A Machine Learning Approach for Minimal Coordinate Multibody Simulation

Over the years, a wide range of generalized coordinates have been proposed to describe the motion of rigid and flexible multibody systems. Depending on the type of formulation, a different equation structure is obtained for the model. Most formulations rely on a redundant number of Degrees Of Freedom (DOFs) and some associated constraints, leading to a set of Differential-Algebraic Equations (DAEs) to model the system dynamics. On the other hand, the ‘Minimal Coordinate’ formulation describes the dynamics through a minimal amount of DOFs and leads to a system of Ordinary Differential Equations (ODEs). For many applications, this ODE structure is an important benefit, as it enables a natural integration for state-estimation and model-based control. The backside of this approach is that it is generally not-straightforward to find a minimal number of parameters to unequivocally describe the system configurations, especially for complex mechanisms. In this work, a machine learning approach based on Auto-Encoders is proposed to find a non-linear transformation that leads to a minimal parameterization of the motion. It is shown that such non-linear transformation can be used to project into minimal coordinates while its inverse permits to perform the simulation in the reduced dimension and re-obtain the original coordinates.