Hybrid fuzzy sliding-mode under-actuated control for trajectory tracking of mobile robot in the presence of friction and uncertainty

In the beginning, the kinematic model, dynamic model of a differential mobile robot (DMR), and the dynamic model of left- and right-wheel DC motors are combined to be a controlled system. The control inputs of the proposed controlled system include the input voltages for the left- and right-wheel motors, i.e., two inputs. On the other hand, the system outputs contain two-dimension position and its orientation, i.e., three outputs. Due to the under-actuated characteristic, the sliding surface using directly controlled output is designed so that the number of control input and sliding surface is the same, and that the indirectly controlled output is also controlled. Under uncertain environment including friction and uncertainty, the sliding-mode under-actuated control (SMUC) with suitable conditions is designed such that an asymptotical tracking result is obtained. To enhance system performance, an on-line fuzzy modeling of friction and uncertainty is employed to design a fuzzy model-based sliding-mode under-actuated control (FSMUC). Finally, the proposed hybrid fuzzy sliding-mode under-actuated control (HFSMUC) combining SMUC and FSMUC with a transition maintains both advantages of SMUC and FSMUC and simultaneously avoids the disadvantages coming from SMCU and FSUMC.