## 5 Experimental Results
### High Speed and Small Path Curvature  
The reference path profile used in simulation is a polynomial curve with small curvature radius. Figure 12 shows the desired acceleration and velocity of the test vehicle. The vehicle starts the run at initial velocity 20 m/s. As shown in Figure 12a,b, the vehicle begins to accelerate from zero, then it runs at a constant speed of 18.2 m/s. The above condition demonstrates that the vehicle runs at a case of high vehicle and small path curvature, which can verify the control effect. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Notation** & **Value** & **Unit** \\ \hline Vehicle total mass & m & 1110 & kg \\ Lateral distance between centers of tire & B & 1.69 & m \\ Yaw inertia of the vehicle & I\({}_{\text{z}}\) & 1343.1 & kg\(\cdot\)m\({}^{2}\) \\ Distance from the front axle to the mass center & a & 1.04 & m \\ Distance from the rear axle to the mass center & b & 1.56 & m \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The parameters of vehicle. Figure 11: Block diagram of actuator control layer. Figure 12: Desired acceleration and velocity in the high-speed case. (**a**) Desired acceleration. (**b**) Desired velocity. Desired tire lateral and longitudinal forces from tire force distribution layer for the four wheels during the automatic driving are shown in Figure 13. It is clear that when the autonomous electric vehicles runs at an accelerated velocity in the road with small curvature, the desired longitudinal force of each wheel is about 500 kN, which is devoted to ensure the vehicle motion in longitudinal direction. Simulation results show that the presented control distribution algorithm in the multi-objective hierarchical control architectures can be used to obtain preferable distribution results. The dynamic behaviors of the proposed control architectures and the traditional LQR control system are compared in Figures 14-16. As shown in Figure 14, the real trajectories are plotted together with the simulated trajectory, and the vehicle follows the path reference with an acceptable performance. It is clear that, compared to the LQR controller, the proposed architectures has less tracking error. Figure 14: Path tracking in the \(x\)-\(y\) plane. Figure 13: Desired tire forces provided by the tire Force Distribution layer: (**a**) Front left tire force; (**b**) front right tire force; (**c**) rear left tire force; and (**d**) rear Right tire force. Figure 15 shows that the vehicle slip angle are controlled in a smaller range by the proposed control architecture than traditional LQR control system. The results show that the proposed control architecture can restrict the vehicle slip angle within 0.8 deg, whereas the traditional LQR control system make the vehicle slip angle be bounded by 2.5 deg. It means that the vehicle has better maneuverability. Figure 16a shows the simulation results of changeable weight coefficients. When the vehicle accelerates on a road with a small curvature radius, the coefficient \(g_{1}\) is larger than \(g_{2},g_{3}\), which means the energy saving control of in-wheel motors is more important. With the increasing of vehicle speed and curvature, the weight coefficient \(g_{2}\) and \(g_{3}\) gradually increase to ensure the stability of the vehicle and reduce tire wear. After 6 s, due to the small curvature radius, the weight coefficients \(g_{1},g_{2},g_{3}\) tends to be stable, where \(g_{1}\) is larger than \(g_{2}\) and \(g_{3}\). Figure 16: Experience results in high speed and small curvature case: (**a**) Weight coefficients; (**b**) stability margin; (**c**) electrical efficiency; and (**d**) tire energy dissipation. Figure 15: Vehicle slip angle. Figure 16b-d indicate that, compared with LQR controller, the proposed control architecture can effectively reduce the stability margin, power consumption, and tire energy dissipation. Among them, the effect of motor energy saving control is the most obvious, and the other two have also been optimized, which coincides with the curve of weight coefficients.