Wall-Climbing Mobile Robot for Inspecting DEMO Vacuum Vessel

Abstract

The vacuum vessel (VV) inside and outside inspection of the Demonstration Fusion Power Plant (DEMO) is very difficult due to various constraints, such as non-magnet effect material requirements, constrained space, and neutrons on its surfaces. We propose a design method for wall-climbing mobile robots (WMR) based on the vortex principle and investigate key technologies to meet VV inspection requirements. We developed a kinematic model based on the robot’s motion control requirements and a trajectory tracking control algorithm according to the tractrix principle, enabling the robot to follow the path for autonomous inspection. The impeller is designed based on the vortex principle. The aerodynamic characteristics and structural strength of the impeller were also analysed and optimised. A sliding-mode robust pressure control system was designed for the robot’s negative pressure adsorption, and its effectiveness was verified by simulation. Finally, an initial test prototype verified the structural design and vortex adsorption performance. We also addressed the potential applications of the WMR in DEMO and other fusion reactors.

1. Introduction

The fusion reactor can generate high energy when light hydrogen atoms aggregate, forming heavier elements such as helium and a light neutron. The machine where this fusion reaction occurs is called a tokamak. Tokamak instructions have five key components: magnet, vacuum vessel (VV), blanket, divertor, and cryostat [1,2,3]. Demonstration Fusion Power Plant (DEMO) is still in the conceptual design stage, and the configuration of VV is being studied. During the assembly of the tokamak, the manufacturing and assembly of VV contain a considerable amount of welded and brazed joints of various materials and complicated structure elements. In DEMO, the VV is a double wall structure manufactured from 316 L stainless steel. Figure 1 shows the machine prototype and 3D model of the VV. During the assembly phase, all fan-shaped segments are joined by welding [4,5,6,7], resulting in several welds in the inner and outer welding areas of the VV, which must be tested for quality and reliability. Manual inspection of the weld quality is very time-consuming; therefore, using a robot for the inspection task is an optimal solution.

The VV is a rotating body with a maximum diameter of 25.52 m in the equatorial plane and a minimum diameter of 7.24 m, similar to the letter “D”. Designing a wall-climbing mobile robot (WMR) for non-magnetic material surfaces that carries tools into the VV to complete the inspection task is a greater challenge. There are different kinds of WMRs, and the principles behind their mechanisms are different. The vacuum-sucking technique is usually used in traditional WMRs. These robots are mainly created by negative pressure devices to create a vacuum or vacuum-like environment, using atmospheric pressure to attach the robot to the wall [8,9]. However, the shortcomings of this kind of robot are obvious: The vacuum adsorption unit must be in close contact with the wall because if the wall surface is rough or has a groove, the air leakage reduces the adsorption force, and the robot will fall [10,11]. To address the effect of air leakage on the robot’s adsorption force, ref. [12] designed a wall-crawling robot that can achieve rough wall-crawling by generating and maintaining a negative pressure adsorption force through the rotational inertia effect of air. Ref. [13] describes a multi-chambered WMR for concrete wall inspection. The adsorption force comprises seven controlled vacuum chambers and a large gas storage chamber, reducing the effects arising from air leakage. Ref. [14] investigated the optimisation of the magnetic adsorption unit’s (MAU) structure based on virtual prototyping techniques to improve the working performance of the robot. For the WMR control system, refs. [15,16] established a numerical simulation model of a WMR based on a computational fluid dynamics (CFD) package and studied its liquid-sealing control technology for negative pressure adsorption. Ref. [17] proposed a design method for negative absorption systems providing stable pressure at variable flow rates using CFD software. Ref. [18] designed a sliding mode control method with a sliding mode backstepping controller (SMBC) and a terminal sliding mode controller to increase the dynamic system regulation’s robustness. Ref. [19] presented a small negative pressure WMR based on an ARM microprocessor system and analysed its dynamic characteristics. For the trajectory control algorithm, ref. [20] studied the intelligent path planning algorithm and obstacle avoidance of a mobile robot based on a swarm intelligence algorithm, proving the algorithm’s correctness through software simulation. Ref. [21] proposed a nonlinear model predictive control (NMPC)-based trajectory tracking algorithm for mobile robots. Ref. [22] proposed a trajectory-tracking algorithm based on Improved Dual-Heuristic Dynamic Programming, and its effectiveness was verified by simulation. Integrating existing technologies and developing a WMR that meets the needs of VV inspection tasks for the confined spaces within DEMO are key points of this study.

