Investigating the Obstacle Climbing Ability of a Coal Mine Search-and-Rescue Robot with a Hydraulic Mechanism

: Due to the perilous conditions in coal mine accidents, trapped people need to be rescued as soon as possible. The danger and complexity of this environment have brought great difﬁculties for search and rescue. The emergence of rescue robots has addressed this problem, and the improvement of their search-and-rescue ability is a key concern for rescue robot designers. Based on previous experience of a tracked mobile robot, this paper proposes a new solution via the addition of adjustive rocker arms. For this purpose, a hydraulic unit is installed between the rocker arms and the robot, which enables the rocker arms to be pulled back and forth, enabling its adaptation to more complex environments. In addition, based on kinematics equations, by analyzing the motion rules and characteristics of climbing typical obstacles including stairs, grooves, and lug steps, the present research not only works out the centroid coordinates but also explores the maximal obstacle height. The results show that when the rocker arms are extended by hydraulic pressure, the obstacle-climbing height of the robot increases 16.7 percent. This demonstrates the improvement in obstacle climbing ability and rescue efﬁciency in complex environments.


Introduction
Robots were originally mainly used in industrial production such as for automobiles and household appliances. Germany, Japan, and other countries have actively developed industrial robot technology, which brings them higher efficiency, lower labor force requirements, and a strong economy. In the 21st century, robotics has thrived in the rapid development of computers and control technology. Moreover, with the advancement of society, robots are not merely used to serve industrial production but also to handle more complex and diverse tasks. Therefore, with the advantage of strong adaptation to the environment, more and more mobile robots have been used in disaster relief, dangerous goods transportation, and other dangerous or difficult operations.
In the 1980s, researchers proposed the application of mobile robots in disaster relief. However, such mobile robots were not invented until 1995. In 2001, rescue robots were used in the United States' "9/11" incident, attracting the attention of many researchers. Although the robots had performed well in this rescue operation, there were also many problems, such as instability, inferior waterproofing, limited vision, and so on [1]. After this incident, the scientific research institutions in the United States paid more attention to rescue robot research. Of these, iRobot's Packbot and the Warrior series of tracked rescue robots have been well used [2]. For example, the latter can be operated remotely; it is about 90 cm long, 80 cm wide, and 53 cm high and its total mass is 250 kg. Equipped with a mechanical arm, it can enter areas that are difficult to reach for human beings. In addition, unmanned aerial robots are also widely used in disaster relief. In addition to the military and commercial applications of drones, they are efficient in supporting emergency management [3]. The cameras and sensors carried by drones can also facilitate The rocker arm and the main body of the conventional tracked search-and-rescue robot are interconnected, the rocker arm cannot be extended, and the robot's ability to cross obstacles is fixed. The structure of an existing tracked search-and-rescue robot is shown in Figure 1. Appl. Sci. 2022, 12, x FOR PEER REVIEW 3 of 15 gravity can be changed flexibly, enabling it to cross wider grooves and steps, improving the robot's ability to climb obstacles. At the same time, the main crawler and the rocker arm are driven by separate motors to enhance its driving capability.

Robot Design Scheme
The rocker arm and the main body of the conventional tracked search-and-rescue robot are interconnected, the rocker arm cannot be extended, and the robot's ability to cross obstacles is fixed. The structure of an existing tracked search-and-rescue robot is shown in Figure 1. The whole design scheme of the search-and-rescue robot proposed in this paper is shown in Figure 2. In the Figure 2: 1 indicates the main crawler of the robot, 2 is the rocker arm crawler, and 3 is the hydraulic mechanism between the rocker arm and the robot body.

Hydraulic Mechanism Analysis
The structure of the search-and-rescue robot was drawn using SolidWorks software to obtain a design sketch. This design scheme refers to the work in [27], installing a hydraulic mechanism between the rocker arm and the main body of the robot (part 3 in Figure 2). The working principle is that the hydraulic cylinder in mechanism 3 converts hydraulic energy into mechanical energy to perform a linear reciprocating motion. The The whole design scheme of the search-and-rescue robot proposed in this paper is shown in Figure 2.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 3 of 15 gravity can be changed flexibly, enabling it to cross wider grooves and steps, improving the robot's ability to climb obstacles. At the same time, the main crawler and the rocker arm are driven by separate motors to enhance its driving capability.

