Info

(a) RAC with disturbance compensation (b) RAC without disturbance compensation

Fig. 13. Experimental results of discrete-time RAC with and without disturbance compensation

Next, experiments of discrete-time RAC with and without disturbance compensation of the base are done. To validate the performance of disturbance compensation, the feedback gains of the RAC are A = r = diag{0.3 0.3 0.2 0.2 0.2}. Using these values of the gains the basic control performance of the RAC becomes worse. The time constant of the filter for the disturbance compensation is Tf = 0.1 [s]. The experimental results of the RAC with and without disturbance compensation are shown in Figure 13(a) and (b), respectively. And Figure 14 shows the time history of the estimated disturbance. From Figures 13 and 14, it can be seen that the position and attitude errors of the base are reduced by using the disturbance compensation.

Fig. 14. Estimated disturbance (digital version)
Fig. 15. Experimental result of discrete-time RAC considering singular configuration

Finally, an experiment of avoidance of singular configuration is done. In this case, the basic desired position and attitude of the base (vehicle) is set as the initial values, and the threshold of the determinant of the Jacobian matrix is Js = 0.45 . And the feedback gains are A = r = diag{0.6 0.6 0.25 0.25 0.25}. The experimental result is shown in Figure 15. From Figure 15, we can see that the end-tip of the manipulator and base follow the desired trajectories avoiding the singular configuration of the manipulator and the tracking errors are very small.

6. Conclusion

In this chapter, our proposed continuous-time and discrete-time RAC methods was described and the both experimental results using a 2-link underwater robot were shown. For the continuous-time RAC method, experimental results showed that the RAC method has good control performance in comparison with a computed torque method and the RAC method with disturbance compensation can reduce the influence of the hydrodynamic modelling error. In practical systems digital computers are utilized for controllers. Then, we addressed discrete-time RAC methods including the ways of disturbance compensation and avoidance of singular configuration. Experimental results show that the control performance of the discrete-time RAC method is similar to the continuous version. Our future work is to carry out experiments in 3-dimensional space to evaluate the validity of the RAC methods.

7. References

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Systems, Springer-Verlag, 3-540-00054-2, Berlin Fossen, T.I. (1994). Guidance and Control of Ocean Vehicles, John Wiley & Sons, 0-471-94113-1, NY Godler, I.; Honda, H. & Ohnishi, K. (2002). Design Guidance for Disturbance Observer's Filter in Discrete Time, Proceedings of 7th International Workshop on Advanced Motion Control, pp. 390-395, 0-7803-7479-7, Maribor, Slovenia, Jul. 2002 Levesque, B. & Richard, M.J. (1994). Dynamic Analysis of a Manipulator in a Fluid Environment,

International Journal of Robotics Research, Vol. 13, No. 3, pp. 221-231, 0278-3649 Luh, J.Y.S; Walker, M.W. & Paul, R.P.C. (1980). Resolved-Acceleration Control of Mechanical Manipulators, IEEE Transactions on Automatic Control, Vol. 25, No. 3, pp. 468-474, 0018-9286

Maheshi, H.; Yuh, J. & Lakshmi, R. (1991). A Coordinated Control of an Underwater Vehicle and Robotic Manipulator, Journal of Robotic Systems, Vol. 8, No. 3, pp. 339-370, 07412223

McLain, T.W.; Rock, S.M. & Lee, M.J. (1996). Experiments in the Coordinated Control of an Underwater Arm/Vehicle System, In: Underwater Robots, Yuh, J.; Ura, T. & Bekey, G. A., (Ed), pp.137-158, Kluwer Academic Publishers, 0-7923-9754-1, MA McLain, T.W. & Rock, S.M. (1998). Development and Experimental Validation of an Underwater Manipulator Hydrodynamic Model, International Journal of Robotics Research, Vol. 17, No. 7, pp. 748-759, 0278-3649 McMillan, S.; David, D.E. & McGhee, R.B. (1995). Efficient Dynamic Simulation of an Underwater Vehicle with a Robotic Manipulator, IEEE Transactions on Systems, Man and Cybernetics, Vol. 25, No, 8, pp. 1194-1206, 0018-9472 Sagara, S. (2003). Digital Control of an Underwater Robot with Vertical Planar 2-Link Manipulator, Proceedings of the 8th International Symposium on Artificial Life and Robotics, pp. 524-527, 4-9900462-3-4, Beppu, Jan. 2003 Sagara, S.; Shibuya. K. & Tamura, M. (2004). Experiment of Digital RAC for an Underwater Robot with Vertical Planar 2-Link Manipulator, Proceedings of the 9th International Symposium on Artificial Life and Robotics, pp. 337-340, 4-9900462-4-2, Beppu, Jan. 2004 Sagara, S.; Tamura, M.; Yatoh, T. & Shibuya, K. (2006). Digital RAC for Underwater Vehicle-Manipulator Systems Considering Singular Configuration, Artificial Life and Robotics, Vol. 10, No. 2, pp. 106-111, 1433-5298, Springer Sarkar, N. & Podder, T.K. (2001). Coordinated Motion Planning and Control of Autonomous Underwater Vehicle-Manipulator Systems:Subject to Drag Optimization, IEEE Journal of Oceanic Engineering, Vol. 26, No. 2, pp. 228-239, 0364-9059 Tarn, T. J; Shoults, G.A. & Yang, S.P. (1996). A Dynamic Model of an Underwater Vehicle with a Robotic Manipulator Using Kane's Method, In: Underwater Robots, Yuh, J.; Ura, T. & Bekey, G. A., (Ed), pp.137-158, Kluwer Academic Publishers, 0-7923-9754-1, MA Yamada, S. & Sagara, S. (2002). Resolved Acceleration Control of an Underwater Robot with Vertical Planar 2-Link Manipulator, Proceedings of the 7th International Symposium on Artificial Life and Robotics, pp. 230-233, 4-9900462-2-6, Beppu, Jan. 2002 Yatoh, T. & Sagara, S. (2007). Resolved Acceleration Control of Underwater Vehicle-Manipulator Systems Using Momentum Equation, Proceedings of OCEANS 2007 MTS/IEEE vancouver, paper number 070427-004, 0-933957-35-1, Vancouver, Oct. 2007 Yatoh, T. & Sagara, S. (2008). Digital Type Disturbance Compensation Control of Underwater Vehicle-Manipulator Systems, Proceedings of OCEANS'08 MTS/IEEE Kobe-Techno-Ocean'08, paper number 071109-002, 978-1-4244-2126-8, Kobe, Apr. 2008 Yuh, J. (Ed). (1995). Underwater Robotic vehicles: Design and Control, TSI Press, 0-9627451-6-2, NW

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