Time-optimal general asymmetric S-curve profile with low residual vibration

This paper presents a novel optimization process for the proposed general asymmetric S-curve (AS-curve) profile to achieve fast movement and low residual vibration. The general AS-curve profile, which is the superset of traditional symmetric S-curve and prior asymmetric S-curve profiles, enables independent manipulation of accelerations and jerks at the starting and arrival phases. To minimize the positioning time (traveling time plus settling time) while reducing residual vibration, we formulate the optimization of the general AS-curve profile by allocating the time intervals under the physical limits and the residual vibration constraints. To this end, the complete solutions to the general AS-curve profile are provided to construct physical limits. By executing the point-to-point motion profiles with different motion parameters and measuring the residual vibration signals, we obtain a surrogate numerical model using the multi-task Gaussian process regression to construct the residual vibration response, and then utilize this model to predict the settling time and maximum residual vibration amplitude. Finally, the time-optimal motion profiles are validated by the 7-DOF Sawyer robot showing that the proposed motion profile optimization method is capable of reducing the residual vibration significantly compared with the traditional symmetric S-curve.