Normal Forms of Robotic Systems with Affine Pfaffian Constraints: A Case Study

We study robotic systems subject to Pfaffian constraints in the affine form. A control system representation of such a system is given in the form of a control-affine system. Normal forms under feedback are considered and used both as a description of configuration singularities of the robotic system as well as a tool for solving the motion planning problem. An example of a space manipulator is analysed in detail to illustrate the theoretical concepts.