Underwater Vehicles Part 9 ppsx

Schooling for Multiple Underactuated AUVs 309 radrad 15.0)0(,05.0 3 = ψ , and 5.0)0()0()0( 321 = = = uuu sm / with all other variables taking zero values. Other design parameters are taken as = ui k 3,,1,12,8,12 "= = = ikk rii ψ and 3.0,60,5.0,3.0 = = == ψβα γ γ γ γ u . Same as in the straight line case, both of α V and β V take the form as (6) with the parameters chosen as 3,2,20,8,15,12 = = = = = = βαββαα ccbaba and 9.0 = h . Corresponding simulation results are presented in Fig. 7 and 8. The vehicles schooling in the triangular movement is shown in Fig. 7 with no collision between any of two vehicles (see Fig. 8). Fig. 7. Schooling of the vehicles in a triangular movement. Fig. 8. Schooling geometry for a triangular movement. 5.3 Equilateral triangular schooling with obstacle avoidance In this case, we consider an equilateral triangular schooling of the vehicles with obstacle avoidance. The obstacle is modelled as a circle located at )10,40( = p q with radius as 3m. For Underwater Vehicles 310 the schooling, two virtual leaders are chosen as in Fig. 3 (c) with the initial positions taken as )10,32()0( 1 = v q and )10,310()0( 2 = v q . The vehicles’ initial conditions are taekn as =)0( 1 q radradradqq 15.0)0(,05.0)0(,1.0)0(),11,37()0(),15,2()0(),1,0( 32132 ===== ψψψ and )0( 1 u smuu /5.0)0()0( 32 === with all other variables taking zero values. Other design parameters are taken as = ui k 3,,1,12,10,18 " = = = ikk rii ψ and ,240,15.0,2.0,15.0 = = = = u γ γ γ γ γβα 6= ψ γ . Both α V and β V are also taken as the form as (6) with the parameters as ,30,12 == αα ba 90,5,4,6,30,34 ======= γβαγγββ cccbaba and 9.0 = h . Simulation results are depicted in Fig. 9~12. Fig. 9 shows the vehicles schooling in the equilateral triangular movement with obstacle avoidance. From Fig. 10, we can see that there is not any collision between vehicles. Fig. 11 presents the vehicles’ velocity and heading matching in the schooling, and Fig. 12 shows the histories of proposed formation control laws for ui τ and ri δ . Fig. 9. Schooling of the vehicles in an equilateral triangular movement with obstacle avoidance. Fig. 10. Schooling geometry for an equilateral triangular movement with obstacle avoidance. Schooling for Multiple Underactuated AUVs 311 Fig. 11. Group velocity and heading matching. Fig. 12. Histories of proposed formation control laws. Underwater Vehicles 312 6. Summary In this chapter, we have investigated an asymptotic schooling scheme for multiple underactuated underwater vehicles. For each vehicle, there are only two control inputs – surge force and yaw moment available for its three DOF motion in the horizontal plane. The main difficulty in the tracking of this kind of vehicle is how to properly handle the vehicle’s sway dynamics. To deal with this problem, in this chapter, we have introduced a certain polar coordinates transformation, through which the vehicle’s dynamics can be reduced to a two-inputs strict-feedback form. The vehicles schooling has been conducted by properly selected smooth potential function, which consists of three different parts: one is for the interaction between vehicles, another is for group navigation, and the third one is for obstacle avoidance. The proposed formation algorithm guarantees the vehicles asymptotic schooling and velocity and heading matching while keeping obstacle avoidance. Proposed schooling scheme has been derived under the condition of 0)( min >≥ utu , which inversely can be guaranteed by proposed formation control laws being combined with some suitable initial conditions. Therefore, the proposed schooling method only can guarantee the local stability. Moreover, it is notable that the following issues should be considered in our future works. • Finite cut-off ( + ∞ < b in Definition 1) of potential function, which was applied in the previous works (Leonard and Fiorelli, 2001; Olfati-Saber, 2006; Do, 2007), also plays an important role in the vehicles schooling in this chapter. However, since +∞<b , it is easy to verify that 0/),,( = ∂ ∂ ζ ζ baf p if b≥ ζ . For this reason, the proposed schooling scheme only guarantees certain local minimum. It is of interest to upgrade the present result to the one where the global minimum can be guaranteed in our future works. • Another practical concern is for the robustness of proposed schooling scheme. In practice, there various uncertainty terms have to be faced, such as vehicle’s modelling error, measurement noise, and disturbance, etc. All of these terms should be considered in our future practical applications. 