Stochastic Atmosphere Modeling for Risk Adverse Aerocapture Guidance

In this paper we consider the problem of aerocapture guidance inside an atmosphere with the density randomly perturbed according to a Gaussian process model. We formulate the problem of solving for a single bank event as a stochastic optimization problem and then, in terms of a 3-DoF Martian aerocapture example, we study the properties of the proposed approach compared to a standard deterministic approach. The stochastic approach is shown to decrease the risk that a large delta-$V$ is required for maneuvering after atmospheric flight to reach a target apoapsis and periapsis.

[1]  Kazuhide Okamoto,et al.  Optimal Covariance Control for Stochastic Systems Under Chance Constraints , 2018, IEEE Control Systems Letters.

[2]  Buford W. Shipley.  Control algorithms for aerobraking in the Martian atmosphere , 1991 .

[3]  Panagiotis Tsiotras,et al.  Minimum-fuel Powered Descent in the Presence of Random Disturbances , 2019, AIAA Scitech 2019 Forum.

[4]  R. Rockafellar,et al.  Optimization of conditional value-at risk , 2000 .

[6]  David A. Spencer,et al.  Aerobraking Cost and Risk Decisions , 2007 .

[7]  Loura Hall.  Optimal Aerocapture Guidance , 2015 .

[8]  C. G. Justus,et al.  Mars-GRAM 2000: A Mars atmospheric model for engineering applications , 2002 .

[9]  Yaakov Bar-Shalom,et al.  Generalized certainty equivalence and dual effect in stochastic control , 1975 .

[10]  J. Lafleur.  The Conditional Equivalence of ΔV Minimization and Apoapsis Targeting in Numerical Predictor- Corrector Aerocapture Guidance , 2011 .

[11]  N. Vinh,et al.  Hypersonic and Planetary Entry Flight Mechanics , 1980 .

[12]  Richard W. Powell,et al.  Six-degree-of-freedom guidance and control analysis of Mars aerocapture , 1993 .

[13]  Shie Mannor,et al.  Risk-Sensitive and Robust Decision-Making: a CVaR Optimization Approach , 2015, NIPS.

[14]  E. Tse.  On the optimal control of stochastic linear systems , 1971 .

[15]  Philippe Artzner,et al.  Coherent Measures of Risk , 1999 .

[16]  H. Simon,et al.  Dynamic Programming Under Uncertainty with a Quadratic Criterion Function , 1956 .

[17]  L. Blackmore,et al.  Convex Chance Constrained Predictive Control without Sampling , 2009 .

[18]  Steven Reece,et al.  An introduction to Gaussian processes for the Kalman filter expert , 2010, 2010 13th International Conference on Information Fusion.