The American Society of Civil Engineers (ASCE) has compiled regular "report cards" on the state of US infrastructure since the 1980s. In its 2021 report (ASCE, 2021), the ASCE found that the nation's infrastructure averaged a "C-," up from a "D+" in 2017 and the highest grade in 20 years. This is good news and an indication we have headed in the right direction, but a lot of work remains. The federal government requires a strategic and holistic plan to renew, modernize, and invest in our infrastructure.

Besides leadership and intensive investment, resilience is one of the key requirements in this strategy. We must utilize new approaches, materials, and technologies to ensure our infrastructure can withstand or quickly recover from natural or manmade hazards.

However, applying technology in risk assessment/inspection, and maintenance of existing structures is still limited especially steel structures because of their special properties in terms of material and variety of nonstandard architectures. Until today, these tasks are still manually conducted by professional human inspectors who visually inspect damages and detect faults on or inside these structures (Ahmed, La, & Gucunski, 2020;Ahmed, La, & Tran, 2020;Billah et al., 2019Billah et al., , 2020)). Although human-carried inspections are usually highly time-consuming, costly, and risky.

For instance, it is highly dangerous for an inspector to climb up and hang on cables to inspect far-reached areas of bridges (Figure 1a) or offshore oil rigs (Figure 1b). Even the inspection of less complicated structures such as ship shells (Figure 1c) and gas/oil tanks/piles (Figure 1d) is also highly challenging due to their large scales.

Utilizing robots with sensing tools to automate inspection is an emerging solution (Ahmed et al., 2019(Ahmed et al., , 2023;;Ahmed, Tavakkoli, et al., 2022;Ding et al., 2020;Gucunski et al., 2023;La, Gucunski, Kee, & Nguyen, 2014;La et al., 2013La et al., , 2015;;La, Gucunski, Kee, Yi, et al., 2014;Le et al., 2017;Otsuki et al., 2023;Peidró et al., 2019;Wang & Kawamura, 2016;Yasmin et al., 2022). Several innovative robot designs including conventional wheeled robots inspired designs (Guo et al., 2014;Kamdar, 2015;La et al., 2019;Pham et al., 2020Pham et al., , 2022;;Pham & La, 2016;Sirken et al., 2017;Zhu et al., 2012) and tank-like tracks widening the contacting areas of the robots on steel surfaces (Lee et al., 2012;Nguyen & La, 2021, 2019a;Seo & Sitti, 2013;Shen et al., 2005;Song et al., 2022) have been presented in recent years. Such designs can work well on structures with large surfaces such as ships or tanks but encounter difficulties on complex surfaces, for example, bridges and oil rigs. Inspired by the mobility capacity of climbing animals, spider-like robots (Bandyopadhyay et al., 2018), legged robots (Mazumdar & Asada, 2009), inchworm-like robots (Lin et al., 2023;Ward et al., 2015), and hybrid robots (Bui et al., 2020;Nguyen et al., 2020;Pham et al., 2021) were designed and examined. However, it is challenging to design a controller for the complexity of robot mechanics in real-world applications. The recent development of aerial robots provides an alternative inspection solution (Elios, 2018;McConnell & Zuleger, 2019). Nonetheless, conventional drones may not be feasible with installing touched sensors required for in-depth inspections of fatigue cracks or thickness of steel structures. Other nonstandard moving mechanisms were proposed accordingly (Eto & Asada, 2020;Md-Yusoff et al., 2022;Nguyen & La, 2019b;Takada et al., 2017). The notable state-of-the-art climbing robots for inspection are listed in Figure 2. SAIR ( 2016) is an improved version of a two-magnetic wheeled robot with modification of the rear wheel as Omni. This function helps the robot to get a large steering angle which is useful in narrow spaces. However, mainly designed for pipe inspection, the robot is unable to pass difficult obstacles. BridgeBot (Sirken et al., 2017) is a soft frame four-magnetic wheeled robot. The idea is to make BridgeBot flexible to fully adhere to any steel surface and pass transitions. Even though, thin edge or small cylindrical structures is impossible for this robot. Proposed as high mobility with four sphere wheels and two-degree-of-freedom rotational magnetic adhesion mechanism, Eto and Asada (2020) can work well on curved surfaces and pass transition except for edges. Priorly proposed bikelike robots such as Tâche et al. (2009) and Caprari et al. (2012) do not have high directional flexibility, limiting mobility in narrow spaces.

