Smooth path and velocity planning under 3D path constraints for car-like vehicles

Existing path and velocity planning methods for car-like vehicles, the paths of which are subject to constraints on the derivative of the curvature in the horizontal plane, do not accurately express the relationships among position, velocity and acceleration in 3D space. Moreover, velocity planning algorithms are efficient only when the curvature and derivative of the curvature have the same velocity demand. As efficiency and comfort are two key issues in promoting planning algorithms, in this paper, the vehicle is allowed to know the nearly shortest-length path and to set a continuous velocity and acceleration profile to track the trajectory reference while taking into account bounds on acceleration (including lateral acceleration) and jerk that are consistent with comfort. First, to construct a nearly shortest path, the 3D path surface is mapped onto the horizontal, profile and frontal planes, and a 2D path smoothing method is applied to solve the 3D path smoothing problem. This method has been used in highway design, but the theoretical understanding of its performance remains limited. This limitation is addressed from the viewpoint of 3D path smoothing in this paper. In addition, the jerk, acceleration, velocity, steering angle and steering angular acceleration profile are merged into a trajectory tracking task to provide a new velocity planning method to find the time-optimal path. Finally, the capabilities of the path and velocity planning methods within general planning schemes are also demonstrated. (C) 2018 Elsevier B.V. All rights reserved.