Dynamic step selection algorithm for piecewise linear approximation of complex control trajectories

The paper proposes a method for replacing a complex function used as a target for automatic control of unmanned vehicles with a simplified piecewise linear function, which requires much less computing resources. A numerical method has been developed for adaptive selection of a variable step for approximating a nonlinear one-dimensional function, the analytical expression of which is not given, by a piecewise linear function. The article shows that selection of approximation step (grid) is an important task for minimizing the calculations required number, if the computing device on board the unmanned vehicle must be miniature. The developed algorithm includes the calculation of successive intervals lengths that eventually cover the entire domain of the function with a predetermined approximation accuracy. The determination coefficient is used as a measure of accuracy. Numerical experiments are presented for calculating the linear-piecewise function parameters for the approximating a target trajectory problem with complex configuration for unmanned aerial underwater vehicle automatic control. The proposed method efficiency is compared with methods with a constant step, as well as with methods for calculating the dynamic step in various approaches. The advantage of the developed method from the point of view of computational costs is proved with the same accuracy, the limitations of the applicability of the method are determined.