Y. A. Kapitanyuk, D. A. Khvostov, S. A. Chepinsky

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The paper deals with the problem of dynamic tracking of an external movable object. These problems arise when designing tracking control systems for unmanned aircrafts following ground movable objects. A dynamic model of a solid body in three-dimensional space is selected as a control object model. An external object is described by the kinematic model of a solid body on the plane. Smooth trajectory is defined as an implicit curve associated with an external movable object. The desired height of movement is selected separately. Relative dynamics of the plant and an external movable object is considered for the synthesis of control algorithm, and methods of differential geometric transformation of the original model to the task-oriented coordinate system are applied. The original problem is formulated in terms of a longitudinal motion and two orthogonal deviations after transformation. The main results are represented by task-oriented model of spatial movement and the corresponding nonlinear control algorithms. An example of solid body motion along a circular trajectory with respect to a given rectilinear motion of an external object is given for the illustration of the proposed method performance.

Keywords: trajectory control, motion control, nonlinear control

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