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This paper proposes an adaptive nonlinear controller to stabilize an autonomous wheeled mobile robot. The controller equations are obtained following a backstepping approach. The robot model is divided into two parts: a state space model with intermediate control inputs and algebraic nonlinear equations relating the true and the intermediate control inputs. The robot parameters are assumed unknown. First, a suitable change of variable is applied to the traditional robot dynamics to reveal the strict feedback structure of this state space model. Next, a three-step adaptive backstepping control design method is applied to obtain the intermediate control input expressions. Finally the true control inputs are found by solving iteratively the nonlinear equations that relates intermediate and true control inputs. The adaptation algorithms are based on the projection method and guarantee that estimated parameters converge and remain inside predefined domains. The proposed design strategy is tested in simulation. The results show good tracking performances despite large parameter variations.