Abstract S-curve commands are ubiquitous in servo drives owing to their simplicity and smoothness. Nevertheless, they need to be adapted for use in flexible systems, where the problem of residual vibration must be addressed. This paper proposes a simple motion planning method for the vibration-free transfer process of an overhead crane using S-curve commands. Based on a position baseline S-curve, which is generated from a bang-off-bang acceleration profile, two approaches are proposed to build the vibration suppression capability. One is an embedding method that injects the essential terminal conditions for vibration-free transportation into the baseline S-curve command without altering its original form. The other is a shaping method inspired from the input shaping technique. In both schemes, the baseline S-curve is parameterized to establish minimum-time optimization problems, in which maximum velocity and maximum acceleration of the actuator are explicitly taken into consideration. The minimum-time solutions are successfully obtained by solving constrained (discrete) nonlinear programs. An online trajectory generation can be realized using the proposed approach. Both simulation and experimental results are given to verify the effectiveness of the proposed method.

中文翻译：

---

具有执行器限制的桥式起重机无振动运输的最短时间 S 曲线命令

摘要 S 曲线命令由于其简单性和平滑性在伺服驱动器中无处不在。然而，它们需要适用于必须解决残余振动问题的柔性系统。本文提出了一种使用 S 曲线命令的桥式起重机无振动传递过程的简单运动规划方法。基于由 bang-off-bang 加速度曲线生成的位置基线 S 曲线，提出了两种方法来构建振动抑制能力。一种是嵌入方法，在不改变其原始形式的情况下，将无振动运输的基本终端条件注入到基线 S 曲线命令中。另一种是受输入整形技术启发的整形方法。在这两个方案中，基线 S 曲线被参数化以建立最小时间优化问题，其中明确考虑了执行器的最大速度和最大加速度。通过求解约束（离散）非线性程序成功地获得了最小时间解。使用所提出的方法可以实现在线轨迹生成。给出了仿真和实验结果来验证所提出方法的有效性。