Sub-optimal and robust path tracking: a geometric approach

Abstract

Path tracking controllers for non-holonomic vehicles are commonly designed with primary focus on robustness to different kinds of disturbances, vehicle dynamics and other effects. Subsequently, the path tracking behavior is improved by parameter optimization or controller extensions. The possible improvement, however, is already limited by the control design itself. To overcome this drawback, this paper presents an alternative approach: In a first step, we formulate the geometrically optimal solution for a Dubins car reaching a straight target path as a globally stabilizing sliding-mode feedback law. In a second step, we introduce a single tuning parameter that achieves robustness with respect to exemplary matched disturbances. The result is a sub-optimal but robust controller. We investigate the impact of tuning this parameter towards optimality or robustness with respect to the transient and stationary tracking behavior in simulation scenarios. Following the presented approach, it is possible to adapt the control law with respect to various disturbances facing and utilizing the trade-off between optimality and robustness. This is a significant advantage in the design of path tracking controllers due to the variety of vehicle actuation and measurement systems and operational design domains.