

The robot (Figure 1B) has five degrees of freedom (DOF) to perform unidirectional crawling. Each DOF is configured by a servo motor (Dynamixel XM430-W350-R). The joining assemblies are 3D printed using ABS and PLA thermoplastics. The end-to-end body length of the robot is 56 cm, with a body width of 4 cm. The robot weighs 1.53 kg, powered by a 3-cell LiPo battery (12 V, 3,000 mAh). Four sensors are mounted on the robot: a Hall sensor in each robot foot, a current sensor (ACS712, 20 A), and an infrared (IR) distance sensor at one end. The robot is an improved version of the previously developed robot reported in (Khan et al., 2020). Table 1 shows a comparison of different specifications of both versions of the robot.

The robot is designed to crawl on metal pipes of different diameters. This is the main reason we chose a magnetic adhesion method for the robot since it provides strong attachment to metal pipes. The foot consists of an electromagnet (5.3 W, 470 N, 12 V) and a Hall sensor. We call this version “the flat robot feet” (Figure 2A) since it was the first version of the robot feet which could allow the robot to crawl on flat metal surfaces. The robot feet with the curved rigid foot-toes and soft foot-toes (also here referred to as rigid toes (Figure 2B) and soft toes (Figure 2C), respectively) utilize the same hardware. However, on the metal pipes, the robot with the flat foot immediately failed to crawl since the magnets could not attach properly to the curved pipes. Figure 3 shows the robot feet deviation from a centerline on a pipe. The flat electromagnetic feet easily slip from a centerline - which defines the robot stability on a pipe. This limits the flat foot to a specific pipe diameter.

Accordingly, as the improved foot-toe design is inspired by the structure of an inchworm’s legs, a curved foot-toe (Figure 2B) design was proposed. It was 3D printed using PLA thermoplastic material. The foot-toe was mounted underneath the electromagnet such that its concave curve induced a full-face grip to the convex pipe curve. The use of the foot-toe proved to be a suitable solution (Khan et al., 2020), increasing the practicality of the earlier flat feet. However, due to its rigid nature, robot stability could only be achieved on a few of the metal pipes.

To address the issue of rigidity, we further investigated another foot-toe design with the aim of creating a versatile pipe crawling robot. Instead of plastic rigid toe, a soft toe was developed. The use of silicone elastomers is common nowadays to fabricate such a soft toe. However, recognizing the importance of suitable silicone elastomer, various elastomers were considered. Table 2 (please see at the end of the paper) provides an overview of potential choices of elastomers. Based on the FEA and the final shape of the soft toe (discussed later), Ecoflex 00-20 (SmoothOn Inc., United States) was chosen to fabricate the soft toe. Instead of being too soft or too stiff under given toe size, this elastomer avoided the restricted adaptation and enabled the foot-toe to adapt to any surface. To obtain sufficient stiffness, instead of using higher-stiffness thermoplastics with limited elastic profile (Khan et al., 2019), stiffness was achieved by ensuring the appropriate toe thickness. The process to obtain the necessary toe thickness is described next.

The toe dimensions were set following the practical design parameters. The dimensions of the toe and its cavity were based on employment of the magnet size (fixed), and the minimum diameter of the pipe on which the robot is required to crawl. For instance, if the robot crawls on a metal pipe with a diameter of 12 cm, the curved cavity must fully attach full face to the surface while inserting its maximum effective adhesion. This ensures that the robot’s feet exert the maximum grip onto a surface. Figure 4 shows the shape of soft toe in more details. In contrast to fixed-width rigid toe, the total diameter D of the soft toe changes to D′ with shrinkage of the symmetric silicone toe width w_o upon attachment to different sizes of pipe. The magnet dimensions are fixed (D_o, L_o). The outer diameter (D) adds to the required stiffness for the robot foot to stay in form. The toe width w_o formed by the silicone between the inner (D_o) and outer diameter (D) was sufficient to stop undesired foot-deformation. The overall toe thickness was set such that the total toe contact surface area A is maximum. Increasing A results in increasing the elastomer’s inherent friction (see Discussion section).

The foot-toe was mounted around the electromagnet such that the magnet continued its exposure to the attachment surface. Meanwhile, the foot-toe prevented the robot feet from becoming imbalanced on the curved pipes. Having found these insights, we conducted FEA on both rigid and soft foot-toes, as detailed in the following section.

