Observation and Control of a Simplified Car

The motion planning solution of a simpliied car presented in (Fliess et al., 1995) admits a geometric formulation through the Fr enet formulae. We present and use this formulation that preserves the invariance with respect to SE(2) to built a global asymptotic observer of the non measured direction of the car via the only measurement of its position. Then we study the tracking of a planned path with an observer-controller. Although, the observer-controller stability proof is only local, the attraction domain seems to be very large as shown by numeric simulations (Matlab scripts are available from the authors via email).