Path following of underwater robots using Lagrange multipliers

•The “virtually constrained motion” control methodology is introduced.•The fundamental principles of mechanics are used to derive control laws.•A novel path-maneuvering controller is designed for underactuated marine craft.

This article proposes a framework for motion control of mechanical systems with application to underwater marine craft. Utilizing analytical mechanics, we establish a link between modeling and simulation of constrained multi-body systems in one hand and motion control of underwater vehicles on the other hand. The beauty of the presented approach consists in simplicity and physical interpretability, where imaginary dampers and springs introduce a deformable body and take care of motion of the vehicle. The proposed method is used to develop a novel path-following controller for UUVs.