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.
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