title: ÐÐ¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ¾ÐµÐ²Ð¾Ð³Ð¾ Ð¿Ð¾Ð²ÐµÐ´ÐµÐ½Ð¸Ñ Ð³ÑÑÐ¿Ð¿Ñ Ð´ÑÐ¾Ð½Ð¾Ð² Ð¿ÑÐ¸ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸Ð¸ ÑÐ¿ÑÐ°Ð²Ð»ÑÑÑÐ¸Ñ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð² Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð¿Ð¾ÑÐµÐ½ÑÐ¸Ð°Ð»Ð° ÐÐµÐ½Ð½Ð°ÑÐ´Ð°-ÐÐ¶Ð¾Ð½ÑÐ¾Ð½Ð°
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Simulation of the swarm behavior of the group of drones using control algorithms based on the Lennard-Jones potential
Creators: name: Ð¥Ð°ÐºÐ¸Ð¼Ð¾Ð², Ð¢ÐµÐ¼ÑÑ
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2021
Subjects: ÑÐ¾ÐµÐ²ÑÐµ ÑÐµÑ Ð½Ð¾Ð»Ð¾Ð³Ð¸Ð¸
ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
Ð´ÑÐ¾Ð½
ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ðµ
swarm technologies
numerical simulation
drone
control

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ð¼Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÐ¾ÐµÐ²Ð¾Ð³Ð¾ Ð¿Ð¾Ð²ÐµÐ´ÐµÐ½Ð¸Ñ Ð³ÑÑÐ¿Ð¿Ñ Ð´ÑÐ¾Ð½Ð¾Ð² Ð´Ð»Ñ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð¸Ñ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾Ð¹ ÑÑÑÑÐºÑÑÑÑ ÑÐ°Ð·Ð»Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð²Ð¸Ð´Ð°. ÐÐ°Ð´Ð°ÑÐ¸, ÑÐµÑÐ°ÐµÐ¼ÑÐµ Ð² Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ: 1. Ð Ð°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ð° Ð°ÐºÑÑÐ°Ð»ÑÐ½Ð¾ÑÑÑ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ¸ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð² ÑÐ¾ÐµÐ²Ð¾Ð³Ð¾ Ð¿Ð¾Ð²ÐµÐ´ÐµÐ½Ð¸Ñ. 2. ÐÐ¾Ð´Ð³Ð¾ÑÐ¾Ð²Ð»ÐµÐ½Ð° ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ ÑÐ¾Ñ Ð´ÑÐ¾Ð½Ð¾Ð². 3. ÐÑÐ¾Ð²ÐµÐ´ÐµÐ½Ñ Ð¿ÐµÑÐ²Ð¸ÑÐ½ÑÐµ ÑÐ¸Ð¼ÑÐ»ÑÑÐ¸Ð¸ Ñ Ð¿Ð¾ÑÐ»ÐµÐ´ÑÑÑÐ¸Ð¼ Ð°Ð½Ð°Ð»Ð¸Ð·Ð¾Ð¼ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½Ð¾Ð¹ ÑÑÑÑÐºÑÑÑÑ. 4. ÐÑÑÑÐµÑÑÐ²Ð»ÐµÐ½Ð° Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð´Ð»Ñ Ð´Ð¾ÑÑÐ¸Ð¶ÐµÐ½Ð¸Ñ Ð±Ð¾Ð»ÐµÐµ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾Ð¹ ÑÑÑÑÐºÑÑÑÑ. 5. ÐÑÐ¾Ð¸Ð·Ð²ÐµÐ´ÐµÐ½Ð° ÐºÐ¾ÑÑÐµÐºÑÐ¸ÑÐ¾Ð²ÐºÐ° Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð´Ð»Ñ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð¸Ñ ÑÑÑÑÐºÑÑÑÑ ÑÐ¸Ð¿Ð° âÑÐµÐ¿Ñâ. 6. ÐÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¾ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐ¸ ÑÑÑÑÐºÑÑÑ ÑÐ¾Ñ Ð¾Ñ ÑÐ¸Ð¿Ð¾Ð² Ð¸ ÐºÐ¾Ð¼Ð¿Ð¾Ð½Ð¾Ð²ÐºÐ¸ Ð´Ð°ÑÑÐ¸ÐºÐ¾Ð². ÐÐ»Ñ ÑÐ¾Ð·Ð´Ð°Ð½Ð¸Ñ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð±ÑÐ»Ð° Ð¸Ð·ÑÑÐµÐ½Ð° Ð¸Ð½ÑÐµÐ³ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½Ð°Ñ ÑÑÐµÐ´Ð° ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ¸ PyCharm Ð´Ð»Ñ ÑÐ·ÑÐºÐ° Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Python, Ð° ÑÐ°ÐºÐ¶Ðµ Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐºÐ¸: NumPy â Ð´Ð»Ñ Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¸Ñ Ð¼Ð°ÑÑÐ¸ÑÐ½ÑÑ Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ð¹ Ð¸ Matplotlib â Ð´Ð»Ñ Ð²ÑÐ²Ð¾Ð´Ð° Ð³ÑÐ°ÑÐ¸ÐºÐ¾Ð² Ð¸ ÑÐ¾Ð·Ð´Ð°Ð½Ð¸Ñ Ð°Ð½Ð¸Ð¼Ð°ÑÐ¸Ð¹. Ð¡Ð¾Ð·Ð´Ð°Ð½Ð½Ð°Ñ ÑÐ°ÐºÐ¸Ð¼ Ð¾Ð±ÑÐ°Ð·Ð¾Ð¼ Ð¼Ð¾Ð´ÐµÐ»Ñ Ð¿Ð¾Ð·Ð²Ð¾Ð»Ð¸Ð»Ð° Ð½Ðµ ÑÐ¾Ð»ÑÐºÐ¾ Ð½Ð°Ð³Ð»ÑÐ´Ð½Ð¾ Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÑÑÑ Ð¿ÑÐ¾ÑÐµÑÑ ÑÐ±Ð¾ÑÐºÐ¸ ÑÐ¾Ñ Ñ ÑÑÑÑÐ¾Ð¼ Ð²ÑÐµÐ¼ÐµÐ½Ð¸, Ð½Ð¾ Ð¸ Ð·Ð°Ð¿Ð¸ÑÑÐ²Ð°ÑÑ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ ÑÐ¸Ð¼ÑÐ»ÑÑÐ¸Ð¹ Ð´Ð»Ñ Ð¿Ð¾ÑÐ»ÐµÐ´ÑÑÑÐµÐ³Ð¾ Ð²Ð¾ÑÐ¿ÑÐ¾Ð¸Ð·Ð²ÐµÐ´ÐµÐ½Ð¸Ñ Ð¸ Ð°Ð½Ð°Ð»Ð¸Ð·Ð°. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ ÑÐ´Ð°Ð»Ð¾ÑÑ Ð½Ðµ ÑÐ¾Ð»ÑÐºÐ¾ Ð¿Ð¾Ð»ÑÑÐ¸ÑÑ ÑÐµÐ³ÑÐ»ÑÑÐ½ÑÑ ÑÑÑÑÐºÑÑÑÑ ÑÐ¾Ñ, Ð½Ð¾ Ð¿Ð¾Ð´ÑÐ²ÐµÑÐ´Ð¸ÑÑ Ð²ÑÐ´Ð²Ð¸Ð½ÑÑÑÑ Ð³Ð¸Ð¿Ð¾ÑÐµÐ·Ñ Ð¾ ÐµÑ ÐºÑÐ¸ÑÑÐ°Ð»Ð»Ð¸ÑÐµÑÐºÐ¾Ð¹ Ð¿ÑÐ¸ÑÐ¾Ð´Ðµ â ÐºÐ°Ðº Ð´Ð»Ñ ÑÑÐµÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ñ, ÑÐ°Ðº Ð¸ Ð´Ð»Ñ ÐºÐ¾Ð½ÑÐ¸Ð³ÑÑÐ°ÑÐ¸Ð¸ ÑÐ¸Ð¿Ð° Â«ÑÐµÐ¿ÑÂ». ÐÐ¾Ð»ÑÑÐµÐ½Ð½ÑÐµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð¼Ð¾Ð¶Ð½Ð¾ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°ÑÑ Ð¿ÑÐ¸ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ°Ñ Ñ ÑÐµÐ°Ð»ÑÐ½ÑÐ¼Ð¸ ÐÐÐÐ.
description: This work is devoted to the numerical modeling of the behavior of the group of drones with the goal of obtaining different types of stable structure. Tasks to be solved in this work: 1. Relevance of the development of swarm behavior algorithms has been considered. 2. The numerical model of drones swarm has been prepared. 3. The initial simulations have been conducted with the consequent analysis of the swarm structure. 4. The model has been optimized based on the results of the analysis in order to obtain a more stable structure. 5. The model has been adjusted in order to obtain another swarm configuration (âchainâ). 6. Swarms with different types of sensor arrays have been compared with each other. As a means of mathematical modelling PyCharm IDE for Python and NumPy (matrix operations) and Matplotlib (animation) libraries for it have been mastered. Thus, the model enabled not only demonstrating real-time assembly process, but also recording the results for subsequent analysis. As a result regular swarm structure has been obtained and the hypothesis of its lattice-like nature has been confirmed â for both spherical and chain-like configurations. The results can be implemented in experiments with real-life UAVs.