A procedure to find equivalences among dynamic models of planar biped robots

In this paper, a method to find equivalences among dynamic models is presented. The models are given in different generalized coordinates for the same mechanical system. This novel method is valid for planar biped robots, i.e., those whose motions are executed only in a plane. We show that no matter which generalized coordinates are used to get the dynamic models, there is always an equivalence among them by using a particular input matrix. We exhibit some advantages of getting the dynamic model using absolute coordinates instead of relative coordinates, and we show how to calculate the input matrix for getting the equivalence between these models. Because of its simplicity, a compass-like biped robot model is used as example to explain in detail the novel procedure. In order to appreciate the benefits of the proposed procedure in biped robots of high degrees of freedom, we also present the equivalence between two dynamic models for the single support phase of a 5 degrees of freedom biped robot using absolute coordinates and relative ones.