Propagation and reconstruction of re-entry uncertainties using continuity equation and simplicial interpolation

This work proposes a continuum-based approach for the propagation of uncertainties in the initial conditions and parameters for the analysis and prediction of spacecraft re-entries. Using the continuity equation together with the re-entry dynamics, the joint probability distribution of the uncertainties is propagated in time for specific sampled points. At each time instant, the joint probability distribution function is then reconstructed from the scattered data using a gradient-enhanced linear interpolation based on a simplicial representation