Planar Tracking Control of an Underactuated Autonomous Underwater Vehicle
This paper addresses the problem of trajectory
tracking control of an underactuated autonomous underwater vehicle
(AUV) in the horizontal plane. The underwater vehicle under
consideration is not actuated in the sway direction, and the system
matrices are not assumed to be diagonal and linear, as often found in
the literature. In addition, the effect of constant bias of environmental
disturbances is considered. Using backstepping techniques and the
tracking error dynamics, the system states are stabilized by forcing
the tracking errors to an arbitrarily small neighborhood of zero. The
effectiveness of the proposed control method is demonstrated through
numerical simulations. Simulations are carried out for an
experimental vehicle for smooth, inertial, two dimensional (2D)
reference trajectories such as constant velocity trajectory (a circle
maneuver – constant yaw rate), and time varying velocity trajectory
(a sinusoidal path – sinusoidal yaw rate).
[1] T. I. Fossen, Guidance and Control of Ocean Vehicles, Chichester,
U.K:Wiley, 1994.
[2] J. Yuh, "Design and Control of Autonomous Underwater Robots: A
Survey," Auton. Robot, vol.8, pp. 7-24, 2000.
[3] R. W. Brockett, "Asymptotic stability and feedback stabilization,"
Differential Geometric Control Theory, Boston: Birkhauser, pp. 181-
191, 1983.
[4] I. Kolmanovsky and N. H. McClamroch, "Developments in
nonholonomic control problems," IEEE Contr. Syst. Mag., vol.15, pp.
20-36, 1995.
[5] H. K. Khalil, Nonlinear Systems, second ed. Prentice-Hall, Upper Saddle
River, 1996.
[6] F. Repoulias and E. Papadopoulos, "Planar trajectory planning and
tracking control design for underactuated AUVs," Ocean Eng., vol.34,
pp.1650-1667, 2007.
[7] A. P. Aguiar and A. M. Pascoal, "Dynamic positioning and way-point
tracking of underactuated AUVs in the presence of ocean currents," in
Proc. 41st IEEE Conf. Decision & Control (CDC-02), Las Vegas,
Nevada, USA, pp. 2105-2110, 2002.
[8] A. Behal, D. M. Dawson, W. E. Dixon, and F. Yang, "Tracking and
regulation control of an underactuated surface vessel with nonintegrable
dynamics," IEEE Trans. Automat. Contr., vol.47, pp.495-500, 2002.
[9] N. E. Leonard, "Control synthesis and adaptation for an underactuated
autonomous underwater vehicle," IEEE J. Oceanic Eng., vol.20,
pp.211-220, 1995.
[10] K. Y. Pettersen, and O. Egeland, "Time-varying exponential stabilization
of the position and attitude of an underactuated autonomous underwater
vehicle," IEEE Trans. Automat. Contr., vol.44, pp. 112-115 1999.
[11] Z. P. Jiang, "Global tracking control of underactuated ships by
Lyapunov-s direct method," Automatica, vol. 38, pp.301-309, 2002.
[12] E. Lefeber, "Tracking control of nonlinear mechanical systems,".Ph.D.
thesis, University of Twente, 2000.
[13] K. D. Do, Z. P. Jiang and J. Pan, "Underactuated ship global tracking
under relaxed conditions," IEEE Trans. Automat. Contr., vol.47,
pp.1529-1536, 2002
[14] F. Repoulias and E. Papadopoulos, "Trajectory planning and tracking
control design of underactuated AUVs," in Proc. IEEE Int. Conf.
Robotics & Automation, ICRA 05, Barcelona, Spain, pp. 1622-1627,
2005.
[15] K. D. Do and J. Pan, "Global tracking control of underactuated ships
with nonzero off-diagonal terms in their system matrices," Automatica,
vol.41, pp.87-95, 2005.
[16] M. Krstic, I. Kanellakopoulos and P. V. Kokotovic, Nonlinear and
adaptive control design. New York: Wiley, 1995.
[1] T. I. Fossen, Guidance and Control of Ocean Vehicles, Chichester,
U.K:Wiley, 1994.
