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

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.