The rigid shapes of such robots restrict their maneuverability for passing extreme obstacles, such as thin edges or acute corners.

Except (Bike, 2016), these mechanical designs do not have a mechanism for touched sensors that are essential in structural inspection tasks, for example, measuring material thickness, paint quality, and structural vibration. Ship Inspection Robot (ETH Zürich & ZHdK, 2015) is a rare robot designed to pass thin edges for internal ship inspection. Nonetheless, the robot cannot deploy on curved curvatures. A high-strength multisteering climbing robot for steel bridge inspection (Motley et al., 2022) is developed by the Advanced Robotics and Automation (ARA) lab for heavy load applications. Four independent steering capabilities of moving wheels make the robot multidirectional. However, with this configuration, the robot only can work on continuous flat surfaces. A hybrid worming-mobile robot (Nguyen et al., 2020) combines both the advantages of wheeled locomotion on continuous surfaces and the flexibility of inchwormlike movement on transitions. The ARA robot's design applies to navigation on various steel structures. However, its complex mechanical system results in difficulty in control architecture and causes limitations in industrial approaches, which require simplicity and optimization. None of the above-mentioned robots can achieve radical climbing capability on complex structures, including flat, concave, convex, and curved curvatures, and edge transition in a simple form of robot design. They are the most challenging architectures described in Figure 3. In practice, the tough environments that a crawling robot needs to deal with include I-shape beams, cylindrical structures, and transitions/joints as shown in Figure 3a,b; flanges in pipelines Figure 3c, and reinforced edges Figure 3d in ships, tanks, or bridges as well as limited space in those structures. This paper presents a novel two-wheeled-climbing robotic system to provide an efficient inspection solution for complex steel structures. We focus on optimizing the climbing capability and the multidirectional locomotion of a bike-liked wheeled-climbing robot, making it maneuver on complex ferromagnetic structures. We also developed a transforming mechanism enabling the robot to reconfigure to overcome concave and convex-edged obstacles, such as L-, T-, and I-shaped beams or thorny corners/edges. Robot architecture allows us to equip a sensor deploying mechanism for both an ultrasonic-based steel thickness measurement sensor and a camera in the most space-efficient package. This study is a full and upgraded version evolved from our initial prototypes of Nguyen et al. (2022) and Ahmed, Nguyen et al. (2022). This upgraded version has improved robot stability when traversing horizontally on cylindrical structures by generating a new locomotion mode. Moreover, a simpler but more efficient method of a flexible material in the contacting part helps enhance the sensor deploying mechanism function. We demonstrated the robot's working principles and functionalities through laboratory and field tests. Video of this deployment can be seen from the ARA Laboratory's website at this link: https://ara.cse.unr.edu/?page_ id=11.

The rest of the paper is organized as follows. Section 2 describes the overall robot design. Section 3 presents a detailed mechanical design and magnetic force analysis of the robot when moving on surfaces with different inclinations. Section 4 analyzes magnetic force on different surface curvatures under both static and dynamic conditions. Section 5 demonstrates various experiments to verify the proposed robot design and validate the magnetic force analysis, robot locomotion, and transformation. Finally, the conclusion and discussion of future work are presented in Section 6.

The front view and the back view of the robot are depicted in Figure 4a.

We added a steel thickness measurement transducer in the space between the two wheels. This location is ideal for protecting the sensor when traveling and allows good contact for measurements, whether the robot is working on flat or curved surfaces. The robot's mass is 1.2 kg, including the sensors (a thickness measurement sensor and a camera).

