Discrete trajectory formation in comparison with the analytical method for smooth movements

Reference trajectory formation is a starting point and used as a target value of control. It is a set of points regarded as the target in every interrupt routine of control procedure and, therefore, called motion profile for a moving system under the tracking. Instead of usual trajectories which are the continuous functions of time, a practical discrete trajectory formation method which has a polynomial nature but more application to the real robot systems is compared to the continuous time version which is the analytical solution presented by different authors in the same year 2004 at different places. The effectiveness of this practical method, ASPOT, is verified through the experiments using a linear motor system. Especially, the most important benefit with respect to the CPU time is shown through the implementation of the algorithms on a DSP. ASPOT takes just 5~6 % of the time for common polynomial case does as well as it producing all derivative states simultaneously