Robot Design Scheme
The rocker arm and the main body of the conventional tracked search-and-rescue robot are interconnected, the rocker arm cannot be extended, and the robot's ability to cross obstacles is fixed. The structure of an existing tracked search-and-rescue robot is shown in Figure 1. The whole design scheme of the search-and-rescue robot proposed in this paper is shown in Figure 2. In the Figure 2: 1 indicates the main crawler of the robot, 2 is the rocker arm crawler, and 3 is the hydraulic mechanism between the rocker arm and the robot body.

Hydraulic Mechanism Analysis
The structure of the search-and-rescue robot was drawn using SolidWorks software to obtain a design sketch. This design scheme refers to the work in [27], installing a hydraulic mechanism between the rocker arm and the main body of the robot (part 3 in Figure 2). The working principle is that the hydraulic cylinder in mechanism 3 converts hydraulic energy into mechanical energy to perform a linear reciprocating motion. The Design scheme of the search-and-rescue robot. 1 indicates the main crawler of the robot, 2 is the rocker arm crawler, and 3 is the hydraulic mechanism between the rocker arm and the robot body.

Hydraulic Mechanism Analysis
The structure of the search-and-rescue robot was drawn using SolidWorks software to obtain a design sketch. This design scheme refers to the work in [27], installing a hydraulic mechanism between the rocker arm and the main body of the robot (part 3 in Figure 2). The working principle is that the hydraulic cylinder in mechanism 3 converts hydraulic energy into mechanical energy to perform a linear reciprocating motion. The flexibility of the hydraulic mechanism allows the robot's rocker arm to extend back and forth, thereby improving the robot's ability to climb over obstacles such as steps.

Simplified Model of the Search-and-Rescue Robot
A simplified model of the search-and-rescue robot with two poses is shown in Figure 3. flexibility of the hydraulic mechanism allows the robot's rocker arm to extend back and forth, thereby improving the robot's ability to climb over obstacles such as steps.

Simplified Model of the Search-and-Rescue Robot
A simplified model of the search-and-rescue robot with two poses is shown in Figure 3.  The definitions of the letters in Figure 3 are shown in Table 1. The definitions of the letters in Figure 3 are shown in Table 1. Center of gravity of the main body of the robot Center of gravity of the robot's rocker arm The minimum center distance of the large wheels at both ends when the rocker arm is retracted and extended The maximum center distance of the large wheels at both ends when the rocker arm is retracted and extended Distance from the center of gravity of the robot body to the center of the rear wheel L 3 Distance between the centers of the two wheels on the robot rocker arm L 4 Distance from the center of gravity of the rocker arm to the center of the rear wheel of the rocker arm γ Swing angle of the rocker arm η Pitch angle of the robot body R Big wheel radius r Small wheel radius Figure 3 shows the simplified structure of the search-and-rescue robot. The coordinate system was established for the robot through RPY transformation [28]. X 0 OY 0 is the fixed coordinate system of the crawler wheel at the rear of the robot body, that is, the global coordinate system. X 1 OY 1 is the main transformed coordinate system, while X 2 OY 2 is the Appl. Sci. 2022, 12, 10485 5 of 14 coordinate system of the rocker arm. The counterclockwise rotation direction was set as the positive direction.

Transformation between the Body Coordinate System and Global Coordinate System
The coordinate system X 1 OY 1 is rotated relative to the coordinate system X 0 OY 0 , i.e., it is rotated δ, θ, and η degrees around the X-, Y-, and Z-axes, respectively. Then the RPY equivalent rotation matrix 0 1 R zyx (η, θ, δ) can be obtained. Because the rotation in each direction is around the corresponding axis of the reference coordinate system, we can obtain [28]: where In the above equation, sin and cos are represented by s and c, respectively. Substituting into Equation (1), one can obtain: The transformation matrix of the body coordinate system X 1 OY 1 relative to the fixed coordinate system X 1 OY 1 can then be obtained: where T rans (Px, Py, Pz) is the translational transformation matrix, and Px, Py, and Pz are the translation vectors of each coordinate axis, respectively. When the robot actually climbs the steps, the robot only rotates around the Z-axis. Therefore, θ = 0, δ = 0, and Pz = 0. Substituting these into the above equation, one can obtain:

