# Modeling of Walking-Gait Parameters and Walking Strategy for Quadruped Robots
## 2 Materials and Methods
### Kinematic Analysis of the Quadruped Robot  
The topological structure of a robot mainly refers to the connection structure between the robot's trunk and limbs, as well as the spatial modeling and joint analysis of each limb of the robot. The joints in the robot body structure refer to controllable autonomous motion joints that can actively adjust the robot's motion angle. Robots with relatively simple body structures often have fewer joints, more convenient control, and lower costs, but can perform fewer actions and have poor bionic performance. The more limb joints a robot has, the more complex are the actions it can complete. However, the cost will also increase, and the structural design of the robot will become more complex, making control more difficult. Therefore, the decision on the number of joints in the limbs is very important.  
The bionic-robot dog consisted of approximately 200 parts, with a total length of 775 mm, a total width of 380 mm, and a standing height of 438 mm. The body structure was mainly divided into three sections, the front limb, the back, and the hind limb. Due  
Figure 2: Changes in joint angles when the biological dog moved.  
to the small change in back angle during the movement of the bionic-robot dog, in order to simplify the structure and make the model simpler, a rigid back without joints was used for the back. Similarly, because the movement patterns of the front and hind limbs were similar during movement, the front and hind limbs adopted the same structure. The entire machine had a total of 12 joints, and all 8 active joints were driven by Maxon DC brushless motors, with the motor model being the EC45 Flat. The transmission between the motor and each limb used a belt transmission. Figure 3 shows an assembly diagram of the bionic-robot dog established in the 3D software SolidWorks 2022.  
Figure 4 is a linkage schematic of the mechanical structure of the bionic-robot dog. \(M\) is the overall mass of the machine. \(l_{0}\) is the distance between the shoulder joints of the front and hind limbs. \(b_{0}\) is the distance between the hip joints of the left and right limbs. \(l_{l}\), \(l_{2}\), \(l_{3}\) and \(m_{1}\), \(m_{2}\), \(m_{3}\) are the lengths and masses of the thigh, calf, and foot, respectively. \(\varphi_{1}\) is the angle at which motor 1, driving the hip joint, rotates. \(\varphi_{2}\) is the angle at which motor 2, driving the knee joint, rotates. \(\theta_{1}\) is the rotation angle of the hip joint. \(\theta_{2}\) and \(\theta_{3}\) are the rotation angles of the knee and ankle joints, respectively.  
The main parameters in the structural design of the bionic-robot dog and the actual parameters of the biological dog are shown in Table 1. The design parameters should be as  
Figure 4: Linkage schematic of the mechanical structure of the bionic-robot dog.  
Figure 3: Mechanical structure of the bionic-robot dog.  
close as possible to the actual parameters of the biological dog. Considering the motion stability of the bionic-robot dog, the robot dog was slightly wider in the width direction than the biological dog. After calculation, the size ratio of the robot dog to the reference biological Labrador dog in this article was around 1.