Applying differential geometry to kinematic modeling in mobile robotics

Abstract

We examine the kinematic model of a mobile robot with tools of differential geometry. These tools allow comprehensive modelling of even complex mobile articulated mechanical systems. Furthermore, they offer a very illustrative structure of the equations of motion by providing a so called trivial connection of pure motion and shape motion. Pure motion is the systems evolution in physical space, shape motion is the movement of the articulated mechanics such as wheels, fins, flaps, legs, etc. Different from the most other publications, we try to give a graphical interpretation of the complex mathematical objects as well as a detailed mathematical treatment of configuration spaces and its tangentials. This is motivated in the observation that people with an engineering background often find it difficult to get into this mathematical domain.