The robot foot lands on a surface by the toe first making contact. The stresses needed to be analyzed since the robot’s own body weight or the electromagnet could exert a strong force on the toe during magnet-attachment. The analysis would ensure that the chosen materials and geometry possessed the necessary compliance and safety under these conditions (Khan and Smithmaitrie 2018). Both the rigid and soft toe designs were analyzed under real-world-like loading conditions, based on the magnet pull up test conducted earlier (Khan et al., 2020). The maximum effective adhesion (approximately 125 N) produced by the electromagnet while fully attached to a metal surface was less than the manufacturer’s rating of 470 N. Thus, 470 N was chosen as the maximum normal force acting on the toe. Additional 100, 200 and 300 N loads were incrementally used to record the material response under the loading condition in the FEA implemented using the Creo Simulation software (Creo Simulation, PTC, United States). PLA thermoplastic material was assigned to the rigid toe using a linear model, whereas the silicone elastomer was assigned to the soft toe. A hyperplastic Mooney-Rivlin model was used to create the nonlinear properties of the material (Manti et al., 2015). The bottom of the foot-toe was constrained as a fixed point (boundary condition) to set the ground contact to properly analyze the normal force on the toe acting from the top (the load). By applying the Automatic Geometric Element Mesher (AutoGEM) of Creo software, a total of 2,398 tetrahedral mesh elements were generated for the rigid toe, whereas 6,850 elements were generated for the soft toe. The simulation results are shown in Figure 5. The maximum Mises stress of 3.41315 and 2.11624 MPa, and the maximum displacement of 0.00174 and 0.87773 cm were obtained for the rigid and soft toes, respectively. Table 3 (please see at the end of the paper) summarizes the FEA under 100, 200, 300, and 470 N loading conditions. The detailed simulated FEA results are shown in Supplementary Figures 1 and 2.

This demonstrates that the overall deformation and stress for both foot-toe designs were within the safe limit. Considering this initial assessment, toe fabrication was initiated, as detailed in the following section.

A 3D printer was used to fabricate a rigid toe weighing 7 g using PLA thermoplastic material (Figure 6).

To fabricate the soft toe, a cavity mold was produced using a 3D printer, consisting of two parts: cavity and negative. Ecoflex 00-20 elastomer parts A and B were mixed and poured into the cavity mold. The mixture was kept at room temperature for 4 hours to form the elastomeric toe by decoupling the cavity mold from the negative part. The toe weighed 156 g. The rigid foot-toe was mounted on the robot foot under the magnet and fixed with screws. The magnet and inner diameter of the rigid toe were matched for tighter toe-grip. To mount the soft toe, the electromagnet was placed inside its cylindrical cavity, tightly gripping the electromagnet without any slippage during the attachment/detachment process. This was designed such that the magnet diameter was roughly 1.5 times that of the inner toe-cavity, resulting in a strong grip. The hybrid rigid-soft foot is a combination of the rigid frame with the electromagnet and the soft toe. It was fully compliant on flat and round metal surfaces. Figure 6 illustrates the fabrication of the foot-toes. After fabrication, the robot-foot designs were tested and compared in the various experiments described in Section 3.

This test compared the foot designs with all the test surfaces based on their adaptation level. The surface adaptation metric was proposed, and calculated according to the percentage of foot-bottom area fully attaching to a surface. Figure 7 shows the three scenarios and their results.

The first scenario (Figure 7A) shows the flat foot tested on multiple pipes and a flat surface. The second scenario (Figure 7B) shows the curved rigid foot, while the third scenario (Figure 7C) shows the hybrid rigid-soft foot. The angles (θo,θ) formed by joining the robot feet (diameter = do) and pipe (diameter = d) were noted by recording images on a camera placed in parallel to the pipe. These images were processed to obtain the angles formed between the robot feet and pipes from a physically marked reference point. The summation (Σθ = θo + θ) from a reference point was normalized as the percentage foot-to-surface adaptation. For example, if the foot and pipe were fully attached (i.e., Σθ = 0), the resulting surface adaptation was 100%. The results obtained by this test showed consistency with the crawling success rate (reported later in this paper). It showed that the foot-toe design significantly influenced robot crawling success.

From the FEA, we noted that the foot-toe designs could experience acceptable deformation and stress. Due to the materials used, the rigid toe may either not deform, or permanently deform if the applied load surpasses the PLA thermoplastic strength limit. However, the elastomeric soft toe underwent elastic deformation such that it could recover its original shape even after bending, shrinking, or elongating under a specific applied load condition. To further examine this specifically for the metal pipe crawling scenarios, its deformation profile was obtained. A camera recorded the foot-toe deformation (toe-curve spread) once the robot foot had attached to the metal pipe. The recording was analyzed to obtain the deformation profile as shown in Figure 8. The experiment was conducted on various pipes with diameters of 12, 16 (painted and non-painted), 22, and 60 cm. The fully recoverable foot-toe deformation showed the robot feet had the capacity to adhere to outer pipe surfaces of any diameter.

