Abstract This paper promotes an idea of describing singularities of non-holonomic robotic systems by normal forms under feedback of associated control systems. In order to increase the explanatory power of the presentation this idea has been applied to the dynamics of a planar free-floating space robot composed of a base (a spacecraft) and a k -DOF (Degrees Of Freedom) on board manipulator. A general Lagrangian dynamics model of the robot is provided. Relying on the preservation of the linear and angular momenta, the affine Pfaffian constraints of motion are obtained. These constraints are expressed in specific coordinates resulting in a pre-normal form of the dynamics model of the robot, represented as a control-affine system, and an associated differential form. The pre-normal form is further transformed by feedback to a normal form, using some tools of the theory of differential forms. Normal forms of the space robot dynamics for k = 2 up to k = 8 DOF on board are computed that describe the ultimate structure of the dynamics model as well as characterize configuration singularities of the space robot.

中文翻译：

---

非完整机器人系统的范式和奇点：自​​由漂浮空间机器人的研究

摘要 本文提出了一种在相关控制系统反馈下用范式描述非完整机器人系统奇异性的思想。为了增加演示文稿的解释力，该想法已应用于由基座（航天器）和 ak-DOF（自由度）机载操纵器组成的平面自由浮动空间机器人的动力学。提供了机器人的一般拉格朗日动力学模型。依靠保持线性和角动量，获得运动的仿射 Pfaffian 约束。这些约束以特定坐标表示，导致机器人动力学模型的预正规形式，表示为控制仿射系统，以及相关的微分形式。前范式通过反馈进一步转化为范式，使用微分形式理论的一些工具。计算 k = 2 到 k = 8 自由度的空间机器人动力学的正规形式，描述动力学模型的最终结构以及表征空间机器人的配置奇异性。