$\C$ in the horizontal plane in such a way that the bicycle does not fall over and its velocity is bounded. The simplified bicycle model we use in this paper, developed by Neil Getz [@Get94; @GetMar95], views the bicycle as a point mass with a side slip velocity constraint, and models its roll dynamics as those of an inverted pendulum, see Figure \[fig:bicycle\]. The model neglects, among other things, the steering kinematics and the wheels dynamics with the associated gyroscopic effect. In [@HauSacFre04], Hauser-Saccon-Frezza investigate the maneuvering problem for Getz’s bicycle using a dynamic inversion approach to determine bounded roll trajectories. They constrain the bicycle on the curve and, given a desired velocity signal $v(t)$, they find a trajectory with the property that the velocity of the bicycle is $v(t)$ and its roll angle $\varphi$ is in the interval $(-\pi/2,\pi/2)$, i.e, the bicycle doesn’t fall over. In [@HauSac06], Hauser-Saccon develop an algorithm to compute the minimum-time speed profile for a point-mass motorcycle compatible with the constraint that the lateral and longitudinal accelerations do not make the tires slip, and apply their algorithm to Getz’s bicycle model.

The problem of maneuvering Getz’s bicycle along a closed curve is equivalent to moving 