Nonlinear modeling and control of a unicycle

A unicycle system is composed of a unicycle and a rider. This system is inh erently unstable, but together with a skilled rider can be autonomously con trolled and stabilized. A dynamical investigation, a control design and a n umerical solution of a nonlinear unicycle autonomous model are presented. T he use of a nonlinear model for the control design is shown in this paper t o be of great importance. A three-rigid-body physical model was selected fo r the dynamical study of the system. In a linearized model important physic al characteristics of the unicycle system disappear (e.g. interactions betw een the longitudinal and lateral systems are being neglected), and therefor e it is not recommended to be used for the control design. A nonlinear cont rol law, which replaces the rider in stabilizing the model, was derived in the present work, using a nonlinear unicycle model. A simulation study show s good performance of this controller. Time spectral element methods are de veloped and used for integrating the nonlinear equations of motion. The app roach employs the time discontinuous Galerkin method which leads to A-stabl e high order accurate time integration schemes.