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Aiming at the controllability of the nonholonomic system, take the differential driving wheels of the cleaning robot as a research object, with universality of the nonholonomic system considered, equation of nonholonomic constraint of the cleaning robot was also derived. In addition, by means of Chow theorem, the controllability of the cleaning robot was demonstrated. And backlash in the differential driving wheels of the cleaning robot was performed. Meanwhile, causation which gives rise to the backlash was analyzed. Then, based on the idea of PID parameters fuzzy adaptive control, the fuzzy adaptive PID controller was designed. And fuzzy adaptive PID parameters on-line learning was implemented. According to MATLAB simulations and experiments, the results show that through fuzzy adaptive PID parameters algorithm, response of driving wheels of the cleaning robot is quick, and steady state errors are also narrowed. Improvement in robustness of the cleaning robot nonholonomic system has been done.