This paper presents a smooth state feedback control algorithm for set point stabilization of a three-link planar nonholonomic manipulator (NHM). Compared to known control algorithms for such a manipulator, the one presented here is able to control the NHM in its singular positions. In the control algorithm synthesis, we consider the kinematic model of the NHM. Our control algorithm solution is based on an extension of models state variables. Smooth point stabilization is achieved by implementing the transverse function approach. The control algorithm synthesis is performed with utilization of a Lie group representation. Because the Lie algebra associated with the NHM is not nilpotent, we apply a homogeneous nilpotent approximation. Analytical results have been reinforced by simulations and experiments, which were executed using a newly built three-link planar NHM. To the best of our knowledge, this manipulator is the third of its kind in the world, but due to its distinct kinematic structure, it is a unique mechanism.

中文翻译：

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具有奇异性的新型非完整机械臂的光滑状态反馈控制

本文提出了一种用于三连杆平面非完整机械手（NHM）的设定点稳定的光滑状态反馈控制算法。与用于这种机械手的已知控制算法相比，此处介绍的一种算法能够将NHM控制在其单个位置。在控制算法综合中，我们考虑了NHM的运动学模型。我们的控制算法解决方案基于模型状态变量的扩展。平滑点稳定是通过实施横向函数方法来实现的。利用李群表示来执行控制算法综合。由于与NHM相关的李代数不是幂等的，因此我们应用齐次幂等近似。通过模拟和实验增强了分析结果，它们是使用新建的三连杆平面NHM执行的。据我们所知，该操纵器是世界上同类操纵器中的第三种，但由于其独特的运动学结构，它是一种独特的机构。