The Euclidean Group, Invariants and Robotics

Robot manipulators are generally modelled as a collection of rigid bodies or links connected pairwise by joints. The Euclidean group of proper isometries of 3-space and its subgroups therefore play a central role in kinematic and dynamic modelling of robot systems. Engineers frequently use a system called Denavit-Hartenberg (DH) parameters for the description of serial robot manipulators – the type most commonly used in large-scale industrial applications. From a mathematical point of view, these should be invariant quantities with respect to an action of the Euclidean group. The Euclidean group is closely related to the associative algebra of dual quaternions and this relation provides an approach to identifying polynomial invariants that validate the DH parametrization. This is joint work with Mohammed Daher and Petros Hadjicostas.