Development of Efficient Nonlinear Benchmark Bicycle Dynamics for Control Applications

We present a symbolic method for modeling a nonlinear multibody bicycle with holonomic and nonholonomic constraints. The method, developed for robotic multibody dynamics, is applied to a benchmark bicycle, in which all six ground contact constraint equations are eliminated, leaving analytic coupled ordinary differential equations corresponding to the bicycle rear body roll, steer angle, and rear wheel rotation degrees of freedom without any approximation. We have shown that the nonlinear dynamics of the bicycle satisfies an underactuated manipulator equation and demonstrated an analytic method to solve the vehicle pitch angle from a quartic equation. This reduced analytic model offers insights in understanding complex nonlinear bicycle dynamic behaviors and enables the development of an efficient model suitable for real-time control outside of the linear regime.