We introduced a WMR based on the vortex technique, which runs on all material surfaces and achieves tasks by switching the carried tool, such as the visualization tool used to inspect the weld defect and VV inner wall surface. The proposed robot has size and flexibility advantages and does not require modification or additional construction on existing VV. The design, motion control, dynamic analysis, and capability analysis are presented in this paper. Finally, a prototype was built, and the robot’s functionality was approved.

2. Design of the WMR

2.1. Requirements for the WMR

As previously mentioned, the most cost-effective way to investigate the weld quality is a visual inspection. However, the drawback of this method is that visual inspection can only inspect some defects on the surface. Among other methods, ultrasonic inspection is the most suitable method for the application [23,24] because it detects discontinuities by directing a high-frequency sound beam through the base plate on a predictable path. If the sound path strikes an interruption in the material continuity, part of the sound is reflected, received by the instrument, amplified and traced. Therefore, the WNR requires the ability to carry a lightweight wireless ultrasound probe and a visual camera with a total mass of <1 kg and a total payload of 4 kg, including the mass of the robot. In addition, the robot should be able to move on the non-magnet surface in any direction.

2.2. The Concept of the WMR

The WMR shown in Figure 2 was designed based on the vortex principle. The main components of the WMR are the impeller, impeller drive system, robot drive system, and electric control system. The mass of the WMR structure itself is about 1.5 kg. The length of the robot is 290 mm, and the distance from the chassis to the horizontal floor is 4 mm, with a maximum that cannot exceed 10 mm. These dimensions include a minimum inner arc radius of 1750 mm and a minimum outer arc radius of 1626 mm for the maintenance area inside the vacuum chamber of the WMR. By calculating the dimensions of the vacuum chamber, the WMR meets more than 98% of the maintenance needs for the inner and outer surfaces of the fusion reactor vacuum chamber [25]. While working, the WMRs can be stored in the end toolbox of the MPD heavy-duty robot arm in clusters and brought into the VV via the DEMO from the intermediate maintenance window to complete the task. Alternatively, the WMRs can also enter the vacuum chamber in groups through the lower window of the VV to complete the task.

The impeller is driven by a DC brushless motor with high rotational speed. When the impeller rotates, the air flows from the centre to the edge, generating a low pressure in the centre of the impeller and an attractive force between the WMR and the wall. The wheel with high friction rubber is driven by another DC motor and offers mobility. The size of the robot is 20 × 250 × 130 mm. In addition, the robot’s radius can be optimized and changed according to the task. In the conceptual design stage, the force analysis is conducted with 0 acceleration. When the WMR moves on the DEMO wall in an upside-down position, the adhesion force of the robot must satisfy $F_a>mg$, where $m$ is the mass of robot, and $F_a$ is the adhesion force. When the WMR moves on a vertical wall, the crucial role is the friction force $F_f$. The friction force should satisfy $F_f=\mu F_n$, where $\mu$ is the friction coefficient and $F_n$ the adhesion force to the surface. To hold the WMR and its components on the wall, $F_f$ must be higher than the weight $mg$ of the robot. The friction coefficient was assumed to be $\mu =0.64$, and $F_f>mg$ should be satisfied. In our case, the design payload capability was 2 kg, and together with the mass of the robot, the total mass was 3.5 kg. The driving force was designed to be 40 N. However, this was the preliminary calculation in conceptual design, and more aspects were considered in the simulation by assigning materials to components and changing the structure’s geometry.

3. Kinematic Analysis of WMR

3.1. Kinematic Modelling

The WMR has a typical three-wheel structure, with the one front wheel being passive universal wheel and the two rear wheels being drive wheels. The left and right drive wheels are driven by two geared motors that move forward and reverse to complete the detection task. Changing the speed of the left and right drive wheels controls the crawling speed of the WMR and angular speed of rotation. Each drive gear motor forms a closed loop speed circuit with the drive wheels. The speed of the drive wheel can be changed by adjusting the output voltage of the motor.

