On the use of the dual Euler-Rodrigues parameters in the numerical solution of the inverse-displacement problem

The Euler-Rodrigues parameters (ERP) are revisited in this paper, the motivation being the need for a systematic methodology to formulate the inverse-displacement problem associated with a six-revolute (6R) serial robot. Although significant progress was made in the solution of the problem in the eighties and nineties, there is not one algorithm adopted by the research and applications communities, but rather various algorithms that lead to the resolvent polynomial of 16th degree or lower. In this paper the problem is formulated using the dual ERP. Motivated by the lack of a methodology that would allow R&D professionals to readily implement a generic solution algorithm in industrial environments requiring real-time inverse-displacement problem (IDP) solutions. An inverse-displacement numerical solution of 6R robots of arbitrary architecture is proposed. This is the main thrust of the paper. The contribution of the paper is a systematic procedure to formulate the problem and implement its solution by numerical means. The procedure is illustrated with the example of an industrial robot whose architecture does not allow for a closed-form solution.