**6. Conclusions**

In this work, an obstacle avoidance trajectory planning controller based on a modified APF algorithm and the MPC algorithm and a trajectory tracking controller based on the linear time-varying MPC algorithm were designed for the AV to realize the active obstacle avoidance function. The modified APF model proposed in this paper added a road boundary repulsive potential field and ameliorated the obstacle repulsive potential field based on the traditional APF model, overcoming some defects of the traditional model. To make the modified APF model satisfy the kinematic constraints of the vehicle, the MPC algorithm was combined with the modified APF model, and a reasonable objective function was constructed to minimize the deviation between the planning trajectory of the modified APF model and the predicted trajectory of the MPC algorithm. Considering that there were many kinds of constraints during vehicle lateral control and for the sake of guaranteeing real-time capability, accuracy, and robustness of the trajectory tracking control algorithm at different speeds, a linear time-varying model predictive trajectory tracking controller was established on the basis of linearizing the vehicle monorail dynamic model. The controller determined the vehicle front wheel angle as the control variable, and multiple constraints of vehicle dynamics and kinematics were combined to design the objective function that could achieve the requirements of fast and accurate tracking of the desired trajectory.

Ameliorating the human-like degree of the planning trajectory is the core of improving the acceptance of the autonomous driving system. Therefore, in this study, a human driver's obstacle avoidance experiment was implemented based on a six-degree-of-freedom driving simulator equipped with multiple sensors, including a steering wheel angle sensor, accelerator pedal sensor, brake pedal sensor, virtual millimeter wave radar sensor, and virtual LIDAR sensor. The obstacle avoidance trajectories under different speeds from different drivers were collected, and the longitudinal distance at the beginning of the obstacle avoidance operation and the maximum distance during the obstacle avoidance process underwent statistical analysis. These two parameters can provide

a basis for the determination of the A value and B value in the elliptical repulsive potential field (shown in Figure 4), making the planned trajectory more human-like.

Finally, a co-simulation model based on CarSim/Simulink was established for the o ff-line simulation testing of the obstacle avoidance trajectory planning controller and the trajectory tracking controller designed in this study. The co-simulation results demonstrated that the vehicles could smoothly avoid obstacles under di fferent speeds. The results of relevant parameters during the obstacle avoidance process were in accordance with the human drivers' obstacle avoidance trajectory characteristics in Section 4, which indicated that the proposed trajectory planning controller and the trajectory tracking controller were more human-like under the premise of ensuring the safety and comfort of the obstacle avoidance operation.

A few deficiencies in this study need to be improved in the future work. Di fferent road environments may have an impact on driver's obstacle avoidance behavior. A future study will pay close attention to collect the driver's operation data under di fferent road environments and analyze the di fference. In addition, the parameters of the obstacle avoidance controller in complex scenarios need to be further optimized.

**Author Contributions:** Q.S., Y.G. and R.F. conceived of and designed the research; C.W., Q.S. and W.Y. conducted the experiments; Q.S., C.W., Y.G. and R.F. wrote the manuscript. All authors discussed and commented on the manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported in part by the National Key Research and Development Program of China under Grant 2019YFB1600500, in part by National Natural Science Foundation of China (51908054, 51775053), in part by the Key Research and Development Program of Shaanxi under Grant (2020GY-163, 2019ZDLGY03-09-02), and in part by the Fundamental Research Funds for the Central Universities, CHD 300102220202.

**Conflicts of Interest:** The authors declare no conflict of interest.