Transformation between the Centroid Coordinate System and Body Coordinate System
The translation transformation matrix of the robot rocker arm coordinate system relative to the main body coordinate system is as follows: The homogeneous matrix of the mass center of the robot body and the rocker arm in its own coordinate system is as follows: From the literature [28], the centroid matrix from the robot coordinate system to the fixed coordinate system can be obtained: where L 2 is the distance from the mass center of the robot to the coordinate system X 0 OY 0 . When the rocker arm is fully extended, the simplified model of the robot is as shown in Figure 3b. From the figure, we can see that the entire robot is stretched at this time. This is mainly reflected in the distance between the coordinate system X 0 OY 0 and the coordinate system X 1 OY 1 , which changes from L 1 to L 11 . If other data remain unchanged, the related transformation matrix will also change accordingly.
Similarly, the mass center matrix of the robot in the fixed coordinate system is:

Analysis of the Rocker Arm in a Retracted State during Step Crossing
By determining the relationship between the center of mass and the angle of rotation, the theoretical height for the robot climbing the step can be analyzed [29].
Considering Figure 4d, it can be concluded that the robot can climb the step smoothly only when the center of gravity is higher than the edge of the step. Therefore, further analysis of this part was performed to establish a coordinate system with the axis of the rear crawler wheel of the robot as the coordinate origin.