7. Acknowledgements This work was supported by the Ministry of Land, Transport and Maritime Affairs in Korea under Grant PMS162A and by the Korea Ocean Research & Development Institute under Grant PES120B. 8. References Bacciotti. A. & Rosier, L. (2005). Liapunov Functions and Stability in Control Theory. Springer- Verlag, Berlin, Heidelberg, 2005 Brockett, R. W. ; Mullman, R. S. & Sussmann, H. J. (1983). Differential Geometric Control Theory. Boston, MA : Birkhauser, 1983 Do, K. D. (2007). Bounded controller for formation stabilization of mobile agents with limited sensing ranges. IEEE Transactions on Automatic Control, Vol. 52, No. 2, pp. 569-576 Do, K. D. & Pan, J. (2005). Global tracking control of underactuated ships with nonzero off- diagonal terms in their system matrices. Automatica, Vol. 41, No. 1, pp. 87-95 Schooling for Multiple Underactuated AUVs 313 Do, K. D. ; Jiang, Z. P. & Pan, J. (2002a). Underactuated ship global tracking under relaxed conditions. IEEE Transactions on Automatic Control, Vol. 47, No. 9, pp. 1529-1536 Do, K. D. ; Jiang, Z. P. & Pan, J. (2002b). Universal controllers for stabilization and tracking of underactuated ships. Systems & Control Letters, Vol. 47, No. 4, pp. 299-317 Do, K. D. ; Jiang, Z. P. & Pan, J. (2004). Robust adaptive path following of underactuated ships. Automatica, Vol. 40, Nol 6, pp. 929-944 Dunbar, W. B. & Murray, R. M. (2002). Model predictive control of coordinated multi- vehicle formations, Proceedings of the 41st IEEE Conference on Decision and Control, pp. 4631-4636, Las Vegas, Nevada, USA, December 2002 Edwards, D. D. ; Bean, T. A. ; Odell, D. L. & Anderson, M. J. (2004). A leader-follower algorithm for multiple AUV formations, Proceedings of Workshop on Autonomous Underwater Vehicles, 2004 IEEE/OES, pp. 40-46, Sebasco Estates, Maine, USA, June 2004 Fax, J. A. & Murray, R. M. (2004). Information flow and cooperative control of vehicle formations. IEEE Transaction on Automatic Control, Vol. 49, No. 9, pp. 1465-1476, Fiorelli, E. ; Leonard, N. E. ; Bhatta, P. ; Paley, A. ; Bachmayer, R. & Fratantoni, D. M. (2006). Multi-AUV control and adaptive sampling in Monterey Bay. IEEE Journal of Oceanic Engineering, Vol. 31, No., 4, pp. 935-948 Fossen, T. I. (2002). Marine Control Systems. Trondheim, Norway : Marine Cybermetics, 2002 Fredriksen, E. & Pettersen, K. Y. (2006). Global k-exponential way-point maneuvering of ships : Theory and experiments. Automatica, Vol. 42, No. 4, pp. 677-687 Gue, J. ; Wei, Y. Y. ; Chiu, F. C. & Cheng, S. W. (2004). A maximum entropy method for multi-AUV grouping, Proceedings of IEEE/MTS Oceans’04, pp. 532-536, Kobe, Japan, November 2004 Jiang, Z. P. (2002). Global tracking control of underactuated ships by Lyapunov’s direct method. Automatica, Vol. 38, No. 2, pp. 301-309 Jiang, Z. P. & Nijmeijer, H. (1999). A recursive technique for tracking control of nonholonomic systems in chained form. 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HUGIN-AUV concept and operational experience to date, Proceedings of IEEE/MTS Oceans’04, pp. 846-850, Kobe, Japan, November 2004 Murray, R. M. & Sastry, S. S. (1993). Nonholonomic motion planning : Steering using sinusoids. IEEE Transactions on Automatic Control , Vol. 38, No. 5, pp. 700-716 Newman, J. N. (1977). Marine Hydrodynamics. The MIT Press, Cambridge, Massachusetts, USA, and London, England, 1977 Underwater Vehicles 314 Olfati-Saber, R. (2006). Flocking for multi-agent dynamic systems : algorithms and theory. IEEE Transactions on Automatic Control, Vol. 51, No. 3, pp. 401-420 Olfati-Saber, R. & Murray, R. M. (2002). Distributed cooperative control of multiple vehicle formations using structural potential functions, Proceedings of 15th IFAC World Congress, Barcelona, Spain, July 2002 Olfati-Saber, R. & Murray, R. M. (2003). Flocking with obstacle avoidance : cooperation with limited communication in mobile networks, Proceedings of the 42nd IEEE Conference on Decision and Control, pp. 2022-2028, Maui, Hawaii, USA, December 2003 Pettersen, K. Y. & Nijmeijer, H. (2001). Underactuated ship tracking control : Theory and experiments. International Journal of Control, Vol. 74, No. 14, pp. 1435-1446 Prestero, T. (2001). Verificatin of a six-degree of freedom simulation model for the REMUS autonomous underwater vehicles. Masters Thesis, Department of Ocean Engineering and Mechanical Engineering, MIT, 2001 Rey nolds, C. W. (1987). Flocks, herds, and schools : A distributed behavioral model, Proceedings of ACM SIGGRAPH’87, pp. 25-34, Anaheim, California, USA, July 1987 Reyhanoglu, M. (1997). Exponential stabilization of an underactuated autonomous surface vessel. Automatica, Vol. 33, No. 12, pp. 2249-2254 Rimon, E. & Koditschek, D. E. (1992). Exact robot navigation using artificial potential function. 