Dynamics And Nonlinear Adaptive Control Of An Autonomous Unicycle

Studies the dynamics and active control of a mechanical unicycle with the human rider replaced by a turntable. The unicycle equations of motion are derived, linear in all states except yaw rate which is not considered a perturbation quantity. Using the specialized linear equations with yaw rate also linearized, the dynamics of the open loop system are studied and shown to decouple into longitudinal and lateral systems for zero turntable angular velocity, and linear controllers are proposed for stabilization. The systems reduce to lower order models by exploitation of the time scale separation of the open loop dynamics. A variation of the LQG control design method is derived and used in both the lateral and longitudinal controller designs. This method allows recovery of LQ regulator inner loop without use of pole zero cancellation strategy, hence potentially offering greater parameter uncertainty robustness. The lateral controller is continuously gain scheduled and implemented in a bang-bang setting in order to deal with coulomb friction effects between the tire and the ground. An estimation algorithm is defined to continuously determine estimates of the friction and hence adapt the bang-bang control algorithm.