For a three-link vertical underactuated manipulator (TVUM) with only one active joint, the control target is to swing up its endpoint from the straight-down equilibrium point (SDEP) and to stabilize the endpoint at the straight-up equilibrium point (SUEP) eventually. Up to now, there are few effective control strategies to achieve the above control target. In this article, we propose an effective control method based on the trajectory optimization to realize the system control target, and the main steps of this article are: 1) a continuous trajectory that consists of two segments with design parameters is planned for the actuated link, along which the actuated link can be swung up from the initial states to the final states; 2) the design parameters are optimized by using the intelligent optimization algorithm to guarantee that the states of the underactuated links are continuous at the junction. In this way, the underactuated links are also moved to their final states with the actuated link simultaneously; 3) a tracking controller is designed by using the sliding-mode method to track the trajectory with optimized design parameters, so the endpoint is swung up from the SDEP to the SUEP directly; and 4) a stabilizing controller is further devised through the LQR method to keep the endpoint being stable at the SUEP. Finally, simulation results show that the proposed control method achieves the swing-up and stable control target of the system, and the control performance of the proposed method is superior than that of the existing control methods through the comparisons.

中文翻译：

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基于轨迹优化的单主动关节三连杆垂直欠驱动机械臂有效控制方法


对于只有一个主动关节的三连杆垂直欠驱动机械臂（TVUM），控制目标是使端点从直下平衡点（SDEP）向上摆动，并稳定在直上平衡点（SUEP） ） 最终。迄今为止，实现上述控制目标的有效控制策略还很少。在本文中，我们提出了一种基于轨迹优化的有效控制方法来实现系统控制目标，本文的主要步骤是：1）为驱动连杆规划一条由具有设计参数的两段组成的连续轨迹，沿着该驱动连杆可以从初始状态摆动到最终状态； 2）利用智能优化算法对设计参数进行优化，保证欠驱动连杆在连接处状态连续。这样，欠驱动连杆也与驱动连杆同时移动到其最终状态； 3）采用滑模方法设计跟踪控制器，以优化的设计参数跟踪轨迹，使端点直接从SDEP向上摆动到SUEP； 4)通过LQR方法进一步设计稳定控制器，以保持端点稳定在SUEP。最后仿真结果表明，所提出的控制方法实现了系统的摆动和稳定控制目标，并且通过比较，所提出的方法的控制性能优于现有的控制方法。