Singularity Analysis of a Snake Robot and an Articulated Mobile Robot With Unconstrained Links

In this paper, we analyze the conditions related to singular configurations with unconstrained links and present related theorems and lemmas for a snake robot and an articulated mobile robot. A snake robot and an articulated mobile robot have links that have passive or active wheels and the links are serially connected by active joints. The singular configuration should be avoided if the robots are automatically controlled because they cannot execute intended motion when they are in the singular configuration. We derive a novel necessary and sufficient condition for the singular configurations of the snake robot; this removes some limitations of the traditional condition for a snake robot without unconstrained links. We also derive the necessary and sufficient conditions for the singular configurations of the articulated mobile robot, and the structural conditions under which a real articulated mobile robot does not have a singular configuration. These conditions are proved by analyzing the elements of matrices included in the kinematic model and considering the geometrical meaning of the elements. In addition, we propose evaluation indices representing the distance from the singular configurations of a snake robot. We verify the effectiveness of these indices through simulations.