Analysis of the Rocker Arm in a Retracted State during Step Crossing
By determining the relationship between the center of mass and the angle of rotation, the theoretical height for the robot climbing the step can be analyzed [29].
Considering Figure 4d, it can be concluded that the robot can climb the step smoothly only when the center of gravity is higher than the edge of the step. Therefore, further analysis of this part was performed to establish a coordinate system with the axis of the rear crawler wheel of the robot as the coordinate origin. As shown in Figure: (a) the start of the climbing process, and the rocker arm starts to touch the step; (b) the robot is ready to climb, and the rocker arm is already on the step; (c) crossing over; (d) the critical point of climbing-at this point, the center of gravity of the robot and the contact point are on the same vertical line; (e) the end of the climb, at which point the robot has climbed the step completely.
The mathematical model of the climbable obstacle height of the robot can be obtained from the geometric relationship of Figure 5: The mathematical model of the climbable obstacle height of the robot can be obtained from the geometric relationship of Figure 5: where R is the radius of the large wheel of the robot, H is the height of the step, X G is the coordinate of the mass center on the X-axis, and Y G is the coordinate of the mass center on the Y-axis.  where R is the radius of the large wheel of the robot, H is the height of the step, X0 is the coordinate of the mass center on the X-axis, and Y0 is the coordinate of the mass center on the Y-axis. It can be seen from Figure 4a that η = 0 at this time. Combined with Equation (7), one can obtain: where γ is the swing angle of the rocker arm, and η is the pitch angle of the robot. The design parameters of the robot are: To determine the relationship between the height H of the step and the angle γ, η, first, the first and second derivatives of γ and η in Equation (9) must be determined. When the robot climbs the step, γ is in the range (0, 2π), and η is in the range (0, π/2). Therefore, when the first-order derivative is zero and the second-order derivative is less than zero, H is the largest. That is, when the rocker arm is horizontal (η + γ = 2π), the robot reaches the maximum height Hmax of climbing the step. Finally, the parameters of the robot are substituted into Equations (9) and (10). The mathematical model related to H is solved using the simulation software optimization toolbox and is simulated to obtain the relationship between the height H of the robot across the step and the swing angle γ of the rocker arm, as well as the pitch angle η of the robot body.
In Figure 6, γ is the rocker arm swing angle, and η is the pitch angle. From the simulation results, one can learn that when γ = 5.4605 rad and η = 0.8227 rad, the maximum height when the robot climbs the step is Hmax = 187.74 mm. That is, η + γ = 6.2832 ≈ 2π. It can be seen from Figure 4a that η = 0 at this time. Combined with Equation (7), the coordinate formula of robot centroid can be obtained: where γ is the swing angle of the rocker arm, and η is the pitch angle of the robot. The design parameters of the robot are: G = 38 kg; m 1 = 30 kg; m 2 = 8 kg; L 1 = 510 mm; L 2 = 255 mm; L 3 = 300 mm; L 4 = 115 mm; h 2 = 70 mm; R = 100 mm; r = 30 mm.
To determine the relationship between the height H of the step and the angle γ, η, first, the first and second derivatives of γ and η in Equation (9) must be determined. When the robot climbs the step, γ is in the range (0, 2π), and η is in the range (0, π/2). Therefore, when the first-order derivative is zero and the second-order derivative is less than zero, H is the largest. That is, when the rocker arm is horizontal (η + γ = 2π), the robot reaches the maximum height H max of climbing the step. Finally, the parameters of the robot are substituted into Equations (9) and (10). The mathematical model related to H is solved using the simulation software optimization toolbox and is simulated to obtain the relationship between the height H of the robot across the step and the swing angle γ of the rocker arm, as well as the pitch angle η of the robot body.
In Figure 6, γ is the rocker arm swing angle, and η is the pitch angle. From the simulation results, one can learn that when γ = 5.4605 rad and η = 0.8227 rad, the maximum height when the robot climbs the step is H max = 187.74 mm. That is, η + γ = 6.2832 ≈ 2π.
When the robot crosses the barrier, it first needs the rocker arm to be able to touch the end of the step, and then the rocker arm and the main body need to be in a straight line during the crossing process. The robot's center of gravity should exceed the contact point between the robot and the step so that the crossing can be carried out smoothly. It can be seen from the figure that when the pitch angle is 0, the swing angle of the rocker arm has no effect on the obstacle height of the robot; when the swing angle of the rocker arm is 0, a change of the pitch angle will result in a change of the obstacle height of the robot. This shows that the pitch angle has a greater influence on the robot's obstacle height, which is consistent with the robot's obstacle clearance. This also shows that the above analysis is correct. where R is the radius of the large wheel of the robot, H is the height of the step, X0 is the coordinate of the mass center on the X-axis, and Y0 is the coordinate of the mass center on the Y-axis. It can be seen from Figure 4a that η = 0 at this time. Combined with Equation (7), one can obtain: where γ is the swing angle of the rocker arm, and η is the pitch angle of the robot. The design parameters of the robot are: To determine the relationship between the height H of the step and the angle γ, η, first, the first and second derivatives of γ and η in Equation (9) must be determined. When the robot climbs the step, γ is in the range (0, 2π), and η is in the range (0, π/2). Therefore, when the first-order derivative is zero and the second-order derivative is less than zero, H is the largest. That is, when the rocker arm is horizontal (η + γ = 2π), the robot reaches the maximum height Hmax of climbing the step. Finally, the parameters of the robot are substituted into Equations (9) and (10). The mathematical model related to H is solved using the simulation software optimization toolbox and is simulated to obtain the relationship between the height H of the robot across the step and the swing angle γ of the rocker arm, as well as the pitch angle η of the robot body.
In Figure 6, γ is the rocker arm swing angle, and η is the pitch angle. From the simulation results, one can learn that when γ = 5.4605 rad and η = 0.8227 rad, the maximum height when the robot climbs the step is Hmax = 187.74 mm. That is, η + γ = 6.2832 ≈ 2π. When the robot crosses the barrier, it first needs the rocker arm to be able to touch the end of the step, and then the rocker arm and the main body need to be in a straight line during the crossing process. The robot's center of gravity should exceed the contact point between the robot and the step so that the crossing can be carried out smoothly. It can be seen from the figure that when the pitch angle is 0, the swing angle of the rocker arm has no effect on the obstacle height of the robot; when the swing angle of the rocker arm is 0, a change of the pitch angle will result in a change of the obstacle height of the robot. This shows that the pitch angle has a greater influence on the robot's obstacle height, which is consistent with the robot's obstacle clearance. This also shows that the above analysis is correct. Figure 7 is a simplified diagram of the robot climbing a step when the rocker arm is extended. At this point, the robot rocker arm is fully extended, the overall size of the robot becomes longer, and the center of mass also moves forward. As shown in Figure 7: This process is similar to Figure 4. (a) the start of the climbing process, and the rocker arm starts to touch the step; (b) the robot is ready to climb, and the rocker arm is already on the step; (c) crossing over; (d) the critical point of climbingat this point, the center of gravity of the robot and the contact point are on the same vertical line; (e) the end of the climb, at which point the robot has climbed the step completely. Figure 8 shows the robot at the critical point of climbing-at this point, the center of gravity of the robot and the con-tact point are on the same vertical line.   When the robot crosses the barrier, it first needs the rocker arm to be able to touch the end of the step, and then the rocker arm and the main body need to be in a straight line during the crossing process. The robot's center of gravity should exceed the contact point between the robot and the step so that the crossing can be carried out smoothly. It can be seen from the figure that when the pitch angle is 0, the swing angle of the rocker arm has no effect on the obstacle height of the robot; when the swing angle of the rocker arm is 0, a change of the pitch angle will result in a change of the obstacle height of the robot. This shows that the pitch angle has a greater influence on the robot's obstacle height, which is consistent with the robot's obstacle clearance. This also shows that the above analysis is correct. Figure 7 is a simplified diagram of the robot climbing a step when the rocker arm is extended. At this point, the robot rocker arm is fully extended, the overall size of the robot becomes longer, and the center of mass also moves forward. As shown in Figure 7: This process is similar to Figure 4. (a) the start of the climbing process, and the rocker arm starts to touch the step; (b) the robot is ready to climb, and the rocker arm is already on the step; (c) crossing over; (d) the critical point of climbingat this point, the center of gravity of the robot and the contact point are on the same vertical line; (e) the end of the climb, at which point the robot has climbed the step completely. Figure 8 shows the robot at the critical point of climbing-at this point, the center of gravity of the robot and the con-tact point are on the same vertical line.  It can be seen from Figure 3b that when the rocker arm extends, the distance between the coordinate system X0OY0 and the coordinate system X2OY2 changes from L1 to L11. At this point, L11 = 710 mm.

