Feasibility Study on the Implementation of Cubic Motion Curve for Vehicle Trajectory Planning

Abstract

Cubic Motion curve has been introduced to integrate the information of path and motion. Since this is a new approach, a feasibility study has been carried out to analyse the practicality of Cubic Motion curves used as the input for the study of vehicle dynamic response. This study requires the development of three modules, namely, the Cubic Motion module, the vehicle dynamic model, the driver model (VDM-DM) module, and, lastly, the integrated module. The Cubic Motion module will generate Cubic Motion curve. The VDM-DM module applies the 2 DOF bicycle model and links it with Reński's driver model. Finally, an integrated module will merge both previous modules as a complete system for trajectory and vehicle response as the output. The double lane change and the Slalom test were the case studies used to develop an understanding of the applicability of the three types of Cubic Motion input, namely, natural, adjusted tangent, and additional vertex cubic motion. The finding of this study is that Cubic Motion is in fact a compact representation of curve with motion attributes and can be directly associated with a vehicle dynamic response study.

Research on the trajectory tracking of a curved road in an active lane change scenario based on model predictive control algorithm

“…However, ensuring that lane changes are straight when transitioning between curved lanes is challenging. 31,32 Therefore, there is a need to carry out further research and discussions on trajectory planning for the lane changes on curved roads. The following is a discussion on planning a curved lane change trajectory based on the trajectory planning for a straight lane change, mainly including the lane changes from the outer lane to the inner lane and from the inner lane to the outer lane.…”

Time‐dependent lane change trajectory optimisation considering comfort and efficiency for lateral collision avoidance

“…The multinomial curve [11,12] was adopted in the lane-changing trajectory because the multinomial function can adjust the order to achieve the desired performance [13]. For example, if the constant of the first derivative of a cubic polynomial trajectory was zero, the planned lateral velocity (in the geodetic coordinate system) was smooth [14]. If the constant of the first and second derivatives of the quintic polynomial was zero, the lateral curvature of the trajectory was smooth [15,16].…”

Investigation of a Longitudinal and Lateral Lane-Changing Motion Planning Model for Intelligent Vehicles in Dynamical Driving Environments

“…The polynomial trajectory is very popular because the order of which can be tuned to achieve desired performances [30], [31]. The cubic polynomial trajectory has a smooth lateral velocity by setting the constant of its first derivative to 0, the quintic polynomial trajectory has a smooth curvature by setting constants of its first and second derivatives to 0, and the seven-order polynomial has a smooth jerk of lateral acceleration by setting constants of its first, second, and third derivatives to 0 [32]- [34].…”