Online Planning of Multi-Segment Trajectories with Trigonometric Blends

In this paper, the approach based on FIR (Finite Impulse Response) filters, that has been shown to be very efficient for planning time-optimal trajectories composed by polynomial segments, is extended to the design of trajectories characterized by profiles of velocity, acceleration, jerk or even higher derivatives composed by trigonometric functions.A simple discrete-time filter, able to provide as output this kind of trajectories when a rough input signal composed by step functions is applied, is proposed, with two main consequences: 1) the generation of the trajectory results very efficient, even with high degree of continuity and the planning can be performed online; 2) the equivalence between the considered class of trajectories and linear filters allows an immediate frequency characterization of the motion law. In this way, it is possible to define the trajectories by considering constraints expressed in the frequency-domain besides the classical time-domain specifications, such as bounds on velocity, acceleration, and so on. Two examples illustrates the main features of the proposed trajectory planner, in particular with respect to the problems of multi-point trajectory generation and residual vibrations suppression by proper reference inputs application.