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This work deals with the modeling and control of automated drilling operations. Advances in drilling automation are of substantial importance because improvements in drilling control algorithms will result in more efficient drilling, which is beneficial from both economic and environmental points of view. While the primary application of the results is extraction of natural resources, potentially there exists a wide range of applications, including offshore exploration, archaeological research, and automated extraterrestrial mining, where implementation of new methods and control algorithms for drilling processes can bring substantial benefits.