Quadrocopter Control by Network Operator Method Based on Multi-Point Stabilization
Askhat Diveev, Elizaveta Yu. Shmalko, Oubai Hussein · Mekhatronika Avtomatizatsiya Upravlenie · 2020
Thepaper presents a solution to the problem of optimal control of a quadrocopter under phase constraints by the numerical method of a network operator based on multi-point stabilization. According to this approach, the task of control system synthesis is initially solved. As a result, the quadrocopter is stabilized with respect to a certain point in the state space.Atthe second stage, a sequence of stabilization points is searched in the state space such that switching the stabilizationpoints at fixed times ensures the movement of the quadrocopter from the initial state to the terminal state with an optimalvalueof the quality criterion taking into account phase constraints. To solve the problem of stabilization system synthesis,the network operator method is used. The method is numerical and, unlike the well-known analytical methods, allows tosynthesize a control system automatically without a specific analysis of the right parts of the model. The method allowsto find the structure and parameters of a mathematical expression in the encoded form using the genetic algorithm. Thenetwork operator code is an integer upper-triangular matrix. At the stage of solving the synthesis problem, the mathematical model of quadrocopter motion is decomposed into angular and spatial motions in order to separate control componentsforangular and spatial motions, respectively. The synthesized stabilization system consists of two subsystems connected inseriesforspatial and angular motion. As controls for spatial motion, moments around the axes and the total thrust of allquadcopter propellers were used. And the inputs for the angular motion stabilization system are the desired angles of inclination of the quadrocopter. The stabilization problem is considered as a general synthesis task for a control system. Usingthe network operator method, one control function is searched that provides stabilization of the object at a given point in the considered state space from the set of initial conditions. At the stage of the search for equilibrium points, the evolutionaryparticleswarm algorithm is used. A numerical example of solving the problem of optimal control of a quadrocopter withfourphase constraints is given.