[2] J. Yuh, "Design and Control of Autonomous Underwater Robots: A
Survey," Auton. Robot, vol.8, pp. 7-24, 2000.
[3] R. W. Brockett, "Asymptotic stability and feedback stabilization,"
Differential Geometric Control Theory, Boston: Birkhauser, pp. 181-
191, 1983.
[4] I. Kolmanovsky and N. H. McClamroch, "Developments in
nonholonomic control problems," IEEE Contr. Syst. Mag., vol.15, pp.
20-36, 1995.
[5] H. K. Khalil, Nonlinear Systems, second ed. Prentice-Hall, Upper Saddle
River, 1996.
[6] F. Repoulias and E. Papadopoulos, "Planar trajectory planning and
tracking control design for underactuated AUVs," Ocean Eng., vol.34,
pp.1650-1667, 2007.
[7] A. P. Aguiar and A. M. Pascoal, "Dynamic positioning and way-point
tracking of underactuated AUVs in the presence of ocean currents," in
Proc. 41st IEEE Conf. Decision & Control (CDC-02), Las Vegas,
Nevada, USA, pp. 2105-2110, 2002.
[8] A. Behal, D. M. Dawson, W. E. Dixon, and F. Yang, "Tracking and
regulation control of an underactuated surface vessel with nonintegrable
dynamics," IEEE Trans. Automat. Contr., vol.47, pp.495-500, 2002.
[9] N. E. Leonard, "Control synthesis and adaptation for an underactuated
autonomous underwater vehicle," IEEE J. Oceanic Eng., vol.20,
pp.211-220, 1995.
[10] K. Y. Pettersen, and O. Egeland, "Time-varying exponential stabilization
of the position and attitude of an underactuated autonomous underwater
vehicle," IEEE Trans. Automat. Contr., vol.44, pp. 112-115 1999.
[11] Z. P. Jiang, "Global tracking control of underactuated ships by
Lyapunov-s direct method," Automatica, vol. 38, pp.301-309, 2002.
[12] E. Lefeber, "Tracking control of nonlinear mechanical systems,".Ph.D.
thesis, University of Twente, 2000.
[13] K. D. Do, Z. P. Jiang and J. Pan, "Underactuated ship global tracking
under relaxed conditions," IEEE Trans. Automat. Contr., vol.47,
pp.1529-1536, 2002
[14] F. Repoulias and E. Papadopoulos, "Trajectory planning and tracking
control design of underactuated AUVs," in Proc. IEEE Int. Conf.
Robotics & Automation, ICRA 05, Barcelona, Spain, pp. 1622-1627,
2005.
[15] K. D. Do and J. Pan, "Global tracking control of underactuated ships
with nonzero off-diagonal terms in their system matrices," Automatica,
vol.41, pp.87-95, 2005.
[16] M. Krstic, I. Kanellakopoulos and P. V. Kokotovic, Nonlinear and
adaptive control design. New York: Wiley, 1995.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:63504", author = "Santhakumar M. and Asokan T.", title = "Planar Tracking Control of an Underactuated Autonomous Underwater Vehicle", abstract = "This paper addresses the problem of trajectory
tracking control of an underactuated autonomous underwater vehicle
(AUV) in the horizontal plane. The underwater vehicle under
consideration is not actuated in the sway direction, and the system
matrices are not assumed to be diagonal and linear, as often found in
the literature. In addition, the effect of constant bias of environmental
disturbances is considered. Using backstepping techniques and the
tracking error dynamics, the system states are stabilized by forcing
the tracking errors to an arbitrarily small neighborhood of zero. The
effectiveness of the proposed control method is demonstrated through
numerical simulations. Simulations are carried out for an
experimental vehicle for smooth, inertial, two dimensional (2D)
reference trajectories such as constant velocity trajectory (a circle
maneuver – constant yaw rate), and time varying velocity trajectory
(a sinusoidal path – sinusoidal yaw rate).", keywords = "autonomous underwater vehicle, system matrices,tracking control, time – varying feed back, underactuated control.", volume = "5", number = "2", pages = "485-6", }