论文标题
摆动游乐场秋千：扭矩控件用于诱发持续振荡
Swinging a playground swing: torque controls for inducing sustained oscillations
论文作者
论文摘要
自1960年代以来，已经研究了操场秋千的模型。但是，在其中大多数中，挥杆的位置是直接控制的。这简化了问题，但隐藏了用于保持秋千的扭矩机制。本文研究了这些机制。带有扭矩作为对照的两种模型，我们认为的对照与现代机器人技术的流行模型相同：杂技和反应轮摆。但是，通过静态反馈控制来维持挥杆的常规振荡的控制任务是新颖且具有挑战性的，尤其是当关节在将秋千连接到框架的关节中抑制时。我们开发两种类型的控件来完成此任务。一种用于小型阻尼，基于通过合适的初步反馈控制来使未障碍系统线性化。另一个用于大型阻尼。在稳定状态下，所得的闭环系统描述了一个和谐驱动的阻尼摆（以其复杂行为而闻名的简单系统），包括某些参数值的混乱运动。为了解决此类复杂性，我们将自由参数构建到控件中，然后根据模拟调整它们，以避免混乱并实现在操场上看到的常规振荡。
Models of a playground swing have been studied since the 1960s. However, in most of them, the position of the swinger is controlled directly. This simplifies the problem but hides the mechanics of torques applied to keep the swing moving in a regular pattern. This article studies these mechanics. Two models of a swing with torques as controls that we consider are identical to popular models of modern robotics: the Acrobot and reaction wheel pendulum. However, the control task of sustaining the swing's regular oscillations by a static feedback control is new and challenging, especially when damping in the joint connecting the swing to the frame is considered. We develop two types of controls to accomplish this task. One works for small damping and is based on linearizing the undamped system by a suitable preliminary feedback control. The other works for large damping. In the steady state, the resulting closed-loop system describes a harmonically driven damped pendulum (a simple system known for its complex behavior), including chaotic motion for some parameter values. To address such complexities, we build free parameters into the controls, then adjust them based on simulations to avoid chaos and achieve regular oscillations that are seen on playgrounds.
