Dynamics and nonlinear adaptive control of an autonomous unicycle: theory and experiment

Equations of motion for an autonomous unicycle are given as derived using Kane´s formalism, and the unstable nonminimum-phase behavior of the linearized system is illustrated. Lateral and longitudinal dynamics nominally decouple for low yaw rates but couple nonlinearly for large yaw rates and yaw accelerations. Time scale separation is employed to reduce the model order for inner loop controller design, where an unusual LQG (linear quadratic Gaussian) structure is proposed. Strong dependence of the lateral dynamics on wheel speed necessitates continuous gain scheduling of the lateral controller. A significant nonlinearity exists due to dry friction in yaw between the wheel and floor. Bang-bang control is employed to overcome this. The proposed unicycle has been built and the implemented controller structures and test results are indicated in the paper