We used three-dimensional (3D)-printed ABS plastic to manufacture the frame for a lightweight robot. When powered by a 700-mAh LiPo battery, a human operator can remotely control the robot to work for 30 min. Figure 4b shows the overall mechanical design of the robot. The robot's dimension is 150 mm × 80 mm × 90 mm. We place the ring magnets at the cores of the two rubber-covered wheels, driven by two high-torque gear direct current motors (100 kg ⋅ cm torque each). The steering actuators and transforming mechanisms are controlled by two servos (32 kg cm torque each). The front and the back of the frame are linked by a bearing acting as a dynamic joint.

For high mobility, two revolute joints are installed, making two steering units (Figure 5). These two units allow the robot to work in two modes: bicycle-like and multisteering modes. The bicycle-like mode is utilized when the robot operates on large surfaces with only one activated steering unit (Figure 5a). On narrow surfaces, the robot can change direction by activating the rear steering unit instead of the front one (Figure 5b). In locations that require sideway movements, the multidirectional mode is enabled. In this mode, two steering units are active simultaneously as in Figure 5c. The maximum turning angle is kept at less than 90°to maintain the robot's stabilization in this mode. In F I G U R E 5 Design concept shows the maneuverability of the robot with active joints colored green (for the front joint) and blue (for the rear joint). Two independent steering actuators allow the robot to enable bicycle-like moving modes: (a) when only the front steering unit is activated, (b) when only the rear steering unit is activated to change direction on narrow surfaces, (c) when two steering units are activated simultaneously; the robot can move sideways, and (d) the mix of bicycle and multidirectional modes. On horizontal traversing, the bicycle shape is weak in maintaining adhesive torque. This mode improves this disadvantage with wheel paralleling configuration but is still able to turn. ICR, Instantaneous Center of Rotation. and multidirectional mode (Figure 5d) is switched to enhance safety. The kinematic of robot mobility with Instantaneous Center of Rotation is described in Figure 6, which represents all four different modes corresponding to the ones described in Figure 5.

In addition, a free joint (orange joint in Figure 7) working as a dynamic connection between two halves of the robot's body allows the two wheels to stick to surfaces effectively, even on uneven ones, such as two flat curvatures (Figure 7a), positive curvatures (Figure 7b), or negative curvatures (Figure 7c). Our design also enables the robot to pass thin edges and acute corners with two other revolute joints shown in Figure 8. These two joints allow the distance between the two wheels to be adjustable based on surfaces as shown in Figure 8c,d. F I G U R E 7 Free joint (orange) in the middle of the robot's body helps its wheels to better adhere to uneven surfaces, for example, (a) two flat curvatures, (b) positive curvatures, and (c) negative curvatures.

F I G U R E 8 Our design allows the distance between the two wheels to be adjustable with two revolute joints. The robot can pass corners without activating the two joints in normal conditions (a, b). However, the robot can adjust the wheels' distance (the two joints are activated, hence colored purple) to be small to pass a thin edge (c) or large to pass an acute corner (d).

The bicycle robot is also designed to work in extreme situations such as horizontally traveling on a cylindrical structure as shown in control loops. These servo motors orchestrate the movement of different components, including front and rear steering units, front and rear mobile motors, gel pumping mechanisms, and sensor deployment and transformation mechanisms.

The adoption of this well-structured hierarchical control approach empowers the robot to accomplish its designated tasks with notable efficiency and accuracy. The high-level control facilitated by ROS manages data processing and seamless communication, while the low-level control, orchestrated through the Arduino platform, ensures responsive and precise actuation of the robot's servo motors. This intricate interplay allows the robot to execute a diverse range of movements and tasks with agility and precision. This dichotomy of control levels establishes a resilient and versatile robot control system, tailored to diverse application scenarios and environments.

This section provides a detailed mechanical analysis of our robot, including the analysis of the robot transformation, the robot maneuverability, and the sensor deployment mechanism. F I G U R E 10 The robot's control system with Arduino board, and sensor integration with onboard computer. Rx, receiver; Tx, transmitter.