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Douglas-Westwood Limited, Canterbury, UK, 2007 17 MARES – Navigation, Control and On-board Software Aníbal Matos and Nuno Cruz Universidade do Porto Portugal 1. Introduction Autonomous underwater vehicles (AUVs) are an emerging technology with applications in very different fields, such as military, homeland defence, underwater surveys, environment monitoring, and oceanographic studies (Griffiths, 2003). Although the use of AUVs in some of these fields is already well established, there is still a great research effort in areas related to the design and operation of these vehicles. The Ocean Systems Group at FEUP (Faculty of Engineering at the University of Porto) and ISR – Porto (Institute for Systems and Robotics – Porto) conducts research activities in marine robotics and has accumulated expertise in the utilization of AUVs and in the development of particular subsystems. This chapter addresses the design of the navigation and control systems of the MARES AUV (Cruz & Matos, 2008), a state-of-the-art small size AUV developed by the authors and already demonstrated at sea operations in 2007. The implementation of these systems in the vehicle on-board software is also discussed. Fig. 1. MARES AUV ready for an open sea mission. Underwater Vehicles 316 2. MARES AUV MARES, or Modular Autonomous Robot for Environment Sampling (Fig. 1), is a 1.5m long AUV, designed and built by the Ocean Systems Group. The vehicle can be programmed to follow predefined trajectories, while collecting relevant data with the onboard sensors. MARES can dive up to 100m deep, and unlike similar-sized systems, has vertical thrusters to allow for purely vertical motion in the water column. Forward velocity can be independently defined, from 0 to 2 m/s. Major application areas include pollution monitoring, scientific data collection, sonar mapping, underwater video or mine countermeasures. MARES configuration can change significantly according to the application scenario, so that it is difficult to define what is a standard configuration. In table 1 we summarize the main characteristics of the AUV version that was demonstrated at sea in November 2007. Length 1.5 m Diameter 20 cm Weight in air 32 kg Depth rating 100 m Propulsion 2 horizontal + 2 vertical thrusters Horizontal velocity 0-2 m/s, variable Energy Li-Ion batteries, 600 Wh Autonomy/Range about 10 hrs / 40 km Table 1. MARES main characteristics. 2.1 Mechanical All mechanical parts were designed using Solidworks ® CAD software (Fig. 2) and machined from polyacetal in a local machine shop, with small parts in aluminium and stainless steel. Polyacetal is a high performance polymer, with a high degree of rigidity and mechanical strength that makes it an excellent weight-saving metal replacement. It is completely corrosion proof and it is readily available in a wide range of sizes of tubes and rods, at reasonable prices. Fig. 2. MARES CAD model. The vehicle hull evolves around a central watertight cylinder, where all electronic boards are installed, with the battery packs located at the bottom to lower the center of mass. To MARES – Navigation, Control and On-board Software 317 simplify the design, this is the only watertight enclosure and therefore all other equipment has to be waterproof. The other polyacetal sections are designed to carry wet sensors and thrusters and they are fully interchangeable. This allows for very easy sensor swapping and/or repositioning, or even to test different configurations of thrusters. The main cylinder has 9 holes in each end cap, to accommodate standard bulkhead connectors and at the moment there are still several unused, sealed with dummy plugs. The overall vehicle shape resembles that of a torpedo, with ellipsoids both at the nose cone and at the tail. This configuration is very simple to construct and allows for the vehicle length to be easily extended, as compared to other hull shapes without constant cross- sections. The central cylinder provides most of the vehicle flotation and it is also possible to increase its length, for example if more batteries are needed. Typical small-size AUVs use vertical and horizontal fins to adjust heading and pitch, but this requires a minimum forward velocity for the control surfaces to be effective (von Alt et al., 1994; Crowell, 2006). On MARES, four independent COTS thrusters provide attitude control both in the horizontal and in the vertical plane. Two horizontal