Analysis of the Rocker Arm in an Extended State during Step Crossing
If the other relevant data of the robot remains unchanged, Figure 9 is obtained by MATLAB simulation: It can be seen from Figure 3b that when the rocker arm extends, the distance between the coordinate system X 0 OY 0 and the coordinate system X 2 OY 2 changes from L 1 to L 11 . At this point, L 11 = 710 mm.
If the other relevant data of the robot remains unchanged, Figure 9 is obtained by MATLAB simulation: It can be seen from Figure 3b that when the rocker arm extends, the distance between the coordinate system X0OY0 and the coordinate system X2OY2 changes from L1 to L11. At this point, L11 = 710 mm.
If the other relevant data of the robot remains unchanged, Figure 9 is obtained by MATLAB simulation: In the Figure 9: (a), the relationship between H and γ (b), and the relationship between H and η (c).
According to the simulation results, when γ = 5.4320 rad and η = 0.8512 rad, the maximum height for the robot climbing the step is Hmax = 219.01 mm. At this point, η + γ = 6.2832 ≈ 2π, which is still consistent with the analysis. When the rocker arm is extended, the maximum height for the robot climbing the step is increased by 16.7%. It can also be seen from Figure 9 that whether the rocker arm is extended or retracted, the obstacle height of the robot will vary according to the swing angle and pitch angle of the rocker arm. It can be seen that when the hydraulic mechanism is added, the obstacle-climbing ability of the search-and-rescue robot is improved to a certain extent, improving its rescue efficiency when the rescue is underground. According to the simulation results, when γ = 5.4320 rad and η = 0.8512 rad, the maximum height for the robot climbing the step is H max = 219.01 mm. At this point, η + γ = 6.2832 ≈ 2π, which is still consistent with the analysis. When the rocker arm is extended, the maximum height for the robot climbing the step is increased by 16.7%. It can also be seen from Figure 9 that whether the rocker arm is extended or retracted, the obstacle height of the robot will vary according to the swing angle and pitch angle of the rocker arm. It can be seen that when the hydraulic mechanism is added, the obstacle-climbing ability of the search-and-rescue robot is improved to a certain extent, improving its rescue efficiency when the rescue is underground.

