Sliding mode control is a very effective strategy in dealing not only with parametric uncertainties, but also with unmodeled dynamics, and therefore has been widely applied to robotic agents. However, the adoption of a thin boundary layer neighboring the switching surface to smooth out the control law and to eliminate the undesired chattering effect usually impairs the controller’s performance and leads to a residual tracking error. As a matter of fact, underwater robots are very sensitive to this issue due to their highly uncertain plants and unstructured operating environments. In this work, Gaussian process regression is combined with sliding mode control for the dynamic positioning of underwater robotic vehicles. The Gaussian process regressor is embedded within the boundary layer in order to enhance the tracking performance, by predicting unknown hydrodynamic effects and compensating for them. The boundedness and convergence properties of the tracking error are analytically proven. Numerical results confirm the improved performance of the proposed control scheme when compared with the conventional sliding mode approach.
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Ludvigsen, M., Sørensen, A.J.: Towards integrated autonomous underwater operations for ocean mapping and monitoring. Annu. Rev. Control. 42, 145–157 (2016)
Mindell, D.A.: Our Robots, Ourselves: Robotics and the Myths of Autonomy. Viking, New York (2015)
Teague, J., Allen, M.J., Scott, T.S.: The potential of low-cost ROV for use in deep-sea mineral, ore prospecting and monitoring. Ocean. Eng. 147, 333–339 (2018)
Mitra, A., Panda, J.P., Warrior, H.V.: The effects of free stream turbulence on the hydrodynamic characteristics of an AUV hull form. Ocean. Eng. 174, 148–158 (2019)
Go, G., Ahn, H.T.: Hydrodynamic derivative determination based on CFD and motion simulation for a tow-fish. Appl. Ocean. Res. 82, 191–209 (2019)
Chen, C.-W., Jiang, Y., Huang, H.-C., Ji, D.-X., Sun, G.Q., Yu, Z., Chen, Y.: Computational fluid dynamics study of the motion stability of an autonomous underwater helicopter. Ocean. Eng. 143, 227–239 (2017)
Ramírez-Macías, J.A., Brongers, P., Rúa, S., Vásquez, R.E.: Hydrodynamic modelling for the remotely operated vehicle Visor3 using CFD. IFAC Papers Online. 49(23), 187–192 (2016)
Alam, K., Ray, T., Anavatti, S.G.: Design optimization of an unmanned underwater vehicle using low-and high-fidelity models. IEEE Trans. Syst. Man. Cybern: Syst. 47(11), 2794–2808 (2015)
Bessa, W.M., Dutra, M.S., Kreuzer, E.: Depth control of remotely operated underwater vehicles using an adaptive fuzzy sliding-mode controller. Robot. Auton. Syst. (8) 56, 670–677 (2008)
Bessa, W.M., Dutra, M.S., Kreuzer, E.: An adaptive fuzzy sliding-mode controller for remotely operated underwater vehicles. Robot. Auton. Syst. 58, 16–26 (2010)
Peng, Z., Wang, J., Wang, J.: Constrained control of autonomous underwater vehicles based on command optimization and disturbance estimation. IEEE Trans. Ind. Electron. 66(5), 3627–3635 (2019)
Londhe, P.S., Patre, B.M.: Adaptive fuzzy sliding mode control for robust trajectory tracking control of an autonomous underwater vehicle. Intell. Serv. Robot. 12(1), 87–102 (2019)
Ingrosso, R., Palma, D., Indiveri, G., Avanzini, G.: Preliminary results of a dynamic modelling approach for underwater multi-hull vehicles. IFAC Papers Online. 51(29), 86–91 (2018)
Ghavidel, H.F., Kalat, A.A.: Robust control for MIMO hybrid dynamical system of underwater vehicles by composite adaptive fuzzy estimation of uncertainties. Nonlinear Dyn. 89(4), 2347–2365 (2017)
Bessa, W.M., Dutra, M.S., Kreuzer, E.: Dynamic Positioning of Underwater Robotic Vehicles with Thruster Dynamics Compensation. Int. J. Adv. Robot. Syst (9)10 (2013)
Bessa, W.M., Kreuzer, E., Lange, J., Pick, M.A., Solowjow, E.: Design and adaptive depth control of a micro diving agent. IEEE Robot. Aut. Lett. 2(4), 1871–1877 (2017)
