## 4 Simulation and Analysis  
### Simulation Parameters  
To assess the feasibility of the proposed control strategy, MATLAB/Simulink (R2014a, MathWorks Company, Natick, MA, USA, 2014) simulations of coupling and distribution control were performed. The simulation model is composed primarily of an angle distribution planner, a fuzzy PID controller, and a fuzzy PI controller for each wheel. The main FC parameters used in the simulations are shown in Table 2.  
The CE is the key index that characterize the coupling control performance of the four OSMs. Longitudinal and lateral acceleration are the main indicators used to determine stability during MMS. Changes in the steering angles and angular velocities of the four OSMs also must be detected. Thus, the simulations included three parts: the steering responses of four off-center arms, the CE performance, and the longitudinal and lateral acceleration changes under distribution and coupling control. The feasibility of the proposed method can be determined by comparing these two control methods.  
According to the analysis in Section 2.2, the target steering angle in any off-center arm is 90\({}^{\circ}\) during CM switching and 63\({}^{\circ}\) during IR switching. During DM switching, the target steering angle of off-center arms 1 and 3 is set to 45\({}^{\circ}\), while off-center arms 2 and 4 are set to 135\({}^{\circ}\). During SM switching, the target steering angles of off-center arms 1 and 3 is 30\({}^{\circ}\), while arms 2 and 4 use 39\({}^{\circ}\) based on Ackermann steering geometry.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Parameter** & **Description** & **Value** & **Parameter** & **Description** & **Value** \\ \hline \(m\) & Mass of flexible chassis & 202.6 kg & \(d\) & Offset distance & 253 mm \\ \hline \(h\) & Ground clearance & 300 mm & \(l\) & Yaw moment of inertia & 1275 kg m\({}^{2}\) \\ \hline \(L\) & Distance between front and rear & 1210.6 mm & \(B_{u}\) & Viscous friction damping coefficient & 0.09 N m/(rad-s\({}^{-1}\)) \\ \hline \(B\) & Distance between left and right & 610.5 mm & \(B_{m}\) & Viscous friction damping coefficient & 0.07 N m\(\times\)/rad \\ \hline \(p\) & Rated power & 500W & \(T_{e}\) & Electric wheel output torque & 35.4 N\(\cdot\) m \\ \hline \(J\) & Moment of inertia & 0.0007 kg\(\cdot\) m\({}^{2}\) & C\({}_{\text{aff}}\) & Tire cornering stiffness & 4600 N\(\cdot\) rad\({}^{-1}\) \\ \hline \(V_{r}\) & Rated voltage & 48 V & C\({}_{\text{aff}}\) & Tire cornering stiffness & 4600 N\(\cdot\) rad\({}^{-1}\) \\ \hline \(\omega_{mr}\) & Rated rotation speed & 500 r\(\cdot\) min\({}^{-1}\) & C\({}_{\text{aff}}\) & Tire cornering stiffness & 4600 N\(\cdot\) rad\({}^{-1}\) \\ \hline \(r\) & Tire radius & 280 mm & C\({}_{arr}\) & Tire cornering stiffness & 4600 N\(\cdot\) rad\({}^{-1}\) \\ \hline \(T_{f}\) & Tire damping & 500 N/m\(\times\)s\({}^{-1}\) & \(K\) & Constant coefficient & 2.3 \\ \hline \(T_{r}\) & Rolling resistance coefficient & 0.012 & \(l_{o}\) & Moment of inertia & 0.0011 kg\(\cdot\) m\({}^{2}\) \\ \hline \end{tabular}
\end{table}
Table 2: Main FC motion mode switching (MMS) simulation parameters.  
Figure 8: Fuzzy rules for control of steering tracking system: rule surface of (**a**) \(\Delta K_{P}\) and (**b**) \(\Delta K_{l}\).