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Design of a steering control law for an autonomous underwater vehicle using nonlinear \(\mathscr {H}_{\infty }\) state feedback technique

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Abstract

This paper proposes a new robust nonlinear \(\mathscr {H}_{\infty }\) state feedback (NHSF) controller for an autonomous underwater vehicle (AUV) in steering plane. A three-degree-of-freedom nonlinear model of an AUV has considered for developing a steering control law. In this, the energy dissipative theory is used which leads to form a Hamilton–Jacobi–Isaacs (HJI) inequality. The nonlinear \(\mathscr {H}_{\infty }\) control algorithm has been developed by solving HJI equation such that the AUV tracks the desired yaw angle accurately. Furthermore, a path following control has been implemented using the NHSF control algorithm for various paths in steering plane. Simulation studies have been carried out using MATLAB/Simulink environment to verify the efficacies of the proposed control algorithm for AUV. From the results obtained, it is concluded that the proposed robust control algorithm exhibits a good tracking performance ensuring internal stability and significant disturbance attenuation.

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Abbreviations

NED:

North, east and down direction

\(\{B\}\) :

Body-fixed frame

\(\{E\}\) :

NED frame

\(\{R\}\) :

Serret–Frenet reference frame

m :

Mass of the AUV

W :

Total weight of AUV

B :

Buoyancy force exerted by water on AUV

\(I_x,I_y,I_z\) :

Moments of inertia about x-, y- and z-axes in body-fixed frame

(\(x_\mathrm{B}, y_\mathrm{B}, z_\mathrm{B}\)):

Center of buoyancy

(\(x_\mathrm{G}, y_\mathrm{G}, z_\mathrm{G}\)):

Center of gravity

\(T_\mathrm{s}\) :

Total thrust in horizontal plane

\(\delta _\mathrm{s}\) :

Stern angle

\(\delta _\mathrm{r}\) :

Rudder angle

\(d_\mathrm{r/e}\) :

Position of \(\{R\}\) frame relative to \(\{E\}\) frame

\(d_\mathrm{b/e}\) :

Position of \(\{B\}\) frame relative to \(\{E\}\) frame

\(d_\mathrm{b/r}\) :

Position of \(\{B\}\) frame relative to \(\{R\}\) frame

\(s_\mathrm{r}\) :

Curvilinear abscissa along the path

\(\psi _\mathrm{r}\) :

Yaw angle between \(\{E\}\) and \(\{R\}\) coordinate system

s:

Parameters of steering plane

D:

Desired values for path following

r:

Parameters of Serret–Frenet frame

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Authors and Affiliations

  1. Centre for Industrial Electronics and Robotics, Department of Electrical Engineering, National Institute of Technology Rourkela, Rourkela, Odisha, 769008, India

    Subhasish Mahapatra & Bidyadhar Subudhi

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  1. Subhasish Mahapatra
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  2. Bidyadhar Subudhi
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Correspondence to Bidyadhar Subudhi.

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Mahapatra, S., Subudhi, B. Design of a steering control law for an autonomous underwater vehicle using nonlinear \(\mathscr {H}_{\infty }\) state feedback technique. Nonlinear Dyn 90, 837–854 (2017). https://doi.org/10.1007/s11071-017-3697-5

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