Path-tracking for ground vehicles with bounded steering angle and steering rate - optimal control approach

Vehicle path tracking control problem is investigated using optimal control technique. Steering angle is subject to two limitations - both its magnitude and rate are bounded. Although, it is the most natural settings from the application point of view - it has been rarely considered. An approach described in this paper utilizes the shortest-time solution for a 3-rd order linear system known for long time and revisited in the nineties to improve its robustness. Main generalization proposed here concerns state limitations resulting from the bounds over steering magnitude. Linear settings is sufficient if the offsets from the desired path are small. The validity of the "linear"' solution is verified by applying the obtained optimal bang-bang control to a nonlinear system. In case of large lateral and angular offsets from the path the nonlinear analysis is needed. We show that in spite of the low dimension of the system (third) the nonlinear problem presents a variety of challenges, namely, singular optimal trajectory and a Fuller-type phenomena consisting of 'chattering' near the junction of non-singular and singular portions of optimal trajectories. Finally, the controller designed using linear technique is tested with nonlinear model in simulation and experimentally.