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The steering control of an autonomous unicycle is considered. The underlying dynamical model of a single rolling wheel is discussed regarding the steady state motions and their stability. The unicycle model is introduced as the simplest possible extension of the rolling wheel where the location of the center of gravity is controlled. With the help of the Appellian approach, a state space representation of the controlled nonholonomic system is built in a way that the most compact nonlinear equations of motions are constructed. Based on controllability analysis, feedback controllers are designed which successfully carry out lane changing and turning maneuvers. The behavior of the closed-loop system is demonstrated by numerical simulations.

Nonholonomic models of automobiles are developed by utilizing tools of analytical mechanics, in particular the Appellian approach that allows one to describe the vehicle dynamics with minimum number of time-dependent state variables. The models are categorized based on how they represent the wheel-ground contact, whether they incorporate the longitudinal dynamics, and whether they consider the steering dynamics. It is demonstrated that the developed models can be used to design low-complexity controllers that enable automated vehicles to execute a large variety of maneuvers with high precision., Comment: 42 pages, 25 figures, 5 tables, accepted for inclusion in a future issue in Nonlinear Dynamics, Springer