the nonholonomic constraints that the wheels roll without slipping in the Lagrangian, and then extracting the model through the Lagrange-d’Alembert equations as in [@Blo03 Section 5.2]. The resulting model, which we’ll refer to as [*Getz’s bicycle model*]{}, reads as $$\begin{aligned}
&\dot {\bar \kappa} = \tau \nonumber\\
 &M \begin{bmatrix} \ddot \varphi \\ \dot v 
\end{bmatrix} = 
F + B  \begin{bmatrix}
  \tau \\ f
\end{bmatrix}, \label{eq:original_system}\end{aligned}$$ where $\tau$, the time derivative of the [curvature $\bar
  \kappa(t)$]{}, and $f$ are the control inputs and, denoting ${s_\varphi}=
\sin \varphi$, ${c_\varphi}=\cos \varphi$, $$\begin{aligned}
& M = \begin{bmatrix} h^2 & b h {c_\varphi}\bar \kappa \\
b h {c_\varphi}\bar \kappa & 1 + (b^2+h^2 {s_\varphi}^2) \bar \kappa^2 - 2 h {\bar \kappa} {s_\varphi}\end{bmatrix}, \\
& F= \begin{bmatrix} g h {s_\varphi}- (1 - h
   {\bar \kappa} {s_\varphi}) h {c_\varphi}{\bar \kappa} v^2 \\ (1 - h {\bar \kappa} {s_\varphi}) 2 h {c_\varphi}{\bar \kappa}
   v \dot \varphi + b h {\bar \kappa} {s_\varphi}\dot \varphi^2
 \end{bmatrix}, \\
& B =\begin{bmatrix} -b h {c_\varphi}v & 0 \\ -(b^2 {\bar \kappa} -
  h {s_\varphi}(1-h {\bar \kappa} {s_\varphi})) v & 1/m
  \end{bmatrix}.
\end{aligned}$$ In this model, $M$ is the inertia matrix, $F$ represents the sum of Coriolis, centrifugal and conservative forces, and $B$ is 