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.

本文针对所提出的一般非对称 S 曲线 (AS 曲线) 轮廓提出了一种新颖的优化过程，以实现快速运动和低残余振动。通用 AS 曲线配置文件是传统对称 S 曲线和先前的非对称 S 曲线配置文件的超集，可以在开始和到达阶段独立控制加速度和急动。为了在减少残余振动的同时最小化定位时间（行程时间加稳定时间），我们通过在物理限制和残余振动约束下分配时间间隔来制定一般 AS 曲线配置文件的优化。为此，提供了一般 AS 曲线轮廓的完整解决方案以构建物理限制。通过执行具有不同运动参数的点对点运动曲线并测量残余振动信号，我们使用多任务高斯过程回归获得替代数值模型来构建残余振动响应，然后利用该模型预测稳定时间和最大残余振幅。最后，7 自由度 Sawyer 机器人对时间最优运动曲线进行了验证，表明与传统的对称 S 曲线相比，所提出的运动曲线优化方法能够显着减少残余振动。然后利用该模型预测稳定时间和最大残余振幅。最后，7 自由度 Sawyer 机器人对时间最优运动曲线进行了验证，表明与传统的对称 S 曲线相比，所提出的运动曲线优化方法能够显着减少残余振动。然后利用该模型预测稳定时间和最大残余振幅。最后，7 自由度 Sawyer 机器人对时间最优运动曲线进行了验证，表明与传统的对称 S 曲线相比，所提出的运动曲线优化方法能够显着减少残余振动。