A Set-Point Control for a Two-link Underactuated Robot With a Flexible Elbow Joint
A Set-Point Control for a Two-link Underactuated Robot With a Flexible Elbow Joint
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DOI：
10.1115/1.4024427
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发表时间：
2013-09
影响因子：
1.7
通讯作者：
Xin Xin-Xin;Yannian Liu
中科院分区：
文献类型：
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作者：
Xin Xin-Xin;Yannian Liu
本文研究了两连杆欠驱动机器人在垂直平面上运动的设定点控制问题，其中第一个关节上只有一个驱动器，两个连杆(柔性肘关节)之间有一个弹簧。首先，我们给出了这种柔性机器人在直立平衡点(两个杆件处于直立位置)的线性可控性和平衡构型的两个新性质。其次，证明了对于弹簧常数在一定范围内的机器人，对第一关节角度的比例导数(PD)控制可以使机器人全局稳定在UEP处。第三，针对不满足上述弹簧常数范围的机器人，研究了如何将基于能量的控制方法推广到机器人的摆动控制器设计中，该方法的目标是控制机器人的总机械能和第一个关节的角速度。给出了避免控制器出现奇异性的充要条件，并通过研究总机械能的收敛，阐明了闭环系统平衡点的结构和稳定性，分析了机器人在该控制器下的运动。我们给出了数值研究的结果，支持了我们的理论结论。
This paper concerns a set-point control problem for a two-link underactuated robot moving in the vertical plane with a single actuator at the first joint and a spring between the two links (flexible elbow joint). First, we present two new properties of such a flexible robot about the linear controllability at the upright equilibrium point (UEP, where two links are in the upright position) and about its equilibrium configuration. Second, we show that for the robot with a certain range of spring constant, the proportional derivative (PD) control on the angle of the first joint can globally stabilize the robot at the UEP. Third, for the robot not satisfying the above range of spring constant, we study how to extend the energy-based control approach, which aims to control the total mechanical energy and the angle and angular velocity of the first joint of the robot, to design a swing-up controller. We provide a necessary and sufficient condition for avoiding the singularity in the controller, and we analyze the motion of the robot under the presented controller by studying the convergence of the total mechanical energy and clarifying the structure and stability of the closed-loop equilibrium points. We present the results of numerical investigation, which support our theoretical conclusions.