Development of a user interface for input of a curvilinear object movement trajectory with variable speed

DOI: 10.31673/2412-9070.2023.049000

Abstract

The article considers the development of an interface for the most accurate input by the user of the trajectory of the curvilinear movement of the ship in the marine environment with variable speed for the further development of software for modeling the marine water area. Convenient modeling of objects in the sea water area requires a convenient interface that allows the user not only to set an arbitrary curvilinear trajectory of movement, but also checks the possibility of movement of the given object in relation to its size and speed of movement. Therefore, for the implementation of an interactive interface for entering a curvilinear trajectory of a ship, it is necessary to take into account the dynamics of the controlled object. When evaluating the trajectory, the physical limitations of the vessel must be satisfied. They determine the minimum radius of curvature, tangential acceleration and all three speeds (longitudinal, transverse, angular). The projected trajectory should be smooth, and its speeds along all three axes should be constant. Taking into account information about the physical forces affecting the movement of the ship, the formulas for calculating the points of the trajectory were derived, which are subsequently used both for visual representation and for calculations in the simulation of the experiment. The problem was divided to 3 parts: linear movement, the movement along the arc of the circle, movement after the turn. The algorithm for getting the position of the ship at any point of time during the turn was provided/. The article also provides an example of coding derived formulas using C# programming language. The results were provided by demonstrating the developed interface.

Keywords: interactive interface; modeling of object movement; curvilinear movement with variable speed; ship trajectory; interface development, C#.

References
1. Borkowski P. The Ship Movement Trajectory Prediction Algorithm Using Navigational Data Fusion. Sensors. 2017; 17(6):1432. URL: https://doi.org/10.3390/s17061432
2. Hassani V., Lande S. V. Path planning for marine vehicles using Bezier curves. IFAC Pap. 2018. 51. P. 305–310
3. Yang G. J., Choi B. W. Smooth trajectory planning along Bezier curve for mobile robots with velocity constraints. Int. J. Control Autom. 2013. 6. P. 225–234.
4. Choi J. W., Curry R., Elkaim G. Path planning based on bézier curve for autonomous ground vehicles // Proceedings of the Advances in Electrical and Electronics Engineering-IAENG Special Edition of the World Congress on Engineering and Computer Science 2008, San Francisco, CA, USA, 22–24 October 2008. P. 158–166.
5. Miller A., Walczak S. Maritime Autonomous Surface Ship’s Path Approximation Using Bézier Curves. Symmetry. 2020; 12(10):1704. URL: https://doi.org/10.3390/sym12101704
6. Methodology for Controlling the Ship’s Path during the Turn in Confined Waterways / S. Vujičić,
R. Mohović, I. Đ. Tomaš // Scientific Journal of Maritime Research. 2018. 32. P. 28–35.
7. Huang, L.; Wen, Y.; Guo, W.; Zhu, X.; Zhou, C.; Zhang, F.; Zhu, M. Mobility pattern analysis of ship trajectories based on semantic transformation and topic model. Ocean Eng. 2020, 201, 107092
8. Plessen M.M.G., Bemporad A. Reference trajectory planning under constraints and path tracking using linear time-varying model predictive control for agricultural machines. Biosyst. Eng. 2017. 153. P. 28–41.
9. Generation of temporal-spatial Bezier curve for simultaneous arrival of multiple unmanned vehicles / W. Yu, W. Shuo, W. Rui, T. Min // Inf. Sci. 2017. 418. P. 34–45.
10. Model predictive control based trajectory generation for autonomous vehicles-an architectural approach / M. Nolte, M. Rose, T. Stolte, M. Maurer // Proceedings of the 2017 IEEE Intelligent Vehicles Symposium (IV), Los Angeles, CA, USA, 11–14 June 2017. P. 798–805
11. Fossen T. I. Guidance and Control of Ocean Vehicles; John Wiley & Sons: New York, NY, USA, 1994.
12. Borkowski P. Data fusion in a navigational decision support system on a sea-going vessel. Pol. Marit. Res. 2012. 19. P. 78–85.