Smooth Function Modeling for On-Line Trajectory Reshaping Application

Abstract

by continuously retargeting and reshaping the reference RLV trajectory satisfying the feasibility constraints. On-line trajectory reshaping to determine a feasible reference trajectory is computationally a difficult problem for real time applications. ATRC is exploring the principles of vehicle dynamics inversion for online generation of feasible reference trajectory. Two essential components for generating reference trajectory for air-vehicles using “inverse dynamics” methodology are aerodynamic model of the vehicle that is representative of the current state of the vehicle, and a framework for modeling the vehicle trajectory. Physics based modeling software such as Missile DATCOM allows fast computation of aerodynamic coefficients for a given set of flight points and the results can be stored in tabular form. However, for efficient real-time trajectory reshaping application, it is desirable to represent aerodynamic coefficients in smooth functional forms that are governed by a few parameters. Additionaly, in inverse dynamics, the trajectories must also be represented by smooth and continuous functions. In this paper we present modeling of smooth functions using a set of basis functions that are suitable for aerodynamic modeling and trajectory reshaping of the air vehicles. A desirable feature for function modeling is the easy imposition of boundary as well as mid point constraints on the function using a small number of parameters without limiting the scope of the function. In this paper we present a design method for generating orthonormal polynomial basis functions in one and two dimensions with such constraints.