The sensor-based navigation is the problem of how to select a sequence of sensor-based behaviors between start and goal positions of a mobile robot. If the robot does not know its 2-D environment completely or partially, it is obliged to rely on sensor information reflected from closer obstacles in order to avoid them in an on-line manner. In the on-line framework, we should consider how a mobile robot reaches its goal position in an uncertain 2-D environment. In this paper, we survey almost all the previous sensor-based navigation algorithms, classify their convergences of a mobile robot to its goal position into four categories by basic conditions, and then discuss about acceleration of the convergences by additional conditions.