Xin Xin, Liu Yannian, Zhang Kanjian
Faculty of Computer Science and Systems Engineering, Okayama Prefectural University, 111 Kuboki, Soja, Okayama 719-1197, Japan.
School of Automation, Southeast University, and Key Laboratory of Measurement and Control of Complex Systems of Engineering, Ministry of Education, Nanjing 210018, China.
ISA Trans. 2022 Dec;131:264-273. doi: 10.1016/j.isatra.2022.05.028. Epub 2022 May 28.
We deal with the linear controllability of two underactuated multi-link robotic systems in this paper. First, for a general n-link inverted pendulum mounted on a cart in a vertical plane, we prove that it is linearly controllable around the equilibrium point with the cart in a desired position and each link of the pendulum in the upright position regardless of its physical parameters, if and only if the cart is actuated. Second, for an n-link underactuated planar robot with its first joint mounted on a fixed base in a horizontal plane, we prove that it is linearly controllable around the trajectory where each link of the robot stretches straight out and rotates with a constant angular velocity, if and only if its first joint is actuated, regardless of its physical parameters and regardless of the actuation or underactuation of its rest joints. We illustrate the above results via a quintuple pendulum-cart system and a four-link planar gymnastic robot in literature. We give new insights into the linear controllability around an equilibrium point or a trajectory of underactuated robotic planar systems with multiple unactuated joints.
本文研究了两个欠驱动多连杆机器人系统的线性可控性。首先，对于一个安装在垂直平面内小车上的一般n连杆倒立摆，我们证明，当小车处于期望位置且摆的每个连杆处于直立位置时，无论其物理参数如何，当且仅当小车被驱动时，该倒立摆在平衡点附近是线性可控的。其次，对于一个第一关节安装在水平面固定基座上的n连杆欠驱动平面机器人，我们证明，当且仅当其第一关节被驱动时，无论其物理参数如何，也无论其其余关节是被驱动还是欠驱动，该机器人在其各连杆伸直并以恒定角速度旋转的轨迹附近是线性可控的。我们通过文献中的一个五连杆小车摆系统和一个四连杆平面体操机器人对上述结果进行了说明。我们对具有多个未驱动关节的欠驱动机器人平面系统在平衡点或轨迹附近的线性可控性给出了新的见解。
