Optimization of Generalized S-Curve Trajectories for Residual Vibration Suppression and Compliance With Kinematic Bounds

Abstract

This paper proposes a new optimization algorithm that assures the minimum possible duration of generalized S-curve trajectories compliant with kinematic limitations and capable of suppressing residual vibrations when tracked by a resonant plant. Thanks to the possibility of generating such kind of trajectories with a chain of filters, called smoothers, each one characterized by a single parameter, i.e. the duration Ti of its impulse response, the optimization process aims at minimizing the order of the trajectory, and accordingly the number of smoothers in the chain, and leads to rest-to-rest trajectories that, under the given specifications, cannot be made shorter in time. Therefore, the structure of the trajectory is not predetermined but is the outcome of the proposed algorithm together with the optimal parameters defining it. The effectiveness of the proposed approach is proven by applying the designed trajectories to an experimental setup based on a flexible link.

Time-Optimal Pick-and-Throw S-Curve Trajectories for Fast Parallel Robots

“…Several methods have been proposed in the literature to generate time-optimal S-curve trajectories [26]- [28]. In this section, an original algorithm formulation to compute the maximum velocity V and acceleration A of a minimum-time 3 rd order S-curve trajectory is introduced.…”

Novel Gaussian Acceleration Profile for Smooth Jerk-Bounded Trajectories

“…Fig. 5 contrasts the trapezoidal-velocity [12], [15], [26], [28], trapezoidal-acceleration [4], [5], [10], [13], [16], [17], [21], [22], [26], and polynomial profiles [3], [6], [9], [24], [25], [27], [28], against two associated variants of the proposed acceleration profile through computational simulation. The parameters for the first derived form of the proposed profile to carry out this comparison are: Displacement = 60 mm, maximum velocity = 198.8 mm/s, and maximum acceleration = 1500 mm/s 2 .…”

“…A machine motion dynamics is defined by its position, velocity, acceleration, and jerk profiles [4]- [7]. It is well known that high jerk values produce high amplitude vibrations in a machine component.…”

Time-Optimal Asymmetric S-Curve Trajectory Planning of Redundant Manipulators under Kinematic Constraints

“…FIR filters are widely used in the motion control of automation equipment owing to the ease of hardware implementation. Based on FIR filters, the acceleration continuous motion profile was generalized to a generic model with high-order continuity [ 24 ], and a time-optimal characteristic of the reference signal was injected [ 25 ]. The S-curve of a cubic polynomial can contribute to a tradeoff between motion smoothness and computational complexity.…”