Adaptive Trajectory Tracking for a Planar Two-Wheeled Vehicle with Positive Trail

This paper proposes an adaptive trajectory tracking control for an autonomous planar two-wheeled vehicle subject to nonholonomic constraints. Furthermore, the vehicle model considers a so-called positive trail that provides self-alignment of the steering in many vehicle types, including bicycles. The dynamics of the system is described in a port-Hamiltonian form that is suitable for systematic synthesis of passivity-based controllers. This also enables an explicit description of the system dynamics including the nonholonomic constraints by an ODE. By a generalized canonical transformation, an error system is determined preserving the port-Hamiltonian structure. This reduces the tracking problem to a stabilization problem that is solved by a further transformation. The controller is designed for a structure preserving simplified model and applied to the original model handling the omitted effects due to the simplification as disturbance. Finally, an adaptive controller is applied that, in the port-Hamiltonian framework, guarantees the asymptotic tracking of a given trajectory despite large parameter uncertainties.