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Robust control for horizontal plane motions of autonomous underwater vehicles

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Abstract

Nowadays autonomous underwater vehicles (AUVs) are employed as unmanned machines in ocean industries. For instance AUVs play an important role in coastal area monitoring and investigating underwater pipe line in deep seas. In this paper, navigation of an AUV near free surface and the effect of wave disturbance and un-modeled hydrodynamics as uncertain terms in control system are addressed. To stabilize the roll motion of the vehicle a practical control mode in mini-UVs is applied. Firstly, a 6-DOF nonlinear dynamic simulator is developed and dynamic stability of the vehicle is investigated. Then, a feedback linearization method is applied to turn the nonlinear system into a convenient linear one, and then a robust technique is applied to guarantee the stability and performance of the system. In addition, a genetic algorithm method is employed for achieving the best gains in feedback linearization control law. Three constraints are considered for optimization including amplitude of sway, yaw and roll motions. Final results show an effective motion control of the AUV in horizontal plane. Meanwhile a reasonable performance of robust control in presence of wave disturbance and un-modeled hydrodynamics is achieved.

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Abbreviations

\(\left[ {I_{xx} ,I_{yy} ,I_{zz} } \right]\) :

Mass moment (kg m2)

\(\left[ {x_{\text{g}} ,y_{\text{g}} ,z_{\text{g}} } \right]\) :

Location of center of mass (m)

\(\left[ {X_{u\left| u \right|} , Y_{v\left| v \right|} , Z_{w|w|} } \right]\) :

Drag (kg/m)

\(\left[ {X_{{\dot{u}}} ,Y_{{\dot{v}}} ,Y_{{\dot{r}}} ,Z_{{\dot{w}}} ,Z_{{\dot{q}}} } \right]\) :

Added mass (kg)

\(\left[ {K_{{\dot{p}}} ,M_{{\dot{w}}} ,M_{{\dot{q}}} ,N_{{\dot{v}}} ,N_{{\dot{r}}} } \right]\) :

Added mass (kg)

\(\left[ {X_{wq} , X_{qq} , X_{rr} , X_{vr} } \right]\) :

Added mass cross-term (kg/rad)

\(\left[ {Y_{r\left| r \right|} , Y_{wp} , Y_{pq} } \right]\) :

Added mass cross-term (kg/rad)

\(\left[ {Z_{q\left| q \right|} , Z_{vp} , Z_{rp} } \right]\) :

Added mass cross-term (kg/rad)

\(\left[ {Y_{ur} , Z_{uq} } \right]\) :

Added mass cross-term and fin lift (kg/rad)

\(\left[ {Y_{uv} , Z_{uw} } \right]\) :

Added mass cross-terms, fin lift and drag (kg/rad)

\(\left[ {X_{\text{HS}} , Y_{\text{HS}} , Z_{\text{HS}} } \right]\) :

Hydrostatic forces (kg)

\(X_{\text{prop}}\) :

Propeller thrust (N)

\(\left[ {Y_{uu\delta r} , Z_{uu\delta s} } \right]\) :

Fin lift force [kg/(m rad)]

\(\left[ {K_{p\left| p \right|} , M_{q\left| q \right|} , N_{r|r|} } \right]\) :

Added mass cross-term (kg/rad)

\(\left[ {M_{vp} , M_{rp} , N_{pq} , N_{wp} } \right]\) :

Added mass cross-term (kg/rad)

\(\left[ {K_{\text{HS}} , M_{\text{HS}} , N_{\text{HS}} } \right]\) :

Hydrostatic moment (kg/rad)

\(\left[ {M_{w\left| w \right|} , N_{uv} } \right]\) :

Body and fin munk moment (kg)

\(\left[ {M_{uq} , N_{ur} } \right]\) :

Added mass cross term and fin lift (kg m/rad)

\(K_{\text{prop}}\) :

Propeller torque (Nm)

\(N_{uu\delta r}\) :

Fin lift moment (kg/rad)

m :

Mass (kg)

L :

Length (m)

R :

Hull radius (m)

z :

Heave displacement (m)

u :

Surge speed (m/s)

v :

Sway speed (m/s)

w :

Heave speed (m/s)

\(\phi\) :

Roll angle (deg)

\(\theta\) :

Pitch angle (deg)

\(\psi\) :

Yaw angle (deg)

p :

Roll angular speed (rad/s)

q :

Pitch angular speed (rad/s)

r :

Yaw angular speed (rad/s)

\(\delta_{r}\) :

Rudder angle (deg)

\(\delta_{s}\) :

Stern plane angle (deg)

\(M_{\text{wave}}\) :

Wave moment (Nm)

\(M_{r}\) :

Rudder righting moment (Nm)

\(M_{\delta }\) :

Stern plane moment (Nm)

\(\gamma\) :

Wave encounter angle (deg)

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Acknowledgments

This research was supported by the Marine Research Center of Amirkabir University of Technology whose works are greatly acknowledged. The authors would gratefully like to thank the reviewers for their comments that helped us to improve the manuscript.

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Author notes

  1. Mojtaba Kamarlouei

    Present address: Lisbon University of Technology, Lisbon, Portugal

Authors and Affiliations

  1. Department of Ocean Engineering, Amirkabir University of Technology, Tehran, Iran

    Mojtaba Kamarlouei & Hassan Ghassemi

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  1. Mojtaba Kamarlouei
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  2. Hassan Ghassemi
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Correspondence to Hassan Ghassemi.

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Technical Editor: Celso Kazuyuki Morooka.

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Kamarlouei, M., Ghassemi, H. Robust control for horizontal plane motions of autonomous underwater vehicles. J Braz. Soc. Mech. Sci. Eng. 38, 1921–1934 (2016). https://doi.org/10.1007/s40430-015-0403-8

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  • DOI: https://doi.org/10.1007/s40430-015-0403-8

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