Bessa, W.M., Brinkmann, G., Duecker, D. -A., Kreuzer, E., Solowjow, E.: A biologically inspired framework for the intelligent control of mechatronic systems and its application to a micro diving agent. Math. Probl. Eng. 2018 Article ID 9648126 (2018)
Rasmussen, C.E., Williams, C.K.: Gaussian Processes for Machine Learning. MIT Press, London (2006)
Marco, A., Henning, P., Bohg, J., Schaal, S., Trimpe, S.: Automatic LQR tuning based on Gaussian process global optimization. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 270–277 (2016)
Marco, A., Henning, P., Schaal, S., Trimpe, S.: On the design of LQR kernels for efficient controller learning. In: Proceedings of the IEEE 56th Annual Conference on Decision and Control, pp. 5193–5200 (2017)
Neumann-Brosing, M., Marco, A., Schwarzmann, D., Trimpe, S.: Data-efficient auto-tuning with Bayesian optimization: An industrial control study. IEEE Trans. Control. Syst Technol (2019)
Cho, K., Oh, S.: Learning-based model predictive control under signal temporal logic specifications. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 7322–7329 (2018)
Klenske, E.D., Zeilinger, M.N., Schölkopf, B., Hennig, P.: Gaussian Process-Based Predictive Control for Periodic Error Correction. IEEE Trans. Control Syst. Technol. 24(1), 110–121 (2016)
Kocijan, J., Murray-Smith, R., Rasmussen, C.E., Girard, A.: Gaussian process model based predictive control. In: Proceedings of the American Control Conference, pp. 2214–2219 (2004)
Liu, M., Chowdhary, G., Castro da Silva, B., Liu, S., How, J.P.: Gaussian processes for learning and control: A tutorial with examples. IEEE Control Syst. Mag. 38(5), 53–86 (2018)
Joshi, G., Chowdhary, G.: Adaptive control using gaussian-process with model reference generative network. In: Proceedings of the IEEE Conference on Decision and Control, pp. 237–243 (2018)
Healey, A.J., Lienard, D.: Multivariable sliding mode control for autonomous diving and steering of unmanned underwater vehicles. IEEE J. Ocean. Eng. 18(3), 327–339 (1993)
Christi, R., Papoulias, F.A., Healey, A.J.: Adaptive sliding mode control of autonomous underwater vehicles in dive plane. IEEE J. Ocean. Eng. 15(3), 152–160 (1990)
Yoerger, D.R., Slotine, J.J.E.: Robust trajectory control of underwater vehicles. IEEE J. Ocean. Eng. 10 (4), 462–470 (1985)
Bessa, W.M.: Some remarks on the boundedness and convergence properties of smooth sliding mode controllers. Int. J. Autom. Comp. 2(6), 154–158 (2009)
Aran, V., Unel, M.: Gaussian process regression feedforward controller for diesel engine airpath. Int. J. Automot. Technol. 4(19), 635–642 (2018)
Lima, G.S., Bessa, W.M., Trimpe, S.: Depth control of underwater robots using sliding modes and gaussian process regression. IEEE LARS (2018)
Hsu, L., Costa, R.R., Lizarralde, F., Cunha, J.P.V.S.: Dynamic positioning of remotely operated underwater vehicles. IEEE Robot. Autom. Mag. 7(3), 21–31 (2000)
Zanoli, S.M., Conte, G.: Remotely operated vehicle depth control. Control. Eng. Pract. 11, 453–459 (2003)
Guo, J., Chiu, F.C., Huang, C.C.: Design of a sliding mode fuzzy controller for the guidance and control of an autonomous underwater vehicle. Ocean. Eng. 30, 2137–2155 (2003)
Newman, J.N.: Marine Hydrodynamics, 5th edn. MIT Press, Massachusetts (1986)
Slotine, J.J.E., Li, W.: Applied Nonlinear Control. Prentice Hall, New Jersey (1991)
Khalil, H.K.: Nonlinear Systems, 3rd edn. Prentice Hall, New Jersey (2001)
This work was supported by the Alexander von Humboldt Foundation [3.2-BRA/1159879 STPCAPES], the Brazilian Coordination for the Improvement of Higher Education Personnel [BEX 8136/14-9], and the Brazilian National Council for Scientific and Technological Development [308429/2017-6].
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Lima, G.S., Trimpe, S. & Bessa, W.M. Sliding Mode Control with Gaussian Process Regression for Underwater Robots. J Intell Robot Syst (2020). https://doi.org/10.1007/s10846-019-01128-5
- Sliding mode control
- Gaussian process regression
- Underwater robotic vehicle
- Dynamic positioning system
Mathematics Subject Classification (2010)