To describe the robot’s pose, we assumed that the WMR was moving in the vertical Y-Z plane, as shown in Figure 3. The position of the robot is represented by the coordinate system established at the midpoints of the two drive wheels. The heading angle is represented by the angle $\alpha$ formed by the axis of the robot and the Y-axis. The robot posture information is:

$$\left\{\begin{array}{c}\mathit{P}={\left[\begin{array}{ccc}y& z& \alpha \end{array}\right]}^T\\ \mathit{q}={\left[\begin{array}{cc}v& w\end{array}\right]}^T\end{array}\right.$$

(1)

where $y$ and $z$ are the position coordinates of the robot; $\alpha$ is the heading angle of the robot; $v$ and $w$ represent the linear and angular velocities of the robot, respectively [26,27].

We assumed no relative lateral sliding of the robot’s wheels against the wall as well as longitudinal sliding. The WMR’s motion is modelled as follows:

$$\left\{\begin{array}{c}\dot{y}=vcos\alpha \\ \dot{z}=vsin\alpha \\ \dot{\alpha }=w\end{array}\right.$$

(2)

$$v=\frac{w_{r}r+w_{l}r}{2}$$

(3)

where $r$ is the radius of the left and right drive wheels; $w_l$ and $w_r$ are the angular velocities of the left and right drive wheels, respectively, and $v$ is the robot linear velocity. The angular velocity of the robot is:

$$w=\frac{w_{r}r-w_{l}r}{2L}$$

(4)

where $2L$ is the distance between the two driving wheels.

The robot’s positioning was achieved by monitoring the information obtained from the drive motor encoder over a certain period. The robot’s position in practice can be deduced by numerical integration.

$$\left\{\begin{array}{c}{y}_n=y_{n-1}+\frac{cos{\alpha }_{n-1}}{2}{{\displaystyle \int }}_{t_{n-1}}^{t_n}\left(w_r+w_l\right)rdt\\ z_n=z_{n-1}+\frac{sin{\alpha }_{n-1}}{2}{{\displaystyle \int }}_{t_{n-1}}^{t_n}\left(w_r+w_l\right)rdt\\ {\alpha }_n={\alpha }_{n-1}+\frac{1}{2L}{{\displaystyle \int }}_{t_{n-1}}^{t_n}\left(w_r-w_l\right)rdt \end{array}\right.$$

(5)

3.2. Trajectory Tracking Motion Control

To realise the tracking control design of target trajectories for WMRs, we propose a trajectory-tracking motion control algorithm based on the tractrix principle in this paper. As shown in Figure 4, the axis of the WMR is $L$ and the direction is vertically down along the Z-axis. One end of the rod, point B, moves translatable along the Y-axis, and the trajectory obtained by the other end, point A, is the tractrix [28,29]. From the trajectory formation condition, it is clear that the velocity vector at endpoint A always points along the connecting rod $L$ toward point B. The equation of the trajectory of point A can be obtained by:

$$\frac{dz}{dy}=\frac{-z}{\sqrt{L^2-z^2}}$$

(6)

where $\left(y,z\right)$ is the coordinate of point A. The recursive operation of the tractrix can be used to solve the inverse kinematic problem of the WMR’s trajectory tracking to achieve motion control of the WMR.

As shown in Figure 4, the equation of the line along the rod length $L_{AB}$ at the starting point $A^{\prime }\left(y_a,z_a\right)$ of the connecting rod at the moment $t_{i-1}$ can be calculated based on the tractrix principle.

$$z=k_{AB}y+b_{AB}$$

(7)

where $k_{AB}=\frac{z_b-z_a}{y_b-y_a}$, $b_{AB}=\frac{z_a{y}_b-z_b{y}_a}{y_b-y_a}$.

At the next moment $t_i$, point $B^{\prime }\left(y_b,z_b\right)$ moves a small distance $\mathrm{\Delta }d$ in the direction of the Y-axis and by the rod length condition we know that $A^{\prime }$ satisfies.

$$L^2={\left(y-y_b\right)}^2+{\left(z-z_b\right)}^2$$

(8)

The orientation angle of the robot can be obtained as:

$$\alpha =\mathrm{atan}\left(\frac{z_b-z_a}{y_b-y_a}\right)$$

(9)

The coordinates of the position of point $A^{\prime }$ and the equation of the line passing point $A^{\prime }$ at the next iteration $t_{i+1}$ are obtained by combining Equations (7) and (8). The inverse kinematic solution and trajectory planning of the WMR can be accomplished by recursive operations on the above tractrix.

