## 2 System Design and Optimization
### Design and Analysis of the Adsorption of Bionic Structures  
The robot (LAWCDR) mainly mimics the process of a gecko perching on a vertical surface even after the collision, rather than being bounced off. In [23], [PERSON] analyzed the slow motion of an Asian flat-tailed gecko (Hamidactylus platyurus) jumping from trunk to trunk, which allows the gecko to grasp the trunk through the sticky toe pads of its hind paws when it is bounced back from a vertical surface, with the tail providing leverage for the gecko to counteract the moment of flipping backward and again allowing the front paws to contact with the wall. The researchers designed a simulated gecko equipped with four Velcro feet and a tail to control the body flexion of the gecko through internal tendons. Experiments have shown that the simulated gecko with the tail was able to increase the adsorption success rate from 15% to 55%. In nature, the tail helps the gecko increase its landing success rate from nearly 0% to 87%. We mimic the spine of a gecko by shock absorbers and a two servos mechanism. When the wheels come into contact with the wall, the moment causes the body to rotate and affects the forward reaching of the suction cup. The front claws keep stretching out in order to improve the success rate of the adsorption. The wheels (near claws) stay on the wall and provide guidance of the heading before the front claw stretches out and makes contact with the wall. As shown in Figure 4, (a) the wheels (rear claws) start to contact the wall. (b) The wheels (rear claws) are compressed to produce a tilting moment. (c) The robot uses the lift force generated by the propeller to attach the wheels to the wall. (d) The suction cup (head) and support bars (front claws) are driven towards the wall by adjusting the posture with the servos (spine). (e) The suction cup is attached to the wall, establishes a negative pressure environment, and makes the robot adsorb to the wall. The rotor stops working. Panel (f) indicates the bionic function of each component. Figure 3: Four working states of the robot (LAWCDR). (a) Flight state. (b) Preparation state. (c) Adsorption state. (d) Roost state. The structural dimensions of the robot (LAWCDR) are shown in Figure 5. The model of the wheel-wall contact can be represented as  
\[\left\{ \begin{array}{l}M_{\theta}=F_{L}d_{wl}+F_{R}d_{ur}-lk_{f}\omega_{1}^{2}- lk_{f}\omega_{2}^{2}+lk_{f}\omega_{3}^{2}+lk_{f}\omega_{4}^{2}+M_{G}\\ M_{\varphi}=F_{L}l_{3}-F_{R}l_{3}+k_{m}\omega_{1}^{2}-k_{m}\omega_{2}^{2}+k_{m }\omega_{3}^{2}-k_{m}\omega_{4}^{2}\end{array} \right. \tag{1}\]  
where \(M_{\theta}\) and \(M_{\varphi}\) are the \(y\)-axis and \(z\)-axis moment. \(M_{G}\) is the gravitational moment. \(F_{L}\) and \(F_{R}\) are the equivalent contact forces of the left and right wheel on the wall. \(d_{wl}\) and \(d_{ur}\) are the \(z\)-axis distances of the left and right wheel contact points with the wall in the body coordinate system, and \(l_{3}\) is the \(y\)-axis distance from the two front wheels to the center of the body. \(\omega_{i}\) is the rotational speed of the \(i\)th rotor. Take the left wheel as an example. \[d_{wl}=r_{q}\cos(\sigma_{L}-\theta)+l\sin\theta \tag{2}\]  
\[F_{L}d_{wl}-k_{s}\bullet r_{w}\sin(\sigma_{0}+\sigma_{L})\sqrt{h_{1}^{2}+h_{2} ^{2}}=I_{w}\tilde{\sigma}_{L} \tag{3}\]  
where \(I_{w}\) is the rotational inertia of the wheel assembly. \(k_{s}\) is the coefficient of elasticity of the spring. \(r_{w}\) is the rotation radius of the spring assembly. \(r_{q}\) is the rotation radius of the wheel assembly. \(h_{1}\) and \(h_{2}\) are the \(x\)-axis distance and \(z\)-axis distance of the spring mount point in the body coordinate system, respectively. \(\sigma_{L}\) is the angle between the carbon tube of the wheel assembly and the \(z\)-axis in the body coordinate system. \(h_{p}\) is the height of the propeller in the body coordinate system. \(R\) is the radius of the propeller. \(r\) is the radius of the wheel. The length of the spring, \(h_{s}\), is represented in the following equation.