We use reciprocating mechanisms to allow the distance between the two wheels to be adjustable. Due to the high load of attractive force when the two wheels are close, a feed screw is applied for the slidercrank part. The mechanism can transform the robot into three different shapes depending on particular situations, as shown in Figure 11.

The kinematic is analyzed in Figure 12, where W is the wheel center, reciprocating mechanism XYZ, and z XS = , we have

Square then sum both sides of ( 1) and ( 2), we have

(3)

resulting in a function δ f z = ( ).

The robot's shape transformation is the combination of controlling δ in Figure 13 and moving wheels simultaneously. The load (the magnetic force between the two wheels) is shared between the two wheels and the reciprocating mechanism. From Figure 13, with F as the attractive force between the two wheels, M load is the torque that feeds screw bears, and i is the feed screw's transmission ratio, we have

load wheel

(5)

3.2 | Robot maneuverability analysis

We analyze the adhesive force that the robot needs to climb reliably in any normal working conditions. We perform the analysis in an extreme situation where the adhesive force between the magnetic

The reciprocating mechanism's kinematic.

wheels and the contacting structures is minimal Figure 14. Here, X 1 and X 2 are two contact points of the back wheel and front wheel, respectively. We call P the robot's weight, and h is the distance from the center of mass of the robot to X 1 . If F 2 is an adhesive force of the front wheel at X 2 then F 2 is at its minimum when the front wheel hits the corner. To keep the robot safe, the following condition needs to be satisfied:

According to ISO 3691 (IEC60034, 2022) for safe weight lifting, a safety factor of 5 was selected. Therefore, the real adhesive force F 2 needs to be at least five times greater than the result from the above theoretical calculation in (6).

This analysis calculates the necessary motor torque when the robot stands the highest load. The highest load occurs when the robot passes an internal corner between two perpendicular surfaces (Figure 15), the front wheel bears an additional force F 2.2 , which is the adhesive force of the front wheel on the surface 2. Similarly, F 2.1

is the adhesive force of the front wheel on surface 1. F f2 is the friction of the front wheel on surface 2, r is the wheel's radius, k is the static friction coefficient (between rubber and steel in our design). The minimum force of the front wheel that allows the robot to be able to overcome the corner must satisfy

Therefore, the moving motor torque needs to satisfy

According to IEC 60034 (ISO3691, 2020), the actual torque selected is at least double that of the theoretical calculation in (8).

An analysis is conducted to investigate the load torque on the revolute joints. Two forces affect each other as illustrated in

Figure 16: the static friction and the attractive force at the two magnetic wheels. Let F 12 be the adhesive force of wheel 1 affecting F I G U R E 13 Force analysis of the reciprocating mechanism.

F I G U R E 14 A situation where the adhesive force is minimal, resulting in a high chance of falling over. In this case, the adhesive force of the front wheel is significantly reduced when the robot hits an edge.

F I G U R E 15 When the robot passes an internal corner between two perpendicular surfaces, the robot's load increases significantly.

wheel 2, F f be the friction at X 2 . The measured load-force at point L (Figure 16a) has to satisfy the following condition:

Thus, the steering servo torque needs to satisfy

steering 12 2

(10)

On the basis of IEC 60034 (ISO3691, 2020), the actual servo's torque is chosen to be at least twofold compared to that of the theoretical calculation in (10).

This analysis provides a solution when fulling torque dramatically reduces when the robot travels horizontally on a cylindrical structure Figure 17a. Because crank l 2 is short, the torque to keep the robot avoid turnover is weak as below:

To improve the safety factor in this situation, the robot should transform to the mixed mode as Figure 5d. Crank l 1 is much longer than l 2 , so the fulling torque becomes

1 1 2 2

(12)

A four-bar mechanism is designed for generating vertical movements of the transducer, as shown in Figure 18. A compression spring is added together with an angle lock to avoid the overload of servo motors and enhance contact between the transducer and the working surfaces.

