"Reachable domain for spacecraft with ellipsoidal Delta-V distribution" by Changxuan Wen, Chao Peng et al.

Article Title

Reachable domain for spacecraft with ellipsoidal Delta-V distribution

Authors

Changxuan Wen, Chinese Academy of Sciences, Beijing 100094, China
Chao Peng, Chinese Academy of Sciences, Beijing 100094, China
Yang Gao, Chinese Academy of Sciences, Beijing 100094, China

Keywords

reachable domain, maneuverability, orbit uncertainty

Abstract

Conventional reachable domain (RD) problem with an admissible velocity increment, ∆v,in an isotropic distribution, was extended to the general case with ∆v in an anisotropicellipsoidal distribution. Such an extension enables RD to describe the effect of initial velocityuncertainty because a Gaussian form of velocity uncertainty can be regarded as possiblevelocity deviations that are confined within an error ellipsoid. To specify RD in space, theboundary surface of RD, also known as the envelope, should be determined. In this study,the envelope is divided into two parts: inner and outer envelopes. Thus, the problem ofsolving the RD envelope is formulated into an optimization problem. The inner and outerreachable boundaries that are closest to and farthest away from the center of the Earth,respectively, were found in each direction. An optimal control policy is then formulatedby using the necessary condition for an optimum; that is, the first-order derivative of theperformance function with respect to the control variable becomes zero. Mathematicalproperties regarding the optimal control policy is discussed. Finally, an algorithm to solvethe RD envelope is proposed. In general, the proposed algorithm does not require anyiteration, and therefore benefits from quick computation. Numerical examples, includingtwo coplanar cases and two 3D cases, are provided, which demonstrate that the proposedalgorithm works efficiently.