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The Problem of Target Control for a Quadrotor When Moving in a Horizontal Plane Avoiding Obstacles

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Abstract

A solution is sought for the problem of control in a mathematical model of the quadrotor. The main aim is moving an autonomous air vehicle from a given initial position to a target location in a finite time under the condition that the quadrotor must keep a safe distance from obstacles at every intermediate moment in time. The position of obstacles is known beforehand and they are immobile. Allowable values of the control parameters are subject to pointwise constraints. The control must be constructed in a feedback form, based on information about the current state of the object. This allows a control algorithm to be obtained that is resistant to small errors in the current state of the system and external actions. A nonlinear mathematical model of the quadrotor motion in space is presented. Movement in a given horizontal plane is considered in detail. The problem is solved using piecewise linearization and ellipsoidal calculus. An interior estimate is made of the solvability tube containing all positions from which the control problem is solvable. Formulas allowing calculations for feedback control strategy are written. Theoretical results are supplemented by a computational example.

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Notes

  1. Here and below, \(\preceq\) denotes an elementwise inequality relating two vectors with the same length.

  2. Here, \(\mathcal{H}_{+}\) is one of closed half-planes corresponding to the straight line \(\mathcal{H}\).

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Funding

This work was supported by the RF Ministry of Education and Science as part of the Moscow Center for Fundamental and Applied Mathematics Program, agreement no. 075-15-2019-1621; and by the Russian Foundation for Basic Research, project no. 19-01-00613a.

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Authors and Affiliations

  1. Department of Computational Mathematics and Cybernetics, Moscow State University, 119991, Moscow, Russia

    E. P. Kaplunova & P. A. Tochilin

Authors
  1. E. P. Kaplunova
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  2. P. A. Tochilin
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Correspondence to E. P. Kaplunova or P. A. Tochilin.

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Kaplunova, E.P., Tochilin, P.A. The Problem of Target Control for a Quadrotor When Moving in a Horizontal Plane Avoiding Obstacles. MoscowUniv.Comput.Math.Cybern. 45, 152–167 (2021). https://doi.org/10.3103/S0278641921040075

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