We analyze the mechanism using a simplified model shown in

From Figure 19, we have

Applying the similar approach as in ( 1) and ( 2) for ( 13) and ( 14), we have

From Figure 19,

where y x BF = -. Similarly, (18) presents a function β f y = ( ).

From Figure 20, we have

Square and sum both sides of ( 19) and ( 20) then simplify, we have

presenting a function f α ϵ = ( ).

Wheel tires require a particular pattern to warranty the robot's stability in extreme situations; particularly, when the robot's body

The four-bar mechanism. A flexible part (thermoplastic polyurethane [TPU]) acts as a soft contact between the probe and surfaces. An angle lock is added to create a range of free movement of the probe when approaching uneven surfaces.

The four-bar mechanism's kinematic.

F I G U R E 20 The kinematic of the four-bar mechanism (AGHK) with HK is the servo arm.

is horizontal as it travels along a cylinder bar. Figure 21 depicts a cross-section in this situation. With one strip of tire for the entire wheel, the robot's body is inclined because of gravity (Figure 21a), causing drifting when the robot turns. To fix the drifting issue, two separated rubber strips are applied to improve the approaching area between the tire and curved surfaces. As shown in Figure 21b, using two strips, the turning point L is created, and the torque eF mag is generated to stabilize the robot's body.

Since we use an ultrasonic sensor for thickness measurement, couplant is necessary to fill the air gap between the transducer and the test specimen (Otsuki et al., 2022). The couplant with high viscosity is utilized to stick well on surfaces, even in upside-down or vertical positions. We selected the peristaltic pump type for highviscosity gel. We also chose the syringe mechanism for gel storage because it can work on any robot pose. The pump is described in Figure 22.

The previous analysis is only applied when the robot moves on flat steel surfaces. However, there are also structures, which have curved surfaces and extreme cases when magnetic force significantly increases or decreases. So, the following analysis will help determine the impact of the magnetic force created.

We conducted experiments with different steel shapes in real conditions to verify the performance of the magnetic wheel in both static and dynamic conditions.

The wheels tested is N52 neodymium magnet with a dimension of 2.5″ od × 1/2″ id × 1″ thick. In static conditions, the minimum pull force is 205N at 100mm diameter steel cylinder. At an edge, the force drops to 145N. In the 90°internal corner, the force hit 345N. In dynamic conditions, with the robot's velocity of 20 cm/s, adhesive force falls to around 10%.

To measure the adhesive force created by permanent magnets, we set up Figure 24 shows the testing results of a noncoated magnetic wheel on flat and different curved surfaces. On a flat surface magnetic force gets a maximum of nearly 300 N. With 0.5 mm rubber coated, the force decreases by around 9%. Figure 25 the testing results of a noncoated magnetic wheel on 90°internal (345N)

and external corners (145N). These are two extreme cases that the robot deals with complex steel structures.

We also measure the adhesive force of the robot in a moving state as shown in Figure 26. Each measurement is conducted three times. On average, the adhesive force in the dynamic condition is lower than approximately 10% compared to the static state.

In this experiment, the full force the robot's body is measured. The adhesive force is generated by two wheels, and P in Equation ( 22 In the worst situation, when a robot passes a thorny edge, two coated wheels contact least to the structure. The adhesive force of each wheel is lowest by 145N-9% of coated tire reduction-10% of force losing in dynamic conditions =119N.

Two wheels generate 238N, robot's weight is 2 kg, which still satisfies Equation ( 6). Therefore, the robot is safe in surveyed situations.

To evaluate the design and performance of the robot, experiments for evaluating the magnetic force created by magnetic wheels have been conducted. The ability of climbing and failure avoidance were tested. During the test, a LiPo battery (two cells) 7.4 V 900

milliampere-hour (mAh) is used to power the robot for about 30 min of working. One laptop which can connect to a wireless LAN is used as a ground station. The robot's mass m = 2kg, and if we assume that the gravitational acceleration g = 10m∕s 2 , the total weight of the robot is approximately P mg = =20N.

