The proposed quasi-minimum time trajectory for a mobile robot is obtained as follows. First a global quasi-shortest path is generated by Path Shortcut Method on a provided floor map. In the navigation step, a local quasi-shortest collision-free path is obtained by the method and described as a spline curve. Then the time optimized trajectory is generated by the idea of time scaling. An idea of self-positioning with a range sensor is also proposed. The autonomous navigation is effectively executed by the proposed algorithms.