Abstract Part I of this paper presents a study of an autonomous trajectory generation system (ATGS) which is useful for industrial robots carrying out mechanical operations. It is a very simple job with such an ATGS to generate planar curved trajectories f(x, y) = 0, an attractive factor in such applications. Two alternative variations of the ATGS are presented which possess particular characteristics. Part II deals with the trajectory control problem and uses the ATGS as a first stage of a model reference adaptive control loop of a robot. The theoretical results are illustrated by simulation examples worked out using the software packages developed for this purpose.