thrusters located at the tail control both forward velocity and rotation in the horizontal plane, while another set of thrusters, in the vertical direction, control vertical velocity and pitch angle. This arrangement permits operations in very confined areas, with virtually independent horizontal and vertical motion at velocities starting at 0 m/s. This is one of MARES innovations, as it cannot be seen in any AUV of similar size and weight. Furthermore, the modularity of the system allows the integration of other thrusters, for example to provide full control of the lateral motion. It should be stressed that fins are usually more efficient for diving than thrusters, but with simple fins it is not possible to control pitch angle independently of depth. In mission scenarios where bottom tracking is important, such as sonar or video acquisition, a fin controlled AUV will pitch up and down to follow the terrain, affecting data quality. On the contrary, MARES AUV can control both pitch angle and depth independently, being able to maintain data quality even if the terrain has significant slopes. Another advantage of using thrusters is that all moving parts can be fully shrouded and there are no fins protruding from the hull, which minimizes the risk of mechanical failure. In the end, we deliberately traded some of the efficiency with increased maneuverability and robustness. 2.2 Power and energy Most of the power required by an AUV is spent in propulsion, with only a small amount permanently needed for onboard electronics. In MARES, all energy is stored in rechargeable Li-Ion battery packs, currently with a total amount of 600 Wh, at 14.4 V. Battery power is directly available to the motor controllers and, through a set of voltage converters, to the rest of the onboard electronics. Battery endurance greatly depends on vehicle velocity, both in the horizontal and in the vertical plane. For typical horizontal missions, with relatively slow changes in depth, there is sufficient energy for about 8-10 hours of continuous operation (around 20-25 miles or 40 km). These are relatively modest numbers, but they seem to be sufficient for the great majority of envisaged missions. In any case, there is still some available volume for a few more battery packs. It should be stressed that these numbers refer to standard horizontal motion and it is also necessary to account for any significant vertical motion. For example, Underwater Vehicles 318 the vehicle can hover almost motionless in the water column, at a specific depth, but still requiring some small amount of power to provide depth corrections. In this case, the total endurance will be longer in time but relative to a shorter horizontal range. 2.3 Computational system The onboard computational system is based on a PC104 stack (Fig. 3), with a power supply board, a main processor board, and additional boards to interface with peripherals, such as health monitoring systems, actuation devices, and navigation and payload sensors. A flash disk is used to store both the onboard software and also the data collected during operations. Fig. 3. MARES on-board computer. 2.4 Payload The modularity of the vehicle allows for a simple integration of different payload sensors, involving three sub-tasks: mechanical installation, electronics interfacing and software. Mechanically, a new sensor may be installed in a dedicated section of the hull, if it is relatively small. Alternatively, it can be externally attached to the vehicle body, since there are many fixing points available. In any case, it is important to verify the weight of the sensor (and adapter) in the water, to compensate with extra flotation if necessary. Naturally, the overall vehicle trim has also to be adjusted, particularly in the case of bulky or heavy payloads. Most of the payload sensors transported by the AUV need energy and a communications link with the onboard computer. MARES has several spare connectors on both end caps of the main electronics compartment, that can be wired to provide power and receive data from these sensors. At the same time, the computational system has spare communication ports, easily configurable according to the payload specs. As far as software is concerned, the integration of a new payload sensor requires the development of a dedicated software module, known as a device driver. Device drivers establish a communication link between the sensor and the onboard software core, allowing for the configuration of the sensor as well as data logging. [...]