Modelling and control of the motion of a riderless bicycle rolling on a moving plane
A riderless bicycle rolling on moving plane is modelled in the paper as a nonholonomic mechanical system of 12 degrees of freedom. The bicycle is controlled by a pedalling torque, by a directional torque and by a rotor mounted on the crossbar that generates a tilting torque. Equations of motion of the bicycle are derived and reduced to the system of differential equations \[ D \ddot Q + f = E \Gamma, \quad Q=(\theta,\phi,\psi_1)^T, \quad \Gamma=(\Gamma_{\psi 1},\Gamma_{\alpha},\Gamma_{\phi 3})^T, \] where \(\theta, \phi, \psi_1\) are the angles determining the rear wheel position, \(\Gamma_{\psi 1},\Gamma_{\alpha}\) are the pedalling and directional control torques, and \(\Gamma_{\phi 3}\) is the control torque generated by the rotor. Under assumptions, that \(\det D>0\), \(\det E>0\), by introducing the control law \[ E \Gamma=D(\theta,\delta) w + f, \quad w=(w_1,w_2,w_3)^T \] and by choosing the functions \(w_1,w_2,w_3\) linear in the corresponding state variables, the author derives a kinematic model of the bicycle motion and obtains expressions for the control torques.
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