Info

and g(Xp, Up, Xr , Ur ) = - sin Xp sin Xr cos Ur - cos Xp sin Up sin Ur +

and the elevation angle u(up,Xr,ur) = arcsin(sinup cosXr cosur + cosup sinur). (62)

Through the use of trigonometric addition formulas, it can be shown that (59) is equivalent to (19) in the 2D case, i.e., when up = ur = 0 .

5.1 Path parameterizations

Applicable (arc-length) parameterizations of straight lines and helices are now given.

5.1.1 Parameterization of straight lines

A spatial straight line can be parameterized by me R as xp(m) = xf +m cos a cos ¡5 (63)

where pf = [xf, yf, zf ]T e R3 represents a fixed point on the path (for which m is defined relative to), and a e S represents the azimuth angle of the path, while fie S represents the elevation angle of the path (both corresponding to the direction of increasing m).

5.1.2 Parameterization of helices

A helix can be parameterized by me R as

where pc = [xc, yc,zc ]T e R3 represents the origin of the helix center (for which w is defined relative to), rc >0 represents the radius of the horizontally-projected circle of the helix, and X e {-1,1} decides in which direction this horizontally-projected circle is traced; X = -1 for anti-clockwise motion and X = 1 for clockwise motion. Here, an increase in w corresponds to movement in the negative direction of the z-axis of the stationary frame.

6. Conclusions

This work has given an overview of guidance laws applicable to motion control of AUVs in 2D and 3D. Specifically, considered scenarios have included target tracking, where only instantaneous information about the target motion is available, as well as path scenarios, where spatial information is available apriori. For target-tracking purposes, classical guidance laws from the missile literature were reviewed, in particular line of sight, pure pursuit, and constant bearing. For the path scenarios, enclosure-based and lookahead-based guidance laws were presented. Relations between the guidance laws have been discussed, as well as interpretations toward saturated control.

7. References

Aguiar, A. P. & Hespanha, J. P. (2004). Logic-based switching control for trajectory-tracking and path-following of underactuated autonomous vehicles with parametric modeling uncertainty. In: Proceedings of the ACC'04, Boston, Massachusetts, USA

Aicardi, M.; Casalino, G.; Bicchi, A. & Balestrino, A. (1995). Closed loop steering of unicycle-like vehicles via Lyapunov techniques. IEEE Robotics and Automation Magazine 2(1), 27-35

Antonelli, G.; Fossen, T. I. & Yoerger, D. R. (2008). Underwater robotics. In: Springer Handbook of Robotics (B. Siciliano and O. Khatib, Eds.). pp. 987— 1008. SpringerVerlag Berlin Heidelberg

Battin, R. H. (1982). Space guidance evolution - A personal narrative. Journal of Guidance,

Control, and Dynamics 5(2), 97—110 Blidberg, D. R. (2001). The development of autonomous underwater vehicles (AUVs); a brief summary. In: Proceedings of the ICRA'01, Seoul, Korea Breivik, M. & Fossen, T. I. (2004a). Path following of straight lines and circles for marine surface vessels. In: Proceedings of the 6th IFAC CAMS, Ancona, Italy Breivik, M. & Fossen, T. I. (2004b). Path following for marine surface vessels. In: Proceedings of the OTO'04, Kobe, Japan Breivik, M. & Fossen, T. I. (2005a). Guidance-based path following for autonomous underwater vehicles. In: Proceedings of the OCEANS'05, Washington D.C., USA Breivik, M. & Fossen, T. I. (2005b). Principles of guidance-based path following in 2D and

