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The goal of research is to develop an autonomous unicycle featuring with capabilities of autopilot and stabilization. The autonomous unicycle developed in this paper involves conceptualization, design, simulation, implementation and measurements. Longitudinal control, having coupling of wheel speed and platform pitch, is simulated by a straight-line motion. Lateral control, having coupling of platform roll and heading is simulated by a right turn. This paper features bank-to-turn to the plant, LQR to the controller and linear predictor to moment of inertia.