Clothoid segments for optimal switching between arcs during low-speed Ackerman path tracking with rate-limited steering

Abstract

The number of applications for automated ground vehicles has been rapidly increasing. Examples include autonomous mining trucks, tractors, military target vehicles, and durability testing of passenger vehicles. It is convenient to construct desired paths out of tangentially connected circular arc and straight line segments, which have been shown to be optimal in terms of path length. Unfortunately, such paths can not actually be driven if the steering angle is produced by a servo system, which introduces a lag. In previous work we derived optimal schemes for driving such paths under the assumption that the transition between segments was unplanned, i.e. we simply switched to the new segment at some time ahead of actually reaching it. We did this under assumptions of both a linear lag and a nonlinear rate-limited actuator. Here we again consider the case of a rate-limited actuator, but we desire to plan the trajectory that the vehicle will follow when making transitions between segments. An optimal scheme is developed which involves the insertion of three clothoid segments between arc segments. This scheme minimizes the off-path error with respect to the original path. Optimal control theory is used, as well as directly solving numerically for clothoid parameters.

Interpolating clothoid splines with curvature continuity

“…In Horn, it is defined a curve that minimises the square of the curvature, which is also called minimum energy curve; Baran et al proposes to minimise the total length of the clothoid spline. Examples of applications are shape editing as in Havemann et al, path tracking, path planning, traffic modelling, road geometry estimation, fringe projection, and manufacturing . A selection of functionals and BCs is herein proposed.…”

Clothoid fitting and geometric Hermite subdivision

“…Concerning (ii), for a long time clothoids have been used by route designers as transitional curves between straight lines and circular arcs, and between circular arcs of different radii; see for instance [3,33]. Nowadays, they are further used in connection with path planning for autonomous vehicles, e.g., [2,5,10] in computer vision and image processing [8,27], in curve editing for design purposes [24], or representing hand-drawn strokes sketched by a user [9,32]. Concerning (i), many of the above applications are rather time critical and it is often important to have algorithms which are as fast as possible at a given (sometimes moderate) approximation quality.…”