# Trajectory Planning with Time-Variant Safety Margin for Autonomous Vehicle Lane Change +
## 1 Introduction  
Lane changing (LC) is among the most frequent scenarios encountered in daily driving, and considered as one of most important research topics for autonomous vehicles and advanced driver assistance systems [1]. Current research on autonomous driving encompasses different fields, including perception, planning, and control. The lane change maneuver of autonomous vehicle is considered as a challenge since the control involves changes in both the longitudinal and lateral velocity as well as the movement of surrounding vehicles [2]. In this paper, a trajectory planning method for autonomous lane change is investigated on the basis of the existing perceptive information of traffic vehicles. In [3], LCs are classified into mandatory and discretionary ones. This paper focuses on the latter, which is intended to improve the driving condition of the controlled vehicle. Various research studies have focused on the trajectory planning and motion control of autonomous driving technologies [4; 5; 6]. In order to achieve good results in the respective lane change maneuvers, most of these proposed cooperative planning algorithms for autonomous driving employed a rule-based control [7; 8] or an optimization-based control [2; 9]. However, to solve the problems of computational complexity, the trajectory planning algorithm often assumes a given reference trajectory or considers either the longitudinal or the lateral aspects of the planning problem. A dynamic collision avoidance constraints is necessary for the autonomous lane change maneuvers. In [10; 11] the trajectory planning method of lane change maneuvers was studied, but none of the methods considered the position constraint for the collision avoidance. The papers [12; 13] attempt to generate large numbers of trajectory candidates by the state-space sampling method, and choose the best one based on collision detection and kinematic limitations. This method has good effectiveness and robustness, but the computation complexity would be a challenge for the real-time implementation. In [14] a trajectory planning algorithm is designed by the quadratic programming method to achievekinematic constraint in the hazard avoidance scenarios, but the proposed approach assumes constant longitudinal velocity without the consideration of lateral trajectory planning. In [15] a convex optimization method for the trajectory planning during the collision avoidance was applied. However, it employed a given reference trajectories without continuous path re-planning for real application. The trajectory planning is based on an interactive model that captures mutual influences among all surrounding cars. The difficulties of the lane change maneuvers are the mutual interactions between the host vehicle and the surrounding cars. If the information of all traffic vehicles can be known, the first issue is the determination of the right place and moment for lane change. The solution offered in [16] makes the decision using a complicated logic tree, specifying an action for every scenario that can be thought of, but some special cases still may not be covered. Another solution proposed in [17; 18] attempts to replicate human decision-making behavior using Fuzzy Inference System, but the modulation of fuzzification and defuzzification parameters needs considerable experience. Additionally, they only consider two lanes and a predefined number of vehicles, and output binary results. The second issue is to generate proper reaction and trajectory for the lane change maneuver. In practice, one-off trajectory planning is unsuitable in practice, since the unpredicted changes of the surrounding vehicles make the planned path be no longer optimal or even unsafe. A continuous trajectory planning is applied in [12], but this method requires large amount of calculation. A balance should be found between the algorithm complexity and efficiency.