## 2 System Design and Optimization  
### Overall Structural Design of Robot (LAWCDR)  
The overall design of the land-air-wall cross-domain is shown in Figure 1, which mainly includes the ground module, the flight module, and the adsorption module. The ground module consists of the front wheels with shock absorbers and an omni-directional rear wheel. The robot turns by the differential speed of the two front wheels. The shock absorber is mainly responsible for providing a certain cushioning force and correcting heading when the robot contacts the wall during the adsorption process. The shock absorber does not work when it is on the ground, and the spring stretches to its maximum stroke under gravity.  
The flight module mainly includes four rotor motors and the corresponding propellers, which are responsible for flying in three-dimensional space. The adsorption module consists of a suction cup, a vacuum pump, support bars, carbon tubes and silicone tubes connecting the various parts, and two RS485 servos responsible for the movement of the suction cup. While perching on the wall, the support bars prevent the suction cup from peeling off  
Figure 1: The overall structure of the robot (LAWCDR).  
the wall due to the rotational torque generated by gravity. In addition, the wheel and the support bars work together to prevent the propellers from contacting the wall.  
The structure and coordinates of the robot are shown in Figure 2, and the inertial coordinate system is represented by \(O_{w}\), \(O_{b}\), \(O_{h}\), and \(O_{c}\) respectively, where \(O_{w}\) denotes the world coordinate system and \(O_{b}\) denotes the body coordinate system. \(T_{i}\) denotes the lift generated by the \(i\)th rotor. The angular bisector of the second and third motors is taken as the \(y\)-axis, and the angular bisector of the third and fourth motors is taken as the \(x\)-axis. \(O_{h}\) and \(O_{c}\) denote the coordinate systems represented by the first and second joints, and \(O_{c}\) coincides with the suction cup end coordinate system. The \(x\)-axis distance from the rotor to the geometric center of the body is \(l\), the distance from the first joint to the second joint is \(d_{2}\), and the first joint is fixedly connected to the robot. The distance between the second joint and the suction cup is \(d_{1}\). \(h\) denotes the \(z\)-axis distance of \(O_{h}\) of the body coordinate system.  
As shown in Figure 3, the robot can generally be divided into four working states. (a) Flight state: when the servo is adjusted to the best position, the power consumption is reduced according to the mass distribution. (b) Preparation state: as a preparatory state for adsorption, the suction cup is adjusted to appropriate position to reduce the robot's reaction time when the wheels are in contact with the wall. (c) Adsorption state: a single-line LIDAR is used to detect the relative position and attitude between the robot and the wall. The head and front claws of the robot are controlled to face the wall. After the robot detects its contact with the wall, the robot controls the servo to reach forward to achieve adsorption. (d) Roost state: at this time, the propellers and servos are stopped to save power and reduce heat. The robot adsorbs on the wall under the action of the vacuum pump and support bars. Because the body is in a free state, the front wheels are compressed, but they still prevent propellers from contacting the wall.  
Figure 2: Structure and coordinates of the robot (LAWCDR).