<div>Single lane changing is one of the typical scenarios in vehicle driving. Planning
an appropriate lane change trajectory is crucial in autonomous and
semi-autonomous vehicle research. Existing polynomial trajectory planning mostly
uses cubic or quintic polynomials, neglecting the lateral jerk constraints
during lane changes. This study uses seventh-degree polynomials for lane change
trajectory planning by considering the vehicle lateral jerk constraints.
Simulation results show that the utilization of the seventh-degree method
results in a 41% reduction in jerk compared to the fifth-degree polynomial.
Furthermore, this study also proposes lane change trajectory schemes that can
cater to different driving styles (e.g., safety, efficiency, comfort, and
balanced performance). Depending on the driving style, the planned lane change
trajectory ensures that the vehicle achieves optimal performance in one or more
aspects during the lane change process. For example, with the trajectory that
provides the best comprehensive performance under given constraints (initial
speed of 20 m/s, lane width of 3.5 m, and a longitudinal distance of 50 m to the
obstacle in front), the four-wheel steering model predictive control can
effectively track the planned trajectory, with the maximum jerk value being 6.4
m/s<sup>3</sup> and the longitudinal speed after lane change being
approximately 12.6 m/s. Although this study assumes specific longitudinal
displacement before and after the lane change, the methodology is applicable to
other scenarios. For example, it can determine the shortest longitudinal
displacement and the optimal lane change trajectory given predefined vehicle
speeds and maximum lateral acceleration conditions. The lane change trajectories
developed in this study can be directly applied to the system design of
autonomous vehicles.</div>