Comparison of Simulation Effectiveness of Motion Equation Generation Methods for Articulated Rigid Body Systems

Authors: Sedat BAYSEÇ, Sadettin KAPUCU

Abstract: Mathematical models of robotic systems not only provide the designer with the most valuable resource on which ideas about control and motion design can be tested or the performance of a non existing sketch can be checked before a prototype is manufactured, but also provide a versatile teaching and practising aid. The mathematical model of the system includes the characteristics of the manipulator and its drive systems and is definitive of their dynamic behaviour. In most robotic applications, the response of the controller is much faster than the drives and the manipulator and hence its model is generally not required. This paper presents a treatise on the generation of motion equations of robotic manipulators, excluding the drives. Newton-Euler, Lagrange and Hamilton equations and a formulation based on gradient methods are examined and tested on an all-revolute, three degrees of freedom planar articulated linkage. The resulting closed form motion equations are presented for comparison, and the rules of thumb for the use of these equations are given. Finally, some of the well known general purpose simulator softwares, some of which are commercially available, are described.

Keywords: Robot manipulators, Newton-Euler equations, Lagrange's equation, Hamilton's Equations, Gradient methods.