3D. In: Proceedings of the CDC-ECC'05, Seville, Spain Breivik, M.; Subbotin, M. V. & Fossen, T. I. (2006). Kinematic aspects of guided formation control in 2D. In: Group Coordination and Cooperative Control (K. Y. Pettersen, J. T. Gravdahl and H. Nijmeijer, Eds.). pp. 54 — 74. Springer-Verlag Heidelberg Breivik, M. & Fossen, T. I. (2007). Applying missile guidance concepts to motion control of marine craft. In: Proceedings of the 7th IFAC CAMS, Bol, Croatia Breivik, M.; Hovstein, V. E. & Fossen, T. I. (2008). Ship formation control: A guided leader-follower approach. In: Proceedings of the 17th IFAC World Congress, Seoul, Korea Breivik, M. & Fossen, T. I. (2008). Guidance laws for planar motion control. In: Proceedings of the CDC08, Cancun, Mexico B0rhaug, E. & Pettersen, K. Y. (2006). LOS path following for underactuated underwater vehicle. In: Proceedings of the 7th IFAC MCMC, Lisbon, Portugal B0rhaug, E.; Pettersen, K. Y. & Pavlov, A. (2006). An optimal guidance scheme for cross-track control of underactuated underwater vehicles. In: Proceedings of the MED'06, Ancona, Italy

Caccia, M.; Bruzzone, G. & Veruggio, G. (2000). Guidance of unmanned underwater vehicles: Experimental results. In: Proceedings of the ICRA'00, San Francisco, California, USA

Castaño, A. R.; Ollero, A.; Vinagre, B. M. & Chen, Y. Q. (2005). Synthesis of a spatial lookahead path tracking controller. In: Proceedings of the 16th IFAC World Congress, Prague, Czech Republic

Cloutier, J. R.; Evers, J. H. & Feeley, J. J. (1989). Assessment of air-to-air missile guidance and control technology. IEEE Control Systems Magazine 9(6), 27—34 Craven, P. J.; Sutton, R. & Burns, R. S. (1998). Control strategies for unmanned underwater vehicles. Journal of Navigation 51, 79—105 Davidson, M.; Bahl, V. & Moore, K. L. (2002). Spatial integration for a nonlinear path tracking control law. In: Proceedings of the ACC'02, Anchorage, Alaska, USA Do, K. D. & Pan, J. (2003). Robust and adaptive path following for underactuated autonomous underwater vehicles. In: Proceedings of the ACC'03, Denver, Colorado, USA

Draper, C. S. (1971). Guidance is forever. Navigation 18(1), 26 — 50

Encarnagao, P. & Pascoal, A. (2000). 3D path following for autonomous underwater vehicle.

In: Proceedings of the CDC'00, Sydney, Australia Fossen, T. I. (2002). Marine Control Systems: Guidance, Navigation and Control of Ships, Rigs and

Underwater Vehicles. Marine Cybernetics Fossier, M. W. (1984). The development of radar homing missiles. Journal of Guidance, Control, and Dynamics 7(6), 641 — 651

Gomes, P.; Silvestre, C.; Pascoal, A. & Cunha, R. (2006). A path-following controller for the DELFIMx autonomous surface craft. In: Proceedings of the 7th IFAC MCMC, Lisbon, Portugal

Haeussermann, W. (1981). Developments in the field of automatic guidance and control of rockets. Journal of Guidance and Control 4(3), 225 — 239 Hagen, P. E.; St0rkersen, N. J. & Vestgard, K. (2003). The HUGIN AUVs - Multi-role capability for challenging underwater survey operations. EEZ International Healey, A. J. & Lienard, D. (1993). Multivariable sliding-mode control for autonomous diving and steering of unmanned underwater vehicles. IEEE Journal of Oceanic Engineering 18(3), 327—339 Justh, E. W. & Krishnaprasad, P. S. (2006). Steering laws for motion camouflage. Proceedings of the Royal Society A 462(2076), 3629 — 3643 Lapierre, L.; Soetanto, D. & Pascoal, A. (2003). Nonlinear path following with applications to the control of autonomous underwater vehicles. In: Proceedings of the CDC'03, Maui, Hawaii, USA

LaValle, S. M. (2006). Planning Algorithms. Cambridge University Press Lin, C.-F. (1991). Modern Navigation, Guidance, and Control Processing, Volume II. Prentice Hall, Inc.

Lin, C.-L. & Su, H.-W. (2000). Intelligent control theory in guidance and control system design: An overview. Proceedings of the National Science Council, ROC 24(1), 15—30 Locke, A. S. (1955). Guidance. D. Van Nostrand Company, Inc.

