Piecewise Linear Path Following for a Unicycle Using Transverse Feedback Linearization

Abstract

Motion planning and path following together constitute a critical part of the decision-making hierarchy in autonomous ground vehicles. One of the simplest instances of this architecture is when the path planner generates waypoints that define a sequence of collision-free line segments from a start location to goal destination and when the vehicle’s kinematic model is taken to be Dubin’s vehicle. The low-level feedback controller can then be designed by treating the path following problem as a set stabilization problem; one such approach is called transverse feedback linearization (TFL). However, for a Dubin’s vehicle with only one input, the direction of traversal along the path is completely determined by the vehicle’s initial condition. In this article, we provide easily checkable sufficient conditions that only need to be checked once at run time and a simple systematic design procedure, which guarantees that the robot traverses the path while coming within a user-specified distance of the waypoints; the procedure is also empirically verified.