Trajectory tracking for non-holonomic cars: A linear approach to controlled leader-follower formation

This article describes the design of a linear robust dynamic output feedback control scheme for output reference trajectory tracking tasks in a leader-follower non-holonomic car formation problem using the cars´ kinematic models. A simplification is proposed on the follower´s exact open loop position tracking error dynamics, obtained by flatness considerations, resulting in a system described by an additively disturbed set of two, second order, integrators with non-linear velocity dependent control input matrix gain. The unknown disturbances are modeled as absolutely bounded, additive, unknown time signals which may be locally approximated by arbitrary elements of, a, fixed, sufficiently high degree family of Taylor polynomials. Linear Luenberger observers may be readily designed, which include the, self updating, internal model of the unknown disturbance input vector components as generic time-polynomial models. The proposed Generalized Proportional Integral (GPI) observers, which are the dual counterpart of GPI controllers ([11]), achieve a, simultaneous, disturbance estimation and tracking error phase variables estimation. This, on-line, gathered information is used to advantage on the follower´s linear output feedback controller thus allowing for a simple, yet efficient, disturbance and control input gain cancelation effort. The results are applied to control the fixed time delayed trajectory tracking of the leader path on the part of the follower. Simulations are presented which illustrate the robustness of the proposed approach.