The set-up WMR trajectory tracking curve is shown in Figure 5a. The feed rate is constant, and the trajectory-tracking motion control was conducted using the tractrix principle. The displacement curves of each wheel in the timing diagram of the moving process and the kinematic inverse solution are shown in Figure 5 and Figure 6. The four position states in Figure 5 show that the WMR can track the target curve well and moves smoothly throughout the following process. The angle of rotation and angular velocity curve of the robot’s drive wheels in Figure 6 shows that the angular velocity of the WMR is relatively smooth throughout the tracking process, thereby meeting the requirements of VV inspection.

4. Aerodynamic Study and Finite Element Analysis

4.1. Aerodynamic Study

To assess the payload capability of the WMR, the dynamic analysis of the impeller must be conducted to optimize the WMR’s performance. The impeller is the most important component and will determine the capacity of the WMR. It is made of 1 mm-thin aluminium to reduce the weight of the robot. The airflow dynamic model is built up and shown in Figure 7. The simulation was carried out in computational fluid dynamic (CFD) software [30,31]. The analysis optimised the design factors, such as the radius of the impeller, rotational speed, power consumption, and adhesion force. The impeller was covered by a round-shaped cover manufactured from carbon fibre. The simulation results showed no significant dependency on the shape of the cover or the gap between the cover and the impeller.

From the airflow simulation, the flow pattern of the streamlines around the impeller and vector plot in the X-Z plane is shown in Figure 8. The simulation results revealed that the flow pattern is similar to the theory, and the gas is accelerated by the centrifugal force and ejected from the impeller’s nozzles. The gas is sucked into the impeller’s centre area from the bottom, forming the recirculation pattern depicted in Figure 8. The low-pressure region in the central cavity of the impeller and the low static pressure of the recirculation flow under the impeller are major sources of the adhesion force.

Two sets of simulations were conducted to assess the effect of rotational speed, impeller radius, and impeller height on the adhesion force produced by the impeller. The adhesion force was defined as a gas-dynamic force acting on the rotating impeller, pushing it to the surface. In the first simulation, the impeller radius was $R,$ and the impeller height was $h=$10 mm. The adhesion force for different speeds at different impeller radiuses is shown in Figure 9a. In the second simulation, the motor speed was $n,$ and the impeller radius was $R=$100 mm. The adhesion force for impeller height at different speeds is shown in Figure 9b. From the results of the previous two sets of simulation results shown in Figure 9, we concluded that the height of the impeller has less impact on the adhesion force. Therefore, small perturbations such as welding seams, bolt heads, and cavities between walls will not cause many changes in the generated adhesion force. The rotational speed impacts the adhesion force, but the trend is relatively steady compared with the impact of impeller radius on the adhesion force.

The required motor power is shown in Figure 10a when only gas-dynamic forces were considered, and no friction losses or other forces and losses were considered. The power is related to the rotational speed and the impeller radius; therefore, it has a similar trend as the adhesion force. The efficiency is measured as the ratio of the generated adhesion force to the required power and is shown in Figure 10b. From the simulation results, the impeller with a radius of $R=$90 mm needs lower power to generate the same adhesion force, with a relatively smooth variation trend. The structure might have caused the impeller’s increased efficiency with $R=$50 mm; in other words, the radius of the impeller was too small for this application.

4.2. Finite Element Analysis

As the impeller is running at high speed, finite element analysis is necessary for mechanical design. The structure of the impeller was first modelled in SolidWorks, and then the finite element analysis was conducted in FEMAP NX Nastran software [32,33]. To decrease the structure’s complexity, mid-surfacing commands were used. The material of the impeller was 6061-T651 Al Plate. The nodal force 50 N was applied to the surface in the Z direction, and rotation velocity along the Z-axis was set to 10,000 RPM. As for the constraint, the impeller had only 1 DoF of rotation along the Z-axis. The meshed model we built is shown in Figure 11.

In the dynamic simulation, the impeller maximum total deformation in the first and fifth modes are shown in Figure 12 and Figure 13. From the simulation, it can be seen that there will be about 1 mm total deformation in the structure; however, by increasing the contact area, one connector between the motor and the impeller can be designed. A 5 mm-thick connecting flange can increase the diameter from 5 to 40 mm, and the defection will reduce to <0.2 mm.

