## 4 Simulation Results
### Sensitivity Analysis  
The estimated road friction coefficient be used not only for evasive path generation, but also for obtaining the equivalent front and rear cornering stiffnesses of the bicycle model used in MPC via a look-up table. However, the estimation might not be accurate due to the lack of enough excitation. Different road friction coefficients deviated from the estimated nominal value of 0.9 are used for sensitivity analysis to evaluate the robustness of the proposed algorithm. The minimum distance \(D_{L}\)[50] between the host vehicle and the stationary vehicle to be avoided as shown in Figure 17 can be defined as follows. \[D_{L}=\sqrt{\left(x_{1}-x_{2}\right)^{2}+\left(y_{1}-y_{2}\right)^{2}}-\frac{ W_{h}}{2}-\frac{W_{s}}{2} \tag{52}\]  
where \(P_{h}(x_{1},y_{1})\) is the front center point of host vehicle; \(P_{s}(x_{2},y_{2})\) is the front center point of stationary vehicle; \(W_{h}\) is the width of host vehicle; \(W_{s}\) is the width of stationary vehicle. \(D_{L}\) at different road friction coefficients are shown in Table 3. The collision can be avoided for all simulated scenarios. The vehicle sideslip angle can be used to evaluate the yaw stability of the vehicle. The root-mean-square (rms) and maximum (max) values of sideslip angle responses at different road friction coefficients are shown in Table 4. Those values are obtained using the responses from the beginning of control at 3-10 s. The more the road friction coefficient deviates from the nominal value of 0.9, the larger the rms and max values of sideslip angles are. MIMO can stabilize the vehicle in the new target lane for all scenarios. However, SISO exhibits large lateral responses as shown in Figure 10 and cannot stabilize the vehicle in the new target lane for \(\mu\leq 0.75\). The rms and max values of sideslip angle suddenly increase for \(\mu\leq 0.75\) which are indications of yaw instabilities. Thus, MIMO demonstrates better robustness of yaw stability and handling performance for reduced road friction coefficients. In order to evaluate the robustness of the proposed algorithm at different velocities, the longitudinal velocity of host vehicle is increased to 120 km/h in Figure 18. The suddenly appearing obstacle is assumed to be detected at 7.5 m ahead of the LPS. \(D_{L}\) at different road friction coefficients is shown in Table 5. Similar to the results in Table 3, the collision can be avoided for all simulated scenarios. The rms and max values of sideslip angle responses at different road friction coefficients are shown in Table 6. Similar to the results in Table 4, the more the road friction coefficient deviates from the nominal value of 0.9, the larger the rms and max values of sideslip angles are. MIMO can stabilize the vehicle in  
angle can be reduced, and the handling performance of MIMO MPC is better than SISO MPC. For medium road friction, SISO MPC is unable to track the path and loses directional stability. However, MIMO MPC can still reduce the maximum required steering angle and accelerate the response of \(r\) via DYM. In order to prevent tire force saturation, the CA can distribute the longitudinal tire forces to wheels with lower tire work load ratios for generating the desired DYM. Thus, MIMO MPC can achieve robust path tracking and handling enhancement against model uncertainty due to road friction reduced by 22% and 33% at 80 and 120 km/h, respectively. In this paper, the handling performance was mainly discussed for avoiding the collision with a stationary vehicle via lateral dynamics control. For a slow moving vehicle in front of the host vehicle, collision avoidance via AES should be further investigated to demonstrate the effectiveness the proposed algorithm. Since the lateral tire forces at front steering wheels are affected by load transfer that can be created via acceleration or braking, coordinated longitudinal and lateral dynamics control might further enhance the handling performance for collision avoidance. Conceptualization, B.-C.C. and Y.-M.L. ; methodology, B.-C.C. and Y.-M.L.