A trajectory tracking controller based on differential flatness is presented for a nonlinear bicycle model. This controller maps the bicycle dynamics into a point mass located at a center of oscillation with an additional degree of freedom of yaw dynamics. A state transformation is performed that reveals structure in the yaw dynamics resembling a Lie¿nard system. A candidate Lyapunov function inspired by this structure is used to assess the stability of the yaw dynamics while tracking straight-line trajectories and steady turns. The basin of attraction of the controller is limited by actuator constraints and the presence of unstable equilibrium points during turns with high lateral acceleration. The controller properties and the stability of yaw dynamics are demonstrated in simulation.
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Peters et al. (2011) studied this question.
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