We built an indoor structure comprising typical parts of general steel structures (cylinder, L-, I-, U-shaped beams) with structural transition joints to validate the robot's locomotion functionalities. Our robot can traverse smoothly to all locations in the testing structure.

Figure 27 shows the verification of the robot design in extreme conditions. The robot crosses convex and concave surfaces. The robot makes a 90°turn on internal and external corners. Figure 28 illustrates that the robot is working on a cylindrical shape. The robot in bicycle mode gets sliding when trying to transit between two surfaces. The robot can pass it smoothly in multidirectional mode.

Figure 29 shows the robot working on a cylindrical structure.

Figure 30 illustrates the process by which the robot passes a thorny edge. A transforming mechanism is utilized in this situation. Figure 31 describes the process by which the robot transforms in shape to adapt to an acute corner. Once the front wheel can hit the second surface, the transition is conducted easily. Figure 32

Several robot implementations on local and highway bridges have been conducted to verify robot performance in real working conditions. The robots deployed on three bridges with two main structures: cylindrical and I-shape beams. The first test is on a cylindrical type bridge as shown in Figure 35. The bridge's structure includes cylindrical surfaces of 30 and 22 cm diameters.

The robot performs thickness measurements in some areas that are rusty to check how severe the corrosion is. However, our sensor deployment mechanism cannot reach the internal angles of some rusted spots due to the vertical height limit of the four-bar mechanism.

We deployed the robot in a field test during a bi-annual Highway inspection in Nevada, USA. The bridge is located on Highway-80 in Lovelock City. Figure 36 shows the robot's performance in a real application, and the robot was able to traverse stably on the structure and collect data on this bridge.

The robot reliably passes extreme cases of I-shape beam structures, including internal and external corners. In real conditions, thick dust may reduce the pulling force and friction factor.

However, a high safety factor helps the robot get in no trouble (Figure 37).

There is a data synchronization with the robot's pose presented when the robot deploys on a Highway bridge I-75 in Georgia, USA (Figure 38).

The robot successfully passes all the tests both indoors and outdoors. In actual working conditions, dust and rusty particles are further challenges that the robot must deal with. They reduce adhesive force and friction constant.

The robot tests and deployments with an ultrasonic sensor for steel thickness measurement are demonstrated in this video: https:// youtu.be/Qdh1oz_oxiQ.

In our rust detection approach, we harnessed the effectiveness of the Unet architecture alongside a ResNet-18 encoder for the identification of rust on steel structures (Ahmed, Nguyen, et al., 2022).

The choice of this particular encoder was driven by its demonstrable superior performance in comparison to alternative encoders, namely, ResNet-34, RegNet-X-2, Efficient-b0, and Efficient-b2. Similarly, we also leveraged the DeepLab architecture, this time coupled with a ResNet-18 encoder, which yielded enhanced rust detection capabilities when contrasted with other encoder options (Ahmed & La, 2022;Ahmed, Nguyen, et al., 2022).

For our investigation, we compiled a data set comprising 1500 steel images sourced from bridges and assorted steel structures in Vietnam (Pham et al., 2024). This data set was employed to train the architecture-encoder pairs. Upon conducting comprehensive offline training sessions for these pairs, we proceeded to validate their efficacy. This validation phase F I G U R E 37 Robot smoothly traverses an edge of I-shape beam on the deployment on Highway-80. F I G U R E 38 Robot deployment and data collection on a bridge on Highway I-75 in Georgia, USA. Robot positions and steel thickness data are synchronized in real-time. The robot path is represented in white color. Steel thickness measuring positions are red dots. Thickness data (numbers in green color) is shown in inch units. One particularly intriguing trajectory for future exploration involves the integration of advanced 3D cameras. Such an augmentation could pave the way for autonomous localization, navigation, and inspection via image processing, thereby ushering in a new era of fully automated inspection tasks. As we steer towards these future horizons, this paper sets the foundation for a dynamic evolution of steel structure inspection, with the bicycle-like robot poised to become an indispensable tool in this domain.