Use of Parametric Approximation in Real-Time Nonlinear Trajectory Generation

Abstract

This paper outlines real-time nonlinear trajectory generation procedure and explores the assisting role of function approximators in this computational task. Nonlinear Trajectory Generation software package (NTG), developed at Caltech by Mark Milam [14], provides real-time trajectory generation for constrained nonlinear systems. Formal translation of each component of the optimal control form into NTG parameters is prescribed in this paper. Effects of major internal NTG parameters, such as, number of intervals, smoothness, piecewise polynomial orders, number of break points, on the solution of an optimal control problem are investigated. The need for auxiliary regressors in formulating problems involving trajectory generation with tabular data is discussed. Two popular families of regressors, namely B-splines and feedforward Artificial Neural Networks (ANNs) are investigated for this purpose. Collaboration of each of these approximators with standard NTG procedure is demonstrated on illustrative trajectory generation instances.