Analyzing the control surfaces of type-1 and interval type-2 FLCs through an experimental study

In this paper, we present experimental results conducted on the spherical robot Sphero 2.0 by analyzing the control surfaces of Interval Type-2 (IT2) Fuzzy PD (FPD), Type-1 (T1) FPD and conventional PD controllers in order to show how and why the IT2-FPD controllers have capability improve control performances. We firstly present the vision based position control system used in this study. We then tune the design parameters of PD, T1-FPD and IT2-FPD controllers via an optimization based design approach for a training reference trajectory. The control surfaces of the designed controllers are compared in terms of the aggressiveness and smoothness of their control actions. This analysis shows that the IT2-FPD controller has ability to produce both aggressive and smooth control actions in different input spaces, which cannot be accomplished by its conventional and T1 counterparts. To analyze the controller performances for different operating points, we present the real-time results for a testing trajectory. The control surface analysis shows that the IT2-FLC is able to generate sophisticated control surfaces by adjusting the Footprint of Uncertainty (FOU), while the experimental results validate that the potential of the IT2-FPD controller to improve control performances via tuning the FOU parameters.