Synthesized design of a fuzzy logic controller for an underactuated unicycle

In this paper, we propose synthesized design of a fuzzy logic controller (FLC) for control of an underactuated unicycle system. The FLC objective is velocity control of the wheel while keeping the pendulum upright, which is an unstable equilibrium. The synthesized design consists of three phases. First, the FLC structures including the number of rules, membership functions, inference and parametric relations are chosen based on heuristic knowledge about the unicycle. Second, on the basis of a linearized model and linear feedback, the FLC output parameters are determined quantitatively for stabilization of the unicycle. Third, the FLC output parameters are tuned using an iterative learning tuning (ILT) algorithm, which minimizes an objective function that specifies the desired unicycle performance. The rationale for the synthesized FLC design is full utilization of the available information, which is achieved by combining model-based and model-free designs, and hence improves the FLC performance. We minimize the number of FLC rules and fuzzy labels. Six rules are used for regulation or setpoint tasks, whereas 10 rules are used with extra integral control to eliminate steady-state errors induced by system uncertainties and disturbances. Only two fuzzy labels are adopted for each fuzzy variable. The ILT process consists of two phases, exploration for stabilization and exploitation for better performance. The effectiveness of the proposed FLC is validated using intensive simulations and comparisons.