Adaptive tracking control of a nonholonomic pendulum-driven spherical robot by using a model-reference adaptive system

An adaptive approach is developed for the tracking control of a pendulum-driven spherical robot. First, the dynamics model of the robot is derived using Newton-Euler methodology for a system of rigid bodies. The simplified model is marginally stable and nonminimum phase. Next, based on the theory of the model-reference adaptive system, a Model-reference adaptive controller (MRAC) is designed to track the desired command signals. The controller parameters are adjusted based on the error between the reference model and the process outputs and the command signals. Simulations illustrate that the convergence rate depends substantially on the adaptation gains of the MRAC. Hence, gains should be tuned properly by using fuzzy logic systems or a genetic algorithm. Results indicate that the proposed control strategy is highly promising for tracking different command signals even if the system is non-minimum phase and marginally stable. Moreover, this controller is more easily implemented in the real world compared with nonlinear controllers