Interval Type-2 Adaptive Fuzzy Sliding-Mode Dynamic Control Design for Wheeled Mobile Robots

The fuzzy logic control (FLC) has been successfully applied in diverse fields since Zadeh [8] first introduced the fuzzy set theory. Basically, one of the most widely adopted FLCs is the fuzzy-rule-based-system, the Mamdani FLC, which is based on human expertise and knowledge, so that precise and accurate descriptions of the mathematical model of the controlled plant are not required for designing the desired FLC. The concept of type-2 fuzzy sets (T2-FSs) [9] is an extension of the well-known ordinary fuzzy sets, the type-1 fuzzy sets (T1-FSs) which is also characterized by a fuzzy membership function. The membership functions of T2-FSs are three dimensional and include a footprint of uncertainty (FOU), which is a new third dimension of T2-FSs and makes it possible to handle uncertainties [10]. If their secondary membership functions are set to 1, then they are called as the interval type-2 fuzzy sets (IT2-FSs). The architecture of the IT2-FLC is similar to that of the FLC which contains fuzzifier, rule base, fuzzy inference engine, type-reducer, and defuzzifier. IT2-FLCc can provide more robustness than the conventional FLC to handle the uncertainty and disturbance [11-13]. A combined intelligent technique is proposed for controlling the trajectory-tracking of a nonholonomic wheeled mobile robot (WMR), which comprises kinematic control and an interval type-2 adaptive fuzzy sliding-mode dynamic control (IT2-AFSMDC). The kinematic model is introduced first, and then the control gains can be obtained from the back-stepping method as the input of the dynamic model. The IT2-AFSMDC is propounded for the dynamic part, a combination of the interval type-2 fuzzy logic control (IT2-FLC) and the adaptive fuzzy sliding-mode dynamic control (AFSMDC), which inherits the benefits of these two methods, and adaptive law is introduced to cope with the uncertainties and disturbances of the system. The trajectory-tracking stability is proved by the Lyapunov stability analysis. Computer simulations demonstrate the validity of the proposed method. The simulation results show that the tracking performance of the IT2-AFSMDC is better than that of the AFSMDC. SMC techniques [5, 14] provide discontinuous control laws to drive the system states to a specified sliding surface and to keep them on the sliding surface. The dynamic performance of the SMC has been adopted as an effective robust control approach for the problems of system uncertainties and external disturbances. But there still are some drawbacks in the SMC; for example, chattering characteristics occur when the system dynamics is close to the sliding surface. This problem should be eliminated or alleviated. The FSMC [15-16], a hybrid of the SMC and FLC, gives a simple way to design the controller systematically and provides the asymptotical stability of the system. In general, the FSMC can also reduce the rule number in the FLC and still possess robustness.