5. Adsorption Control Analysis

5.1. Modelling of Adsorption Systems

As shown in Figure 14, the WMR must be attached to the wall using the thrust generated by the impeller fan’s high-speed rotation as it moves around the inside of the circular vacuum chamber. The adsorption force generated by the motor’s rotation must not be less than the force of gravity; otherwise, it will cause the robot to slip. Furthermore, the adsorption force cannot be much greater than gravity, or it will waste energy and shorten the use time requiring the control of the impeller fan speed to keep the pressure provided at a specific value to ensure the stable operation of the robot.

For the design of the robotic adsorption control subsystem, we obtained a mathematical model of the adsorption device by analysing the dynamics of the impeller fan. We achieved adaptive adjustment of the WMR’s adsorption pressure by designing a closed-loop controller for the adsorption system. Figure 15 shows the closed-loop control system’s framework for the adsorption of the WMR. The input value was set according to the actual situation during the WMR operation. The system compares the input value with the negative feedback signal provided by the sensor to find the error, which the controller then corrects.

We assumed that the impeller fan motor satisfies the following conditions:

(a)

The waveform of the counter-electromotive force is an ideal flat-topped trapezoidal waveform;

(b)

The magnetic circuit of the motor is not saturated during rotation;

(c)

The eddy current and hysteresis losses of the motor are negligible.

By neglecting the current fluctuations in the motor and the diode voltage drop, the armature voltage balance equation for a rotating DC motor is:

$$U=Ri+L_0\frac{di}{dt}+K_{e}w$$

(10)

where $U$ is the motor armature voltage; $R=2r$ is the equivalent resistance; $i$ is the current in the motor; $K_e$ is the counter-electromotive force coefficient of the motor; $w$ is the equivalent output pressure corresponding to the motor speed; $L_0=2\left(L-M\right)$ is the equivalent inductance [34,35].

The equation for the torque balance of a DC motor is:

$$\left\{\begin{array}{c}{T}_e-T_l=J\frac{dw}{dt}+K_{b}w\\ T_e=K_{T}i\end{array}\right.$$

(11)

where $T_e$ is the electromagnetic torque; $K_T$ is the torque coefficient; $K_b$ is the damping coefficient; $J$ is the rotational inertia; and $T_l$ is the load torque.

This provides the differential equation for motor voltage and equivalent output pressure as follows:

$$\frac{d^{2}w}{d{t}^2}+a\frac{dw}{dt}+bw=cU$$

(12)

where $a=\frac{K_b{L}_0+RJ}{L_{0}J},b=\frac{K_{b}R+K_T{K}_e}{L_{0}J},c=\frac{K_T}{L_{0}J}$.

5.2. Sliding Mode Robust Controller

Equation (12) shows that the WMR adsorption system is a second-order non-linear system. Due to the presence of parameter uncertainty, gas leakage, and unknown disturbances, we designed a robust sliding mode controller to control the adsorption system [36,37]. The control block diagram for the adsorption system is shown in Figure 16. The following is the derivation of the control system. Firstly, Equation (12) is written as a state equation:

$$\left\{\begin{array}{c}{\dot{w}}_1=w_2 \\ {\dot{w}}_2=u+f\left(w\right)\end{array}\right.$$

(13)

where $f\left(w\right)=-a{w}_2-b{w}_1+\mathrm{\Delta }$ is the system unknown variable, $u=cU$ is the control input. Assuming that the pressure command is $w_d$, the error and its derivative are:

$$e=w_1-w_d, \dot{e}=w_2-{\dot{w}}_d$$

(14)

Define the sliding mode function as

$$s=ce+\dot{e}, c>0$$

(15)

$$\dot{s}=c\dot{e}+\ddot{e}=c\dot{e}+{\dot{w}}_2-{\ddot{w}}_d=c\dot{e}+f\left(w\right)+u-{\ddot{w}}_d$$

(16)