The difference in friction between any two surfaces plays an important role in understanding their interaction. The friction coefficient is used to assess the resistance between the two adjacently sliding surfaces (Wang et al., 2014; Manoonpong et al., 2016). The robot foot was tested to obtain the friction coefficient for different metal pipes and a flat metal plate. The experimental setup to obtain friction coefficient of all toe designs and the results are shown in Figure 9. The soft toe was found to increase the friction coefficient in comparison to the flat or rigid curved foot due to the maximum adjacent foot-sliding area. This helps the robot to avoid slipping on painted metal surfaces during crawling.

According to the results of the previous experiments, the proposed hybrid rigid-soft foot outperforms the other two types. Therefore, we used it to further test robot locomotion. The robot performed unidirectional crawling by utilizing two gaits: the stepping gait where the robot lifts its body weight on one of its legs, and the sliding gait where the robot stays inbound to the ground and performs a sliding-like motion (Khan et al., 2020). The robot motor joints M1,3,5 were configured to move, with M2,4 kept locked at an angle for unidirectional crawling. The magnets’ alternating switching pattern follows the gait design. The overall robot hardware and system components, motor signals, magnet switching, and gait patterns are illustrated in Figure 10. Details of the robot locomotion control are not the main focus of this study and can be found in Khan et al. (2020).

Utilizing gaits 1 and 2, the robot performed point-to-point crawling on metal pipes and a flat metal plate. The robot crawling speeds with gaits 1 and 2 were 8.9 and 25 mm/s, respectively. Other representative crawling experiments are presented in Figure 11. Figure 11A shows the robot crawling on a medium-sized pipe (diameter = 16 cm) using gait 1 and the hybrid rigid-soft foot. Another experiment on a very large pipe using gait 1 and the rigid-soft foot is shown in Figure 11B. The robot crawling with the hybrid rigid-soft foot on the flat metal plate is shown in Figure 11C. Robot locomotion behaviors using the sliding gait can be viewed at http://www.manoonpong.com/EROFT/videoS1.mp4.

A high-speed locomotion test showed that the robot can perform highly robust and stable locomotion on industrial pipes. Figure 12 shows an overview of the experiment. The robot leveraged on the friction and adhesion force components added by the soft toe, increasing the stability of the robot. It performed bidirectional crawling without any failure on industrial pipes with a speed of 100 mm/s – surpassing its previous maximum speed of 25 mm/s (Khan et al., 2020), while outperforming existing similar robots on this metric (refer to the speed column in Figure 14).

Earlier in the Figure 3, robot feet were compared for their deviation profiles. To obtain actual deviation profile of the robot from the desired path during locomotion, a top-view camera was used to obtain its actual (Figure 13). This was to observe the change in undesired robot-body oscillation due to the different foot-toes employed, resulting in any robot deviating from a path. The robot was found to benefit from reduced perturbations and foot-slip-based failure due to the compliant toe design during attachment and detachment of the magnetic feet.

Using the hybrid rigid-soft feet, the robot crawled on all surfaces with an improved success rate. The crawling success rate was based on the point-to-point locomotion of the robot for each foot type, the employed gait, and type of surface. Table 4 (please see at the end of the paper) summarizes the robot crawling success rates for all robot locomotion scenarios. Experiments were repeated five times for each scenario. The key insights arising from the experimental results are discussed in the next section.

Based on the above experiments, it can be clearly observed that the robot-foot design played a fundamental role in robot crawling success. The flat foot was suitable only for flat surfaces, or when the pipe diameter was sufficiently large that it appeared flat to the foot. The robot foot with the rigid curved toe showed a certain level of surface conformity, increasing the robot crawling success rate on the pipes. However, under this configuration, the robot could not crawl on the flat surface or very large diameter pipes due to the rigid toe-slit restricting complete attachment, meaning it could crawl only on a few pipes. The hybrid rigid-soft foot proved to be the most effective for continuous compliance with the crawling surface, resulting in maximum success. By leveraging the hybrid rigid-soft foot, the robot also showed its capability to become a versatile pipe crawler on a medium-sized pipe with a very large diameter. The experiments for characterizing the robot feet (i.e., adaptability, deformation, friction, and deviation experiments) showed that the hybrid rigid-soft foot was superior to the flat and curved rigid foot. The hybrid rigid-soft foot deformed to all curvature pipes and retained sufficient stiffness to balance the robot. It produced high friction on all surfaces, enabling the robot to avoid critical slippage instances during crawling.