Pseudospectral motion planning for autonomous bicycles

Motion planning for the autonomous bicycles offers considerable challenges to the area of robotics due to the platform´s nonholonomic, underactuated and nonminimum-phase properties. Instability and nontrivial dynamic coupling make the motion planning of the bicycles a rather complex task. In this paper, the motion planning for the autonomous bicycle is formulated as a dynamic constrained optimization problem subject to the dynamic constraints and the path constraints. The cost function is designed as the integral of the square of the bicycle´s roll angle, in order to acquire a motion trajectory with sufficiently small roll angles, which can increase the balance stability of the bicycle. This optimization problem is solved by the Gauss pseudospectral method (GPM). Simulation results are presented to demonstrate the effectiveness of the proposed method.