Mobile robots motion planning is one of the key technologies in the robot navigation. During the past 40 years of mobile robot development, lots of planning algorithms were proposed. Because of the tremendous difference among environment models and planning methods, it is difficult to compare them experimentally. This survey reviewed the classical planning algorithms in the history of robot development and presented a set of criteria of planners and the formal description of the problem of planning. The paper described each algorithm's principle or main technology in detail and classified the algorithms based on environment model and search strategy. They are classified into four categories, that is, planners based on geometry construction of free spaces, forward graph search algorithms, random sampling-based motion planning algorithms and intelligent planners. Last, The paper compared and summarized their performance and gave an outlook to the future research of the mobile robots motion planning.