GEOMETRIC MODELING: TRACKS AND FLOWS
DOI:
https://doi.org/10.20998/2079-0023.2023.01.09Keywords:
mathematical model, optimization problem, restriction, topological parameter, construction norm and rule, homotopy, accuracyAbstract
Mathematical models to solve optimization connection problems in nonsimply connected regions under typical technological restrictions on geometric and topological parameters of routes, first of all, on curvature and the number of bends, have been investigated and developed. The models are linked with the extant and prospective topogeodesic models of the territory polygonal images. The solution of connection problems involves search for optimum trajectories of routes and nets within unrestricted geometric shape areas. It needs the development of a plethora of general models as fields where connections are carried out. The connections can be of various types such as bendy, Manhattan, even, solid as well as routes of other types. Smeliakov and Pliekhova observe that the global and local regulation of geometric connections to solve connection problems can be presented as the general optimization connection problem that is defined as the problem of the choice of с, where W is a set of alternatives, R is a principle of optimality. In so doing, the set W can be presented as the totality of the phase space f and the restrictions Q that are applied to the parameters of the phase space f. In turn, it is expedient to imagine that the phase space f is the Cartesian product f = X*Y*Z*U of the output data X, disturbances Y, control parameters U and results Z. The analysis of problem indicates that first and foremost the effectiveness of the modelling of the phase space f is linked with the description of the output data X on the area F and space L of possible highways in F. This research is devoted to the solution of the problem to develop a model for connection tasks within the framework of geometric design.
References
Upadhyay S., Ratnoo A. On existence and synthesis of smooth four parameter logistic paths inside annular passages. IEEE Robotics and Automation Letters. 2018, vol. 3, iss. 4, pp. 4375–4382.
Cowlagi R., Tsiotras P. Curvature-bounded traversability analysis in motion planning for mobile robots. IEEE Transactions on Robotics. 2014, pp. 1011–1019.
Bakolas E., Tsiotras P. Kinodynamic trajectory generation through rectangular channels using path and motion primitives. 47th IEEE Conference on Decision and Control. 2008, pp. 3725–3730.
Laumond J.-P., Jacobs P., Taix M., Murray R. M. A motion planner for nonholonomic mobile robots. IEEE Transactions on Robotics and Automation. 1994, vol. 10, iss. 5. pp. 577–593.
Agarwal P., Biedl T., Lazard S., Robbins S., Suri S., Whitesides S. Curvature-constrained shortest paths in a convex polygon. Proceedings 14th Annual ACM Symposium on Computational Geometry. 1998, pp. 392–401.
Plekhova A.A., Smelyakov S.V., Modeliuvannia komunikatsiinykh merezh z urakhuvanniam landshaftu za riznoridnykh umov ta obmezhen [Modelling of communication networks taking into account the landscape under heterogeneous criteria and restrictions], Informatsionnye sistemy [Insformation Systems], vol. 3, no. 11, 1998, pp. 143-146.
Stoyan, Y.G., Eschenko V.G., Vinarsky V.Y. Mathematical methods of geometric design in artificial intelligence system. IFAC Proceedings Volumes. 1992, vol. 25, iss. 28, pp. 101–105.
Smelyakov S. V., Stoyan Y. G. Modelling of the space of paths in problems of constructing optimal trajectories. USSR Computational Mathematics and Mathematical Physics. 1983, vol. 23, iss. 1, pp. 50–55.
Smelyakov S. V. Construction of shortest line of restricted curvature in a non-singly-connected polygonal area. Inclusion methods for nonlinear problems. Computing supplementa. 2003, vol. 16, pp. 237–244.
Sergienko I. V., Shylo V. P. Problems of discrete optimization: Challenges and main approaches to solve them. Cybernetics and Systems Analysis. 2006, vol. 42, pp. 465–482.
Plekhova A. Model i metod rozviazannia zadachi poshuku optymalnoho poiednannia pry obmezhenni kryvyzny [Model and methods for solving problems of searching for certain connections with a curvature constraint]. Radioelektronika i informatika [Radioelectronics and Informatics]. 1998, vol. 3, 1998, pp. 56–59.
Plekhova A. Pobudova optymalnoi trasy obmezhenoi kryvyzny u neodnozviaznii oblasti [Construction of an optimal path of bounded curvature in a non-simply connected domain]. Radioelektronika i informatika [Radioelectronics and Informatics]. 1999, vol. 3, pp. 22–23.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
