A Discrete-Time Filter for the On-Line Generation of Trajectories with Bounded Velocity, Acceleration, and Jerk

The performances of controlled systems can be improved by driving them with smooth reference signals. In case of rough signals, smoothness can be achieved with the help of appropriate dynamic filters. To this purpose a novel discrete-time filter is proposed in the paper. It has been appositely designed for real-time motion applications like those that can be encountered in robotic or mechatronic contexts. The filter generates output signals which are continuous together with their first and second time derivatives. Simultaneously, the first, the second, and the third time derivatives are bounded within freely assignable limits. If such limits are changed on-the-fly, the filter hangs the new bounds in minimum-time. An example case shows the filter while tracking steps, ramps and parabolas by means of bounded-dynamic transients.