... F ( 199 9), Development and Implementation of a Low-Cost LBL Navigation System for an AUV, Proc MTS/IEEE Oceans 99 , Seattle, WA, USA, Sept 199 9 Vaganay, J.; Leonard, J.; Bellingham, J (2006), Outlier Rejection for Autonomous Acoustic Navigation, Proc IEEE Int Conf on Robotics and Automation, Minneapolis, MN, USA, April 199 6 326 Underwater Vehicles von Alt, C.; Allen, B.; Austin, T.; Stokey, R ( 199 4),... AUV 94 , Cambridge, MA, USA, July 199 4 18 Identification of Underwater Vehicles for the Purpose of Autopilot Tuning Nikola Mišković, Zoran Vukić & Matko Barišić University of Zagreb, Faculty of Electrical Engineering and Computing Croatia 1 Introduction Underwater vehicles (UVs) lately found their use in many activities such as underwater mapping, habitat exploration, different types of inspections (underwater. .. of these methods are followed with results obtained either from real vehicles or simulations 328 Underwater Vehicles 2 Mathematical models of underwater vehicles In order to define the full mathematical model of an underwater vehicle (UV) we will use the terminology adopted from Fossen ( 199 4) Vector of positions and angles of an underwater vehicle is defined in the Earth-fixed coordinate frame and... ISBN 047 194 1131 Griffiths, G (2003), Technology and Applications of Autonomous Underwater Vehicles, Taylor and Francis, ISBN 0415301548 Healey, A.; Lienard, D ( 199 3), Multivariable sliding mode control for autonomous diving and steering of unmanned underwater vehicles, IEEE Jornal of Oceanic Engineering, vol 18, no 3, July 199 3 Matos, A.; Cruz, N.; Pereira, F ( 2003), Post Mission Trajectory Smoothing... Multiple Underwater Vehicles, Proc MTS/IEEE Oceans’01, Honolulu, HI, USA, Nov 2001 Cruz, N.; Matos, A (2008), The MARES AUV – A Modular Autonomous Robot for Environment Sampling, Proc MTS/IEEE Oceans’08 Quebec, Quebec, Canada, Sept 2008 Fossen, T ( 199 4) Guidance and Control of Ocean Vehicles, John Wiley & Sons Ltd., ISBN 047 194 1131 Gelb, A ( 197 4) Applied Optimal Estimation, MIT Press, ISBN 047 194 1131... described using a simple where is rudder deflection, heading and and Nomoto model given with parameters which are to be determined The same model can be applied to underwater 3 39 Identification of Underwater Vehicles for the Purpose of Autopilot Tuning vehicles yaw model, - in this case the exciting force is yaw moment The unknown parameters can be determined by pure integration of the Nomoto model, López... bring the system to self-oscillations Then Luyben ( 198 7) used this method in chemical industry to identify a transfer function of extremely nonlinear systems (distillation columns) Since then, inducing self-oscillations proved to be a great tool for controller tuning in processes and for process identification, see Li et al ( 199 1) and Chang & Shen ( 199 2), especially in pharmaceutical industry The IS-O... transformation has to be performed – points , have to be translated into points , This operation will distort the frame so the “upper” 333 Identification of Underwater Vehicles for the Purpose of Autopilot Tuning part of the pool has worse resolution than the “lower” part In order to obtain satisfactory identification results, the camera should be placed in such a way that the frame segment with the worst resolution... same time This way all couplings in the model are identified 335 Identification of Underwater Vehicles for the Purpose of Autopilot Tuning Based on the coupled model presented and derived in Section 2.4, equations (8), (9) and (10) , , can be set for surge, yaw and sway motion, respectively, where , , , , and (8) (9) (10) The identified parameters β 3 and γ 3 should be inverse and reciprocal The identification... simplification gives that linear part of the model can also be neglected, i.e 0 However, the force exerted by thrusters is rarely the same when the propulsor is rotating in both directions This is why a more complex model (1) should be used where sub indices f and b denote ‘forward’ and ‘backward’, and super index i stands for a specific thruster 3 29 Identification of Underwater Vehicles for the Purpose of . A.; Cruz, N.; Pereira, F. ( 199 9), Development and Implementation of a Low-Cost LBL Navigation System for an AUV, Proc. MTS/IEEE Oceans 99 , Seattle, WA, USA, Sept. 199 9 Vaganay, J.; Leonard, J.;. 199 6 Underwater Vehicles 326 von Alt, C.; Allen, B.; Austin, T.; Stokey, R. ( 199 4), Remote Environmental Measuring Units, Proc. IEEE Symp. AUV Techn. AUV 94 , Cambridge, MA, USA, July 199 4. 2, pp. 265-2 79 Krstic, M. ; Kanellakopoulos, I. & Kokotovic, P. ( 199 5). Nonlinear and Adaptive Control Design. John Wiley & Sons, Inc., New York, 199 5 Latombe, J. ( 199 1). Robot Motion