A two-wheeled, uniaxial, differentially driven vehicle possesses many salient advantages when compared to traditional vehicle designs. In particular, high traction factor, zero turn radius, and inherent stability are characteristics of this configuration. Drive torque is provided via a swinging reaction mass hanging below the axle. While mechanically simple, the resulting nonlinear vehicle dynamics can be quite complex. This work develops a planar dynamic model for the two-wheeled vehicle using traditional Hamiltonian techniques. Numerical simulations of the system step response demonstrate behavioral bifurcation and other nonlinear characteristics. However, the simple linear proportional-derivative control designed herein provides robust performance over steady slopes.

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