Analysis of the Rocker Arm in a Retracted State during Stairs Climbing
The ability to climb stairs, shown in Figure 10, is an important performance index of coal mine search-and-rescue robots [30]. Appl

Analysis of the Rocker Arm in a Retracted State during Stairs Climbing
The ability to climb stairs, shown in Figure 10, is an important performance index of coal mine search-and-rescue robots [30]. In the Figure 10: (a) the start of stairs climbing when the rocker is on the first step; (b-e) the stairs climbing process; (c) the three-point contact of the first step, the second step, and the ground; (f) the completion of the stairs climbing process and the robot is fully on the top step. Figure 11 shows a partial schematic diagram of the robot climbing a stairs.  Figure 11 shows a partial schematic diagram of the robot climbing a stairs. Figure 10. The entire process of climbing a stairs.
In the Figure 10: (a) the start of stairs climbing when the rocker is on the first ste (b-e) the stairs climbing process; (c) the three-point contact of the first step, the secon step, and the ground; (f) the completion of the stairs climbing process and the robot fully on the top step. Figure 11 shows a partial schematic diagram of the robot climbing a stairs. Figure 11. Process of climbing a stairs.
In the Figure 11: (a) the point where the robot rocker arm starts to touch the first ste (b) the robot climbing the stairs.
It can be concluded from Figure 11 that for the robot to continuously climb the stai it needs to meet the following conditions: Here, after satisfying Formula (11), the robot can put the rocker arm on the first ste After satisfying Formula (12), the robot will be able to climb the stairs continuously. Equ tions (11) and (12) are necessary conditions for the robot to climb the stairs continuous Through field measurements in the laboratory building, the relevant data were obtaine H = 164 mm, and T = 283 mm. At this point, 2 2 2 H T + =654.17 mm and L1 + L3 = 8 mm. The design parameters of the robot then satisfy Equations (11) and (12), so the rob can climb the stairs smoothly.

Analysis of the Rocker Arm in an Extended State during Stairs Climbing
The ability to climb stairs, shown in Figure 12: It can be concluded from Figure 11 that for the robot to continuously climb the stairs, it needs to meet the following conditions: Here, after satisfying Formula (11), the robot can put the rocker arm on the first step. After satisfying Formula (12), the robot will be able to climb the stairs continuously. Equations (11) and (12) are necessary conditions for the robot to climb the stairs continuously. Through field measurements in the laboratory building, the relevant data were obtained: H = 164 mm, and T = 283 mm. At this point, 2 √ H 2 + T 2 = 654.17 mm and L 1 + L 3 = 810 mm. The design parameters of the robot then satisfy Equations (11) and (12), so the robot can climb the stairs smoothly.

Analysis of the Rocker Arm in an Extended State during Stairs Climbing
The ability to climb stairs, shown in Figure 12: Appl. Sci. 2022, 12, x FOR PEER REVIEW 12 Figure 12. The whole process of climbing a stairs. Figure 12 is a diagram of the stairs climbing process when the rocker arm is extend By adjusting the hydraulic mechanism, the rocker arm is fully extended forward so the rocker arm and the main crawler are in the same straight line, which increases length of the search-and-rescue robot. As a result, the contact between the robot and stairs will become longer, thereby improving the climbing ability and stability of the ro during the stairs climbing process. Figure 13 shows a partial schematic diagram of the robot climbing a stairs.  Figure 12 is a diagram of the stairs climbing process when the rocker arm is extended. By adjusting the hydraulic mechanism, the rocker arm is fully extended forward so that the rocker arm and the main crawler are in the same straight line, which increases the length of the search-and-rescue robot. As a result, the contact between the robot and the stairs will become longer, thereby improving the climbing ability and stability of the robot during the stairs climbing process. Figure 13 shows a partial schematic diagram of the robot climbing a stairs.
By adjusting the hydraulic mechanism, the rocker arm is fully extended forward so that the rocker arm and the main crawler are in the same straight line, which increases the length of the search-and-rescue robot. As a result, the contact between the robot and the stairs will become longer, thereby improving the climbing ability and stability of the robot during the stairs climbing process. Figure 13 shows a partial schematic diagram of the robot climbing a stairs. In the Figure 13: (a) the point where the robot rocker arm starts to touch the first step; (b) the robot climbing the stairs.
It can be concluded from Figure 13 that for the robot to continuously climb the stairs, it needs to meet the following conditions: Through calculation, it is obtained that L11 + L3 = 1010 mm, and the value of 2 2 2 H T + is unchanged, which satisfy Equation (13) and Equation (14), so the robot can also climb the stairs smoothly. After analysis, it can be seen that when the robot rocker arm is fully extended, the sum of the robot body and the rocker arm is the longest. Understandably, after adding the hydraulic mechanism, the robot's ability to climb the stairs will be improved. This shows that the ability of the robot to overcome obstacles is significantly improved after adding a hydraulic mechanism.