The RBF neural network structure proposed by Moody and Darken can approximate any continuous function with arbitrary accuracy [38,39,40]. Therefore, the RBF neural network can be used to approximate $f\left(w\right)$:

$$h_j=\exp \left(\frac{{\Vert \mathit{w}-d_j\Vert }^2}{2b_j^2}\right)$$

(17)

$$f\left(w\right)={\mathbf{W}}^{*T}\mathit{h}\left(\mathit{w}\right)+ϵ$$

(18)

where $\mathit{w}={\left[\begin{array}{cc}{w}_1& w_2\end{array}\right]}^{\mathit{T}}$ is the input to the network, $j$ is the $j$-th node of the hidden layer of the network, $\mathit{h}={\left[h_j\right]}^T$ is the output of the Gaussian basis function of the network, ${\mathbf{W}}^{*}$ is the ideal weight of the network, and $ϵ$ is the approximation error of the network $ϵ\le {ϵ}_N$.

The network input is obtained as $\mathit{w}={\left[\begin{array}{cc}{w}_1& w_2\end{array}\right]}^T$, then the network output is:

$$\widehat{f}\left(w\right)={\Phi }^T\mathit{h}\left(\mathit{w}\right)$$

(19)

where $\Phi$ is the actual network weight, due to

$$f\left(w\right)-\widehat{f}\left(w\right)=W^{*T}\mathit{h}\left(\mathit{w}\right)+ϵ-{\Phi }^T\mathit{h}\left(\mathit{w}\right)=-{\tilde{W}}^T\mathit{h}\left(\mathit{w}\right)+ϵ$$

(20)

Define the Lyapunov function as:

$$V=\frac{1}{2}{s}^2+\frac{1}{2\gamma }{\tilde{W}}^T\tilde{W}$$

(21)

where $\gamma >0, \tilde{W}=\Phi -W^{*}$.

$$\dot{V}=s\dot{s}+\frac{1}{\gamma }{\tilde{W}}^T\dot{\Phi }=s\left(c\dot{e}+f\left(w\right)+u-{\dot{w}}_d\right)+\frac{1}{\gamma }{\tilde{W}}^T\dot{\Phi }$$

(22)

The design control rate is

$$u=-c\dot{e}-\widehat{f}\left(w\right)+{\dot{w}}_d-\eta sgn\left(s\right)$$

(23)

$$\begin{array}{c}\dot{V}=s\left(f\left(w\right)-\widehat{f}\left(w\right)-\eta sgn\left(s\right)\right)+\frac{1}{\gamma }{\tilde{W}}^T\dot{\Phi } \\ =s\left(-{\tilde{W}}^T\mathit{h}\left(\mathit{w}\right)+ϵ-\eta sgn\left(s\right)\right)+\frac{1}{\gamma }{\tilde{W}}^T\dot{\Phi }\\ =ϵs-\eta \left|s\right|+{\tilde{W}}^T\left(\frac{1}{\gamma }\dot{\Phi }-s\mathit{h}\left(\mathit{w}\right)\right) \end{array}$$

(24)

Considering $\eta >{\left|ϵ\right|}_{max}$, the adaptive rate is:

$$\dot{\Phi }=\gamma s\mathit{h}\left(\mathit{w}\right)$$

(25)

Then, we obtained:

$$\dot{V}=ϵs-\eta \left|s\right|\le 0$$

(26)

The above analysis shows that $V\ge 0, \dot{V}\le 0$, $s$ and $W$ are bounded. Since $s=0$ when $\dot{V}=0$, it is clear from La Salle’s invariance principle that this closed loop system is asymptotically stable. It follows that when $t\to \infty$, then $s\to 0$, $e\to 0$ and $\dot{e}\to 0$. However, $V\ge 0, \dot{V}\le 0$, when $t\to \infty$, $V$ and $\Phi$ are bounded; however, it is not possible to prove that $\Phi$ is convergent. By setting the robust term $\eta sgn\left(s\right)$ as the control law, the approximation error of the neural network could be overcome and the system can be stabilised.

