A Discrete-Time Filter for the Generation of Signals With Asymmetric and Variable Bounds on Velocity, Acceleration, and Jerk

Abstract

Reference signals, which are used to drive feedback control loops, are often evaluated on the fly on the basis of the operating conditions. As a consequence, they can be too demanding for the actuation system whose outputs could saturate, thus worsening the tracking performances of the feedback loop. Improved answers can be obtained by smoothing rough references by means of proper filters that are also able to impose bounds on the signal dynamics. This paper proposes a filtering system whose output mimics at best any given input signal compatibly with some smoothness requirements. In particular, generated signals are continuous up to the second time derivative, and their first three time derivatives are constrained between assigned bounds that can be asymmetric and that can also be changed on the fly. The filter, which is internally characterized by minimum time transients, is able to follow, with zero tracking error, piecewise-continuous signals given by combinations of steps, ramps, and parabolas.

Path-Accurate Online Trajectory Generation for Jerk-Limited Industrial Robots

“…Notation: Derivatives are computed by backward differences, omitting the sampling time T 0 . This results in a simple but unusual notation which is explained in the Appendix, similar to [15]. Vectors of all axes are denoted by bold face letters whereas single axes are in normal face with the index as last subscript, e.g.…”

“…In contrast, here the goal is a trajectory that, perhaps after a temporary slowdown, is synchronized with the original robot program, as in Ref. [15]. This is crucial when multiple robots or devices share the same working space.…”

An Efficient Algorithm for the Real-Time Generation of Synchronous Reference Signals

“…The solutions proposed over the years have sometimes been conceived for continuous-time environments [15]- [18] or, in other contexts, for discrete-time applications [19]- [22].…”

“…M STANDS FOR MULTIPLICATIONS OR DIVISIONS, A INDICATES ADDITIONS OR SUBTRACTIONS, WHILE S MEANS SQUARE ROOTS. TERMS m, k b , k d , ke, AND k f ARE EVALUATED ACCORDING TO(11),(14),(16),(18), AND (21) OR(22), RESPECTIVELY.…”

Trajectory generation for immediate path-accurate jerk-limited stopping of industrial robots

“…In contrast to Refs. [5], [10], in most papers the resulting trajectory is represented using a scalar parameter s, sometimes denoted as arc length. Then, the velocity profile is computed as s(t) or asṡ(s) in the phase space.…”