MacKenzie, D. A. (1990). Inventing Accuracy: A Historical Sociology of Nuclear Missile Guidance. MIT Press

Mizutani, A.; Chahl, J. S. & Srinivasan, M. V. (2003). Motion camouflage in dragonflies. Nature 423, 604

Ollero, A. & Heredia, G. (1995). Stability analysis of mobile robot path tracking. In:

Proceedings of the IROS'95, Pittsburgh, Pennsylvania, USA Papoulias, F. A. (1991). Bifurcation analysis of line of sight vehicle guidance using sliding modes. International Journal of Bifurcation and Chaos 1(4), 849—865 Papoulias, F. A. (1992). Guidance and control laws for vehicle pathkeeping along curved trajectories. Applied Ocean Research 14(5), 291 — 302 Pastrick, H. L.; Seltzer, S. M. & Warren, M. E. (1981). Guidance laws for short-range tactical missiles. Journal of Guidance and Control 4(2), 98—108 Piccardo, H. R. & Honderd, G. (1991). A new approach to on-line path planning and generation for robots in non-static environments. Robotics and Autonomous Systems 8(3), 187—201

Rankin, A. L.; Crane III, C. D. & Armstrong II, D. G. (1997). Evaluating a PID, pure pursuit, and weighted steering controller for an autonomous land vehicle. In: Proceedings of the SPIE Mobile Robotics XII, Pittsburgh, Pennsylvania, USA Refsnes, J. E.; S0rensen, A. J. & Pettersen, K. Y. (2008). Model-based output feedback control of slender-body underactuated AUVs: Theory and experiments. IEEE Transactions on Control Systems Technology 16(5), 930 — 946 Roberts, G. N. & Sutton, R. (2006). Advances in Unmanned Marine Vehicles. The Institution of Electrical Engineers

Samson, C. (1992). Path following and time-varying feedback stabilization of a wheeled mobile robot. In: Proceedings of the ICARCV'92, Singapore Sciavicco, L. & Siciliano, B. (2002). Modelling and Control of Robot Manipulators. SpringerVerlag London Ltd.

Sharp, R. S. (2007). Application of optimal preview control to speed-tracking of road vehicles. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 221(12), 1571—1578 Sheridan, T. B. (1966). Three models of preview control. IEEE Transactions on Human Factors in Electronics 7(2), 91 — 102 Shneydor, N. A. (1998). Missile Guidance and Pursuit: Kinematics, Dynamics and Control. Horwood Publishing Ltd.

Siouris, G. M. (2004). Missile Guidance and Control Systems. Springer-Verlag New York, Inc. Skjetne, R.; Fossen, T. I. & Kokotovic, P. V. (2004). Robust output maneuvering for a class of nonlinear systems. Automatica 40(3), 373 — 383 Spearman, M. L. (1978). Historical development of worldwide guided missiles. In: AIAA

16th Aerospace Sciences Meeting, Huntsville, Alabama, USA Subbotin, M. V.; Dacic, D. B. & Smith, R. S. (2006). Preview based path-following in the presence of input constraints. In: Proceedings of the ACC'06, Minneapolis, Minnesota, USA

Valavanis, K. P.; Gracanin, D.; Matijasevic, M.; Kolluru, R. & Demetriou, G. A. (1997).

Control architectures for autonomous underwater vehicles. IEEE Control Systems Magazine 17(6), 48—64

Wernli, R. L. (2000). AUV commercialization - Who's leading the pack?. In: Proceedings of the

OCEANS'OO, Providence, Rhode Island, USA Westrum, R. (1999). Sidewinder: Creative Missile Development at China Lake. Naval Institute Press

Whitcomb, L. (2000). Underwater robotics: Out of the research laboratory and into the field.

In: Proceedings of the ICRA'00, San Francisco, California, USA White, B. A. & Tsourdos, A. (2001). Modern missile guidance design: An overview. In:

Proceedings of the IFAC Automatic Control in Aerospace, Bologna, Italy Yanushevsky, R. (2008). Modern Missile Guidance. CRC Press

Yoshimoto, K.; Katoh, M. & Inoue, K. (2000). A vision-based speed control algorithm for autonomous driving. In: Proceedings of the AVEC'00, Ann Arbor, Michigan, USA Zarchan, P. (2002). Tactical and Strategic Missile Guidance. 4th ed.. American Institute of Aeronautics and Astronautics, Inc.

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