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Motion planning and feedback control for a unicycle in a way point following task: The VFO approach

Michałek M., Kozłowski K.

International Journal of Applied Mathematics and Computer Science

2009

Vol. 19, no 4

533-545

This paper is devoted to the way point following motion task of a unicycle where the motion planning and the closed-loop motion realization stage are considered. The way point following task is determined by the user-defined sequence of way-points which have to be passed by the unicycle with the assumed finite precision. This sequence will take the vehicle from the initial state to the target state in finite time. The motion planning strategy proposed in the paper does not involve any interpolation of way-points leading to simplified task description and its subsequent realization. The motion planning as well as the motion realization stage are based on the Vector-Field-Orientation (VFO) approach applied here to a new task. The unique features of the resultant VFO control system, namely, predictable vehicle transients, fast error convergence, vehicle directing effect together with very simple controller parametric synthesis, may prove to be useful in practically motivated motion tasks.

A Stabilizing Control Law for Invariant Systems on Lie Groups

Apostolou N., Kazakos D.

International Journal of Applied Mathematics and Computer Science

2000

Vol. 10, no 2

273-282

This paper deals with the stabilizability of invariant control systems defined on Lie groups. A stabilization technique is presented which, under certain hypotheses, can lead to a criterion assuring the existence of a feedback controller which steers every initial condition to a specified target point of the state space of these systems.