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Trajectory Tracking Nonlinear Controller for Underactuated Underwater Vehicles Based on Velocity Transformation


[ 1 ] Instytut Automatyki i Robotyki, Wydział Automatyki, Robotyki i Elektrotechniki, Politechnika Poznańska | [ P ] employee

Scientific discipline (Law 2.0)

[2.2] Automation, electronics, electrical engineering and space technology

Year of publication


Published in

Journal of Marine Science and Engineering

Journal year: 2023 | Journal volume: vol. 11 | Journal number: iss. 3

Article type

scientific article

Publication language


  • underactuated marine vehicle in horizontal motion
  • trajectory tracking
  • backstepping
  • integral sliding mode control
  • robustness
  • velocity transformation
  • control algorithm simulation

EN This paper proposes an algorithm that performs the task of tracking the desired trajectory for underactuated marine vehicles (primarily underwater) that move horizontally. The control scheme, which takes into account model inaccuracies and external disturbances, was designed using the quantities obtained after the transformation of the dynamic equations of motion resulting from the decomposition of the inertia matrix. This, in turn, led to the equation of dynamics with a diagonal inertia matrix. A specific feature of the offered controller is its dual role. It not only allows tracking the desired trajectory, but at the same time, makes it possible to estimate the impact of dynamic couplings when the vehicle is in motion. Such an approach to the tracking task is important at the initial design stage when the choice of the control algorithm has not yet been decided and experimental tests have not been performed. This is feasible because the new variables after the velocity transformation include not only vehicle parameters, but also actual velocities and forces. Therefore, it is also possible to track the original variables. The theoretical results were followed up with simulation tests conducted on a model with three degrees of freedom for two underwater vehicles.

Date of online publication


Pages (from - to)

509-1 - 509-24





Article Number: 509

License type

CC BY (attribution alone)

Open Access Mode

open journal

Open Access Text Version

final published version

Date of Open Access to the publication

at the time of publication

Ministry points / journal


Impact Factor

2,9 [List 2022]

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