@inproceedings{35c52638101b42938b964e875251dddd,

title = "Analytical partial derivative calculation of the sims-flanagan transcription match point constraints",

abstract = "The optimization of low-thrust spacecraft trajectories is a complex problem that lends itself to the use of direct method optimization techniques, rather than indirect, primarily due to their ability to converge to a feasible solution from a very poor initial guess. Many low-thrust trajectory optimizers make use of large-scale nonlinear programming packages to solve the parameter optimization problem resulting from the discrete transcription of a continuous optimal control problem. The most well-known of these tools is probably the Sparse Nonlinear OPTimizer (SNOPT). The algorithms of gradient-based optimization packages such as SNOPT's sequential quadratic programming technique rely on knowledge of the system Jacobian. While SNOPT is capable of calculating the Jacobian entries numerically using finite differencing, specifying these partial derivatives analytically results in more efficient solver performance. We present methods for the calculation of exact analytical expressions for the partial derivatives of the match point constraints of the {"}up-to-unit vector control{"} variant of the Sims-Flanagan transcription. These derivatives represent approximately 92% of the dense Jacobian entries for the Sims-Flanagan problem and their analytical specification significantly increases solver execution speed and improves solution quality.",

author = "Ellison, {Donald H.} and Englander, {Jacob A.} and Ozimek, {Martin T.} and Conway, {Bruce A.}",

year = "2014",

month = jan,

day = "1",

language = "English (US)",

series = "Advances in the Astronautical Sciences",

publisher = "Univelt Inc.",

pages = "1559--1578",

editor = "Mackison, {Donald L.} and Ossama Abdelkhalik and Wilson, {Roby S.} and Renato Zanetti",

booktitle = "Advances In The Astronautical Sciences",

note = "24th AAS/AIAA Space Flight Mechanics Meeting, 2014 ; Conference date: 26-01-2014 Through 30-01-2014",

}