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Mekhatronika, Avtomatizatsiya, Upravlenie, 2018, vol. 19, no. 2, pp. 126—133
DOI: 10.17587/mau.19.126-133
**The Reproduction of the Trajectories of Moving Objects in the Systems of Control of Air Space**
**V. V. Chekushkin,** chekvv@gmail.com, **S. N. Zhiganov**, s_zh_72@mail.ru**, A. A. Bykov**, Murom Institute (branch) "Vladimir State University named after Alexander and Nickolay Stoletov", Murom, 602264, Russian Federation, **K. V. Miheev**, kiri-mikheev@yandex.ru, JSC Murom Plant of Radio Measuring Instruments, Murom, 602267, Russian Federation
Corresponding author: **Zhiganov Sergej N.,** Ph. D., Associate Professor of IMS Murom Institute (branch) "Vladimir State University named after Alexander and Nickolay Stoletov", Murom, 602264, Russian Federation
e-mail: s_zh_72@mail.ru
Accepted on November 12, 2017
For real-time developed a method of visual formation of trajectories of air objects of smoothly conjugated segments in the coordinate system of the zone of vision radar. The geometric shape segments of General trajectories are based on iterative change of the location of the reference polyline bezier curves with variable radii of curvature. As the trajectory of the object was used and the piecewise-specified spatial curve consisting of smoothly combine segments as Bezier curves mainly the first and third orders. The geometric shape of each segment of the total trajectory was set based on the location of n control points, i.e. the reference polyline with n nodes. When you specify a geometric shape of the curve were simultaneously determined by the minimum radius of its curvature. In addition there was a reserve in the amount of allowable linear acceleration, which is summed with a vector tangential. In the transition from one curve to another Bezier smooth change of the radius of curvature is ensured by continuous first and second derivatives matched curves. It is shown that to ensure the continuity of the first derivative, it is sufficient that three adjacent reference points of the two curves are collinear, then when you build the trajectories of the two mating curves will have a common tangent at the point of intersection, i.e., equal to the first derivative. To obtain the kinematics of the motion of an object along a path in real-time functions when the speed was obtained functional dependence linking the current value of the time and normalized time. Standardized and real-time links traversed path. Monotonically changing forward and backward functional dependency a journey from time to time was approximated with a high degree of accuracy by polynomials of the best approximation of the 2nd or 3rd degrees. The paper presents recommendations for operators to conduct preparatory calculations provide in General a time interval of formation of a trajectory of movement of air objects.
**Keywords**: trajectory, Bezier curve, acceleration, radius of curvature, the kinematics of the movement
For citation:
**Chekushkin V. V., Zhiganov S. N., Bykov A. A., Miheev K. V. **The Reproduction of the Trajectories of Moving Objects in the Systems of Control of Air Space, *Mekhatronika, Avtomatizatsiya, Upravlenie*, 2018, vol. 19, no. 2, pp. 126—133.
DOI: 10.17587/mau.19.126-133
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