Discrete approximations to optimal trajectories using direct transcription and nonlinear programmingA recently developed method for solving optimal trajectory problems uses a piecewise-polynomial representation of the state and control variables, enforces the equations of motion via a collocation procedure, and thus approximates the original calculus-of-variations problem with a nonlinear-programming problem, which is solved numerically. This paper identifies this method as a direct transcription method and proceeds to investigate the relationship between the original optimal-control problem and the nonlinear-programming 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 Runge-Kutta parallel-shooting approach is developed. Both methods are applied to finite-thrust spacecraft trajectory problems, including a low-thrust escape spiral, a three-burn rendezvous, and a low-thrust transfer to the moon.
Document ID
19900065983
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Enright, Paul J. (Illinois Univ. Urbana, IL, United States)
Conway, Bruce A. (Illinois, University Urbana, United States)