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This paper aims to provide a new problem formulation of path following formechanical systems without time parameterization nor guidance laws, namely, weexpress the control objective as an orbital stabilization problem. It is shownthat, it is possible to adapt the immersion and invariance technique to designstatic state-feedback controllers that solve the problem. In particular, weselect the target dynamics adopting the recently introduced Mexican sombreroenergy assignment method. To demonstrate the effectiveness of the proposedmethod we apply it to control underactuated marine surface vessels.

Path following of a class of underactuated mechanical systems via immersion and invariance-based orbital stabilization