A new fuzzy adaptive control is applied to solve a problem of motion control of nonholonomic vehicles with two independent wheels actuated by a differential drive. The major objective of this work is to obtain a motion control system by using a new fuzzy inference mechanism where the Lyapunov stability can be ensured. In particular the parameters of the kinematical control law are obtained using a fuzzy mechanism, where the properties of the fuzzy maps have been established to have the stability above. Due to the nonlinear map of the intelligent fuzzy inference mechanism (i.e., fuzzy rules and value of the rule), the parameters above are not constant, but, time after time, based on empirical fuzzy rules, they are updated in function of the values of the tracking errors. Since the fuzzy maps are adjusted based on the control performances, the parameters updating ensures a robustness and fast convergence of the tracking errors. Also, since the vehicle dynamics and kinematics can be completely unknown, dynamical and kinematical adaptive controllers have been added. The proposed fuzzy controller has been implemented for a real nonholonomic electrical vehicle. Therefore, system robustness and stability performance are verified through simulations and experimental studies. 1. Introduction In recent years much attention has been focused upon the position and orientation control of nonholonomic mechanical systems. Nonholonomic mechanics describe the motion of systems constrained by nonintegrable constraints, that is, constraints on the system velocities that do not arise from constraints on the configurations alone. A mobile autonomous wheeled vehicle with two wheels actuated by a differential drive mechanism, that is, two independent electric DC motors with common axis, is usually studied as a typical nonholonomic system. Kinematical nonholonomic constraints arise in wheeled vehicles under the no-slip constraints. Due to nonholonomic motion, the vehicle above is also underactuated [1]. In fact there are three generalized coordinates that is, lateral position, longitudinal position, and vehicle orientation to be controlled, while there are two control inputs only, that is, steering and longitudinal inputs. Several approaches have been proposed for the synthesis of kinematical controllers for vehicles with nonholonomic constraints on the motion [2–4]. The kinematical controller is essential to guarantee the vehicle motion along the direction of the orientation. The main idea behind these algorithms is to define velocity control inputs which stabilize the closed
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