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This paper describes a simultaneous localization and mapping (SLAM) algorithm for use in unstructured environments that is effective regardless of the geometric complexity of the environment. Features are described using B-splines as modeling tool, and the set of control points defining their shape is used to form a complete and compact description of the environment, thus making it feasible to use an extended Kalman-filter (EKF) based SLAM algorithm. This method is the first known EKF-SLAM implementation capable of describing general free-form features in a parametric manner. Efficient strategies for computing the relevant Jacobians, perform data association, initialization, and map enlargement are presented. The algorithms are evaluated for accuracy and consistency using computer simulations, and for effectiveness using experimental data gathered from different real environments.