A path following control for unicycle robots

In this work we present a new path following control for unicycle robots that is applicable for almost all the possible desired paths and whose analysis is very straightforward. First we select the path following method that consists of two steps: choosing a “projection” that relates the actual posture to the desired path and imposing a “motion exigency” to ensure that the robot advances. A “projection” that considers all the error coordinates is selected and closed equations are obtained for it. The uniqueness projection is carefully analyzed and a necessary and sufficient condition is also presented. This condition shows that a slight bound on the curvature derivative of desired paths must be imposed to preserve uniqueness. It is remarkable that the selected path following is applicable for paths containing zero-radius turns, a problem that has never been resolved as far as we know. In addition, an asymptotically stable control law is found using the closed form equation of the proposed path following and the second Lyapunov method. Finally, we show the behavior of the path following and the control law through several simulated and experimental results, using a computerized wheelchair built at our research facility. © 2001 John Wiley & Sons, Inc.

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