Constrained Mechanical System

Constrained mechanical systems, encompassing systems with limitations on their movement or configuration, are a focus of ongoing research aiming to improve the accuracy and efficiency of their simulation and control. Current efforts concentrate on developing robust numerical integration schemes, particularly those leveraging Lie group formulations and variational integrators, and employing advanced machine learning techniques like neural ordinary differential equations and graph neural networks to model and predict their behavior. These advancements are crucial for improving the performance of robots, optimizing trajectory planning in robotics and other fields, and enhancing the accuracy of simulations in various scientific and engineering applications.