Discrete approximations to optimal trajectories using direct transcription and nonlinear programming
Abstract
A recently developed method for solving optimal trajectory problems uses a piecewisepolynomial representation of the state and control variables, enforces the equations of motion via a collocation procedure, and thus approximates the original calculusofvariations problem with a nonlinearprogramming problem, which is solved numerically. This paper identifies this method as a direct transcription method and proceeds to investigate the relationship between the original optimalcontrol problem and the nonlinearprogramming problem. The discretized adjoint equation of the collocation method is found to have deficient accuracy, and an alternate scheme which discretizes the equations of motion using an explicit RungeKutta parallelshooting approach is developed. Both methods are applied to finitethrust spacecraft trajectory problems, including a lowthrust escape spiral, a threeburn rendezvous, and a lowthrust transfer to the moon.
 Publication:

Astrodynamics 1989
 Pub Date:
 1990
 Bibcode:
 1990asdy.conf..771E
 Keywords:

 Nonlinear Programming;
 Optimal Control;
 Spacecraft Trajectories;
 Trajectory Optimization;
 Approximation;
 Calculus Of Variations;
 Collocation;
 Equations Of Motion;
 Polynomials;
 Astrodynamics