Experimental Testing
In this paper, experimental tests were conducted with a conventional tracked robot to verify the reliability of the simulation data through experiments.
As shown in Figure 14, a conventional tracked robot of the same size was used here for the experiment. Through the experiment, it was found that the maximum height of the robot over the barrier was about 195 mm, and this result was higher than the simulation result. This is because the robot used in the experiment was equipped with some It can be concluded from Figure 13 that for the robot to continuously climb the stairs, it needs to meet the following conditions: Through calculation, it is obtained that L 11 + L 3 = 1010 mm, and the value of 2 √ H 2 + T 2 is unchanged, which satisfy Equations (11) and (13), so the robot can also climb the stairs smoothly.
After analysis, it can be seen that when the robot rocker arm is fully extended, the sum of the robot body and the rocker arm is the longest. Understandably, after adding the hydraulic mechanism, the robot's ability to climb the stairs will be improved. This shows that the ability of the robot to overcome obstacles is significantly improved after adding a hydraulic mechanism.

Experimental Testing
In this paper, experimental tests were conducted with a conventional tracked robot to verify the reliability of the simulation data through experiments.
As shown in Figure 14, a conventional tracked robot of the same size was used here for the experiment. Through the experiment, it was found that the maximum height of the robot over the barrier was about 195 mm, and this result was higher than the simulation result. This is because the robot used in the experiment was equipped with some equipment at the upper end, which made the robot's center of gravity higher, thus increasing the height of the robot over the barrier.

Discussion
Search-and-rescue robots need to face complex rescue environments, and it is necessary for them to be able to exhibit greater obstacle-crossing performance in a limited environment in the rescue process. The two-stage crawler search-and-rescue robot designed in this paper has a better obstacle-crossing capability than the traditional two-stage crawler robot, which can improve the rescue efficiency. The main compared parameters are shown in Table 2. Table 2. Comparison of parameters before and after improvement

Discussion
Search-and-rescue robots need to face complex rescue environments, and it is necessary for them to be able to exhibit greater obstacle-crossing performance in a limited environment in the rescue process. The two-stage crawler search-and-rescue robot designed in this paper has a better obstacle-crossing capability than the traditional two-stage crawler robot, which can improve the rescue efficiency. The main compared parameters are shown in Table 2. In this paper, a hydraulic mechanism is added to an existing two-stage crawler searchand-rescue robot to enhance the robot's barrier-crossing capability. However, this solution faces some challenges: 1. The overall mass of the robot also increases with the addition of the hydraulic mechanism, which reduces the mobility of the robot and thus affects the rescue efficiency.
2. As the rescue environment is more complex, the added hydraulic mechanism will be affected by the external environment, which will also affect the rescue efficiency.
3. The position of the robot's center of gravity affects the robot's ability to cross obstacles. The robot's structure can be improved to raise its center of gravity, which will further enhance the robot's ability to cross obstacles.
In response to these challenges, further research will take this as an entry point to continue optimizing the overall structure of the rescue robot, which can then be better adapted to a rescue environment.

Conclusions
In this paper, a two-stage crawler search-and-rescue robot is designed. The front rocker arm can adjust the movement posture. At the same time, the front rocker arm and the main body of the robot are connected by a hydraulic mechanism, which can realize the expansion and contraction of the rocker arm, improving the obstacle climbing ability of the search-and-rescue robot. The coordinate systems of each part and the whole of the robot are established through RPY transformation, and the coordinates of the mass center of the robot when the rocker arm is extended and retracted are calculated. Through simulation analysis, the theoretical maximum obstacle height of the robot in the two states is obtained. Through the analysis, it is found that when the robot's rocker arm extends, its obstacle-climbing ability is significantly improved. The detailed simulation results are as follows: 1. The designed robot has a maximum crossing height of 219.01 mm when crossing the obstacle, which is 16.7% higher than a conventional search-and-rescue robot of the same size.
2. The designed robot has a maximum climbing length of 1100 mm when climbing stairs, which is a 24.7% improvement in climbing capacity compared to conventional search-and-rescue robots of the same size.
This provides a new solution for the design of search-and-rescue robots in the future, which at the same time also provides a theoretical basis for the motion control of robots in actual disaster relief and rescue.

Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.

Data Availability Statement:
The data used to support the findings of this study are available from the corresponding author upon request.