A survey of equations of motion in terms of inertial quasi-velocities for serial manipulators

Abstract

In this work we compare equations of motion using the so-called inertial quasi-velocities. As a result of these velocities we obtain two first-order decoupled equations of motion instead of one second-order differential equation of motion. The methods presented here, solve in a way, the problem of nonlinear dynamic decoupling. The first and the second method result from diagonalized Lagrangian robot dynamics (Jain and Rodriguez, IEEE Trans Robot Autom 11:571–584, 1995) and are known as normalized and unnormalized quasi-velocities. The third method described by Junkins and Schaub (J Astronaut Sci 45:279–295, 1997) offers eigenfactor quasi-coordinate velocities formulation for multibody dynamics. As a consequence of using transformation given by Loduha and Ravani (Trans ASME J Appl Mech 62:216–222, 1995) we obtain decoupled equations of motion in terms of modified generalized velocity components. Here we limit all these methods to serial manipulators. The novelty of this paper consists in physical interpretation of the quasi-velocities and discussion concerning equations of motion, the kinetic energy shaping, relationship between each of them and properties useful for simulation and control purposes. Also forward dynamics algorithms and their computational complexity in terms of new velocities are given. Simulation results illustrate the theoretical investigations. We conclude that all methods offer interesting possibilities for dynamic simulation and future control investigations.