Mathematical Modeling on the Control of Hunting Problems


  • Redemtus Heru Tjahjana Diponegoro University
  • Dhimas Mahardika Diponegoro University



mathematical modeling, bullet control model, hunting problems


Modeling a natural phenomenon or the action mechanism of a tool is often done in science and technology. Observations through computer simulations cost less relatively. In the research, a bullet control model moving towards the target was explored. The research aimed to try to simulate the trajectory of the bullet that could be controlled in hunting. To model a controlled bullet, the Dubins model was used. Then, the used approach was control theory. The optimal trajectory and control for bullets were designed using the Pontryagin Maximum Principle. The results show that with this principle and the dynamic system of the bullet, a system of differential equations and adjoining is obtained. The fundamental problem arises because the bullet dynamics model in the form of a differential equation system has initial and final requirements. However, the adjoint matching system has no conditions at all. This problem is solved by using numerical methods. In addition, the research proves the convergence of the calculation results with the required results. The track simulation results are also reported at the end of the research to ensure a successful control design. From the simulation results, the presented method with its convergence has successfully solved the problem of bullet control.


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Author Biographies

Redemtus Heru Tjahjana, Diponegoro University

Department of Mathematics, Faculty of Scince and Mathematics

Dhimas Mahardika, Diponegoro University

Department of Mathematics, Faculty of Scince and Mathematics


Asfihani, T., Subchan, S., M. Rosyid, D. M., & Sulisetyono, A. (2019). Dubins path tracking controller of USV using model predictive control in sea Field. Journal of Engineering and Applied Sciences, 14(20), 7778-7787.

Chen, Z. (2020). On Dubins paths to a circle. Automatica, 117(July), 1-8.

Chen, Z., & Shima, T. (2019). Shortest Dubins paths through three points. Automatica, 105(July), 368-375.

Ding, Y., Xin, B., & Chen, J. (2019). Curvature-constrained path elongation with expected length for Dubins vehicle. Automatica, 108(October), 1-8.

Drchal, J., Faigl, J., & Váňa, P. (2020). WiSM: Windowing surrogate model for evaluation of curvature-constrained tours with Dubins vehicle. IEEE Transactions on Cybernetics, 1-10.

González, V., Monje, C. A., Moreno, L., & Balaguer, C. (2016). Fast marching square method for UAVs mission planning with consideration of Dubins model constraints. IFAC-PapersOnLine, 49(17), 164-169.

Marino, H., Salaris, P., & Pallottino, L. (2016). Controllability analysis of a pair of 3D Dubins vehicles in formation. Robotics and Autonomous Systems, 83(September), 94-105.

Meyer, Y., Isaiah, P., & Shima, T. (2015). On Dubins paths to intercept a moving target. Automatica, 53(March), 256-263.

Ohsawa, T. (2015). Contact geometry of the Pontryagin maximum principle. Automatica, 55, 1-5.

Parlangeli, G. (2019). Shortest paths for Dubins vehicles in presence of via points. IFAC-PapersOnLine, 52(8), 295-300.

Patsko, V., & Fedotov, A. A. (2018). Attainability set at instant for one-side turning Dubins car. IFAC-PapersOnLine, 51(32), 201-206.

Váňa, P., Faigl, J., Sláma, J., & Pěnička, R. (2017). Data collection planning with Dubins airplane model and limited travel budget. In 2017 European Conference on Mobile Robots (ECMR) (pp. 1-6).

Yao, W., Qi, N., Zhao, J., & Wan, N. (2017). Bounded curvature path planning with expected length for Dubins vehicle entering target manifold. Robotics and Autonomous Systems, 97(November), 217-229.






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