This paper proposes a solution to the cross-a-door problem in unknown environments for a robotic wheelchair commanded through a Human-Machine Interface (HMI). The problem is solved by a dynamic path planning algorithm implementation based on successive frontier points determination. An adaptive trajectory tracking control based on the dynamic model of the robotic wheelchair is implemented on the vehicle to direct the wheelchair motion along the path in a smooth movement. An EKF feature-based SLAM is also implemented on the vehicle which gives an estimate of the wheelchair pose inside the environment. The SLAM allows the map reconstruction of the environment for safe navigation purposes. The whole system steers satisfactorily the wheelchair with smooth movements through common doorways which are narrow considering the size of the vehicle. Implementation results validating the proposal are also shown in this work.