This paper presents the conditions and PD controller to swing-up the Acrobot to which a spring is attached at the passive joint (first joint). Because the motion of the system is in the vertical plane, there are some system parameters associated with gravity. The range of a spring constant and controller gain that allow the PD controller to swing-up the system is defined depending on these parameter values. To prove that the PD controller makes the system approach the equilibrium points, one of which is swing-up state (upright equilibrium point, UEP), the motion of the first link is analyzed according to the motion of the second link and the torque on the active joint (second joint) with an actuator. Among these equilibrium points, the conditions that can only converge to the UEP of the system are found.

本文介绍了在被动接头（第一接头）上安装了弹簧的Acrobot的条件和PD控制器。由于系统的运动在垂直平面上，因此存在一些与重力相关的系统参数。取决于这些参数值，定义允许PD控制器向上摆动系统的弹簧常数和控制器增益的范围。为了证明PD控制器使系统逼近平衡点，其中一个是向上摆动状态（垂直平衡点，UEP），根据第二个连杆的运动和第二个连杆的扭矩分析了第一个连杆的运动。带执行器的主动关节（第二关节）。在这些平衡点中，找到了只能收敛到系统UEP的条件。