Nonlinear Modeling and Control of a Unicycle

A unicycle system is composed of a unicycle and a rider. This system is inherently unstable, but together with a skilled rider can be autonomously controlled and stabilized. A dynamical investigation, a control design and a numerical solution of a nonlinear unicycle autonomous model are presented. The use of a nonlinear model for the control design is shown in this paper to be of great importance. A three-rigid-body physical model was selected for the dynamical study of the system. In a linearized model important physical characteristics of the unicycle system disappear (e.g. interactions between the longitudinal and lateral systems are being neglected), and therefore it is not recommended to be used for the control design. A nonlinear control law, which replaces the rider in stabilizing the model, was derived in the present work, using a nonlinear unicycle model. A simulation study shows good performance of this controller. Time spectral element methods are developed and used for integrating the nonlinear equations of motion. The approach employs the time discontinuous Galerkin method which leads to A-stable high order accurate time integration schemes.