Aircraft Trajectory Optimization with Direct Collocation Using Movable Gridpoints.

Abstract

The direct collocation method has been successfully applied to compute aircraft and launcher optimal trajectories. In this method, the optimal control problem is transformed into a non-linear programming (NLP) problem by parameterizing the states and controls at a finite number of nodes. Specifically, the states are represented by piecewise cubic hermit polynomials and the controls by piecewise linear polynomials. In addition, collocation constraints are introduced so that the state polynomials satisfy the state differential equation.