Inertia Parameter Identification for Closed-Loop Mechanisms: Adaptation of Linear Regression for Coordinate Partitioning

Abstract

Abstract Accurate modeling and identification methods have increasing importance for design, verification, and control of multi-body systems. However, operational parameters are often unknown and inaccuracies of inertia parameters are among the main sources of uncertainty in multibody models. This study therefore investigates the application of a linear-regression-based identification approach for rigid multibody systems. A multibody system model, originally described with differential-algebraic equations, is transformed into a set of ordinary differential equations using coordinate partitioning. This allows the identification framework, which requires the system to be described with ordinary differential equations, to be applied for rigid multibody systems described with either relative coordinates, reference point coordinates, or natural coordinates. The methodology is demonstrated through a numerical example of a slider-crank mechanism with a kinematic reference set for the crank arm. The measurement data for identification is produced artificially using a commercial multibody software. The results show that the presented methodology is capable of accurately identifying the system’s inertia parameters even with a relatively short motion trajectory used for training. However, the effects of measurement noise are not covered in this study — this is because the presented model is mathematically equivalent to the models used in robotics, and the tools for measurement noise reduction for those models are already discovered in robotics literature. The presented linear-regression-based identification approach opens new opportunities for developing more accurate multibody models. These models can be considered especially useful for state-estimation and control of multibody systems. When the static model parameters are accurately identified, different state-estimation algorithms can more effectively estimate dynamically changing uncertainties.