Gradient Method for Forming a Formation of Underwater Vehicles Based on a Probabilistic Functional

The paper examines the problem of creating a formation of autonomous underwater vehicles for the coordinated execution of a group mission. The proposed method is based on the construction of a probabilistic functional, which describes the problem of constructing a formation of vehicles and takes into account the possibility of collisions between them; the functional generates an artificial potential field that has a clear interpretation. The creating of the formation is implemented using the gradient principle of sequential optimization of the probabilistic functional. The main assumptions that are made when developing the method are given. In particular, it is assumed that the group of underwater vehicles is homogeneous, and the structure of the creating formation has a "leader-follower" organization. It is believed that all vehicles have access to information about the position and orientation of the leader and other vehicles. The creation of a formation occurs under conditions of continuous movement of the entire group of vehicles. The maximum and non-zero minimum possible speeds of all vehicles are known. In the initial state, before the formation begins, all underwater vehicles are located in arbitrary places in the water area within a certain reasonable distance. In the work, based on standard reasoning, a functional is constructed in general form, which has the meaning of the probability of creating a given formation by a group of vehicles, provided that there are no collisions of the vehicles with each other during the movement. Specific types of probability distributions included in the general functional are introduced and justified. In general, an explicit expression for the gradient of this functional with respect to spatial variables is calculated. A law is derived and a mechanism is given to control the speed of underwater vehicles until the formation is completed. The considered method has a simple software implementation and demonstrates high efficiency, which makes it possible to control the formation of a large group of underwater vehicles in real time. Using the example of a group of 11 underwater vehicles, simulation results are presented that confirm the performance and indicated efficiency of the proposed method.

1. Inzartsev A. V., Kiselev L. V., Kostenko V. V., Matvienko Yu. V., Pavin A. M., Shcherbatyuk A. F. Underwater robotic complexes: systems, technologies, application, Vladivostok, Publishing house of the FSBI Institute of Marine Technology Problems, Far Eastern Branch of the Russian Academy of Sciences, 2018, 368 p. (in Russian).

2. Martynova L. A., Konyukhov G. V., Pashkevich I. V., Rukhlov N. N. Features of group control of AUVs during seismic exploration, Izvestia SFedU. Technical science, 2017, vol. 20, no. 1, pp. 147—156 (in Russian).

3. Semenov N. N., Chemodanov M. N., Shestakov I. V., Akhmetov D. B. Testing a heterogeneous group of autonomous unmanned underwater vehicles for search of objects on the bottom, Computing, Telecommunications and Control, 2023, vol. 16, no. 3, pp. 39—53 (in Russian).

4. Inzartsev A. V., Kiselev L. V., Matvienko Yu. V. Navigation and control of autonomous underwater robots, Izvestia of the SFedU. Technical science. Thematic issue, 2013, pp. 22—32 (in Russian).

5. Schaub H., Vadali S. R., Alfriend K. T. Spacecraft formation flying control using mean orbit elements, Journal of the Astronautical Sciences, 2000, vol. 48, no. 1, pp. 69—87.

6. Smith T. R., Mann H. H., Leonard N. E. Orientation control of multiple underwater vehicles, Proc. 40th IEEE Conf. Decision and Control, 2001, pp. 4598—4603.

7. Lawton J. R., Beard R. W., Young B. J. A decentralized approach to formation maneuvers, IEEE Trans. on Robotics and Automation, 2003, vol. 19, no. 6, pp. 933—941.

8. Burns R., McLaughlin C. A., Leitner J., Martin M. Techsat21: Formation design, control, and simulation, Proc. IEEE Aerospace Conf., 2000, pp. 19—25.

9. Yang Y., Xiao Y., Li T. A Survey of Autonomous Underwater Vehicle Formation: Performance, Formation Control, and Communication Capability, IEEE Commun. Surv. Tutorials, 2021, vol. 23, no. 2, pp. 815—841.

10. Filimonov A. B., Filimonov N. B., Barashkov A. A. Issues of constructing potential fields in problems of local navigation of mobile robots, Autometria, 2019, vol. 55, no. 4, pp. 65—70 (in Russian).

11. Filimonov A. B., Filimonov N. B. Issues of controlling the movement of mobile robots using the potential guidance method, Mekhatronika, Avtomatizatsiya, Upravlenie, 2019, vol. 20, no. 11, pp. 677—685 (in Russian).

12. Aveek K. Das, Rafael Fierro, Vijay Kumar, James P. Ostrowski, John Spletzer, Camillo J. Taylor. A vision-based formation control framework, IEEE Transactions on Robotics and Automation, 2002, vol. 18, no. 5, pp. 813—825.

13. Lewis M. Anthony, Tan Kar-Han/ High precision formation control of mobile robots using virtual structures, Auton. Robots, 1997, vol. 4, no. 4, pp. 387—403.

14. Kurochkin S. Yu., Tachkov A. A. Methods for controlling the group movement of mobile robots, Mekhatronika, Avtomatizatsiya, Upravlenie, 2021, vol. 22, no. 6, pp. 380—389 (in Russian).

15. Filaretov V. F., Yukhimets D. A. Development of a method for forming the trajectories of movement of a group of underwater robots in an environment with obstacles while going around them, Mekhatronika, Avtomatizatsiya, Upravlenie, 2020, vol. 21, no. 6, pp. 403—411 (in Russian).

16. Kostyukov V., Medvedev M., Pshikhopov V. Global path planning algorithm in a two-dimensional environment with polygonal obstacles on the class of piecewise polygonal trajectories, Unmanned Systems, 2024, June, pp. 1—19.

17. Beloglazov D. A., Guzik V. F., Medvedev M. Yu., Pshikhopov V. Kh., Pyavchenko A. O., Saprikin R. V., Soloviev V. V., Finaev V. I. Intelligent technologies for planning the movements of moving objects in three-dimensional non-deterministic environments / Ed. V. Kh. Pshikhopov. M.: Nauka, 2017, 232 p. (in Russian)

18. Guldner J., Utkin V. I. Tracking the gradient of artificial potential fields: Sliding mode control for mobile robots, Int. J. Control., 1996, vol. 63, no. 3, pp. 417—432.