In this paper two well known and two new methods, and corresponding algorithms, of trajectory planning with a constrained end-effector path tracking error are presented and compared. They are: an exact path following method, the Taylor's algorithm of following a straight line with prescribed accuracy, a local optimization method, and a method of local trajectory shortening. It appears that the last two methods provide path following with a prescribed accuracy while keeping a planned trajectory as short as possible. Presented algorithms can extend robot programming languages with a tool of trajectory planning.