Dynamic Modeling and Simulation of Robot Manipulators: The Newton-Euler Formulation

TLDR: A complete derivation of the method is derived, and an automated framework for applying the method on any serial manipulator with revolute joints is presented, and a confirmation of a mathematical proof based on a Lyapunov stability analysis is presented.

Abstract: Dynamic modeling means deriving equations that explicitly describes the relationship between force and motion in a system. To be able to control a robot manipulator as required by its operation, it is important to consider the dynamic model in design of the control algorithm and simulation of motion. In general there are two approaches available; the Euler-Lagrange formulation and the Newton-Euler formulation. This thesis explains briefly the differences of the formulations, and then research the Newton-Euler method in detail. A complete derivation of the method is derived, and an automated framework for applying the method on any serial manipulator with revolute joints is presented. By using the framework, the Newton-Euler formulation is applied on a modern industrial manipulator with six degrees of freedom. The dynamic parameters of the system are estimated, and the validity of the resulting dynamic model is verified by several simulations in open and closed loop. The simulations show that the system is unstable in open loop, and that it achieves global asymptotic stability in closed loop with gravity compensation, by including PD controllers with independent joint control. The latter is a confirmation of a mathematical proof based on a Lyapunov stability analysis, which is presented as well. Equivalent simulations of the dynamic model of the same manipulator derived by the standard Euler-Lagrange formulation show that the efficiency of recursive procedures is way higher that treating the manipulator as a whole. A suggestion for future work is performing thorough dynamic parameter identification. An improved model can ultimately be implemented in the controller of the manipulator, and optimized for a specific job task.