Control of a bicycle using virtual holonomic constraints

The problem of making a bicycle trace a strictly convex Jordan curve with bounded roll angle and bounded speed is investigated. The problem is solved by enforcing a virtual holonomic constraint which specifies the roll angle of the bicycle as a function of its position along the curve. It is shown that virtual holonomic constraints can be generated as periodic solutions of a scalar periodic differential equation. Finally, it is shown that if the mean curvature of the path is sufficiently small the virtual holonomic constraint can be asymptotically stabilised and the speed of the bicycle is asymptotically periodic.