Unit homogenization for estimation of inertial parameters of multibody mechanical systems

Parameter estimation is of great importance in the analysis and design of multibody systems. As the result of research in this framework, several contributions exist in parameter estimation of mechanical systems in general and robotic systems in particular. In this context, numerical approaches can be used to identify the inertial parameters based on measurement data collected from experiments.However, there are some important issues which are crucial from the physical point of view and have not been considered in the development of numerical approaches for parameter estimation. In this paper, we address the problem of a regression matrix with nonhomogeneous physical units. A regression matrix, which contains the most important information about the motion of the system, with nonhomogeneous units cannot and should not be used in numerical methods due to the unit-inconsistency in matrix multiplication required in all numerical approaches. Attention must be paid to this before implementing any parameter estimation algorithm. This paper proposes a procedure to treat this problem in a proper way.