Control of underactuated systems based on machine learning model: case studies

Abstract Besides traditional modelling approaches, machine learning surrogate models have become widespread. In addition to existing concepts, this work investigates the use of neural networks (NNs) to replace dynamic equations in multibody systems. While physics-informed neural networks (PINNs) dominate recent literature, their constraint enforcement via cost-function penalties poses tuning challenges. This paper proposes an alternative: training NNs on data with intentional constraint violations to implicitly learn stabilisation, avoiding PINN limitations. The proposed concept is applied to the inverse dynamics control of underactuated systems, where the task is defined by servo-constraints. Using Scikit-learn’s MLP Regressor, we demonstrate NN-based surrogate modeling in three levels: 1) forward dynamics of minimum-coordinate models, 2) constrained models, and 3) the inverse dynamics control of underactuated multibody systems via servo-constraints, which is a classical approach not yet combined with NNs. The neural network model is used to represent the inverse dynamics model, for which training data are generated through forward dynamic simulations. The study demonstrates that low-degree-of-freedom planar systems can be approximated by middle-scale neural network models of a few hundred perceptrons, requiring training times of minutes on a personal computer. The proposed control architecture can stabilise the servo-constraints and track trajectories, even for non-collocated underactuated systems where traditional methods might fail. The results highlight a simple, industry-friendly path for NN-based MBD control.