The above sliding mode robust control system was built by MATLAB software. The initial parameters of the control system are set as follows: the switching function is $\gamma =1500$, the number of neurons in the neural network is $7$, and the width of the centre point of the Gauss basis function of the $j$ neuron of the hidden layer $b_j=4$ is a constant and the coordinate matrix $\mathit{d}$ of the centre point of the neuron is set to:

$$\mathit{d}=\left[\begin{array}{c}\begin{array}{ccccccc}-3& -2& -1& 0& 1& 2& 3\end{array}\\ \begin{array}{ccccccc}-3& -2& -1& 0& 1& 2& 3\end{array}\end{array}\right]$$

(27)

The robot motor parameters are set as follows: rotor rotational inertia $J=0.01 {\mathrm{kgm}}^2$, electric potential constant $K_e=0.01 \mathrm{V}/\mathrm{rad}/\mathrm{s}$, inductance $L=0.5 \mathrm{H}$, motor viscous friction constant $K_m=K_b=0.1 \mathrm{Nms}$, $R=2 \mathsf{\Omega }$, motor torque constant $K_t=0.01 \mathrm{Nm}/\mathrm{n}$, and applied disturbance $f=-7w_1-4.5w_2+10\sin \left(2\pi t\right)$. The tracking simulation results based on the above model for the control pressure step and sinusoidal signals are shown in Figure 17. The analysis results showed that the sliding mode robust controller could quickly track and enter the steady state whether the input pressure signal is a step signal or a sinusoidal trajectory signal. The adaptive control law can quickly compensate for system modelling errors through autonomous learning and has a high degree of stability. The corresponding time of the closed-loop system is <1 s, and the steady-state error is 0.001 bar, which is a good control effect and meets the design requirements of the WMR control system.

6. Prototype and Test

6.1. Control System

The control system shown in Figure 18 includes constant speed control of the DC brushless motor, radio remote control of driven motors for two wheels, wireless/wired electronics of the camera, and ultrasound for transmitting the information. However, wireless power signals may be problematic in some cases, including the batteries’ weight and ability to transmit-receive signals for sensing and commands. The DC brushless motor with a speed sensor has been used for driving the impeller at speeds exceeding 10,000 RPM, the voltage is 24 V, and the maximum current is 35 A, providing more than 600 W power. The pressure was measured using a Freescale MPX2200DP sensor. In a robot-driven system, a high transmits gear system is used so that the motor can generate enough torque to the wheels, to support the robot and payload on the wall at any position. A radio remote control and drive system for a 1/10 scale electric power car was used directly. The drive system can generate great torque at lower speeds and enough power to hold the robot at zero speed.

6.2. Prototype Testing

One prototype was built based on the analysis and simulation results shown in Figure 19. In the prototype, the electric power derives from the power supplier via cables to avoid carrying a heavy battery. One solution is using a wireless power supply; however, it may generate a magnetic field unable to provide sufficient power. The preliminary experiment uses upper computer software to control the robot. In the operating interface, the reset button is pressed to wake up the robot’s main control chip; the forward button is pressed to allow the robot to follow the set path to complete its movement. To solve the problem of WMRs sliding on smooth walls, a bionic attachment material was chosen to coat the periphery of the wheels and increase the friction between the moving mechanism and the wall [41,42]. Our experimental results show that the developed WMR achieves strong adsorption and free crawling, has excellent wall adaptability and can fulfil the inspection needs on the outer wall of the vacuum chamber. This robot can also be used for the inspection of the inner wall of the reactor in the maintenance phase, but more investigations are expected since the neurons might influence the structure surface, and it is hard to predict the surface quality and radiation dose. Therefore, the radiation protection of onboard electronic equipment must be investigated.

7. Conclusions

We designed a special WMR that can move freely on non-magnetic material surfaces, perform the NDT test for the welding defect, and inspect the first-wall surface of DEMO and other fusion reactors. Based on the structural characteristics of the WMR, we established a kinematic model of the WMR and a trajectory-tracking control method based on the tractrix principle. The impeller is designed based on the vortex principle; aerodynamic and finite element analysis were also studied to optimize the parameters of the robot structure. Based on the principle of negative pressure adsorption for WMRs, a sliding-mode robust pressure control system was designed and validated by simulation. The control law can quickly compensate for system modelling errors through autonomous learning and has a high degree of stability. The corresponding time of the closed-loop system is <$1 \mathrm{s}$, and the steady-state error is <$0.001 \mathrm{bar}$, which is a good control effect that meets the requirements of the WMR pressure control system. Finally, a prototype was built, and the validity of the design method was verified. In the near future, we will test a full self-power robot with a visual camera and ultrasonic sensor and investigate the possibility of adopting this kind of robot system in other areas.