Optimal design of trajectory parameters and position tracking with balance for riderless bicycle

Riderless bicycles are typically nonholonomic, underactuated, and nonminimum‐phase systems. The instability and complex dynamic coupling make the trajectory generation and tracking of the bicycles more challenging. In this paper, we consider both the trajectory generation and position tracking of a riderless bicycle. To achieve smooth motion performances, the desired planar trajectory of the contact point of the bicycle's rear wheel is constructed using a parameterized polynomial curve that can connect two given endpoints with associated tangent angles. The optimal parameters of the polynomial curve are obtained by minimizing the maximum of the roll angle's quasistatic trajectory of the bicycle, and this problem is solved by the particle swarm optimization algorithm. Then, position tracking of the desired planar trajectory with balance is converted into an optimization problem subject to the dynamic constraints. The cost function is designed as the combination of the position errors and the roll acceleration of the bicycle, in order to achieve an accurate tracking performance and to prevent the bicycle from falling down. This optimization problem is solved by the Gauss pseudospectral method. Simulation results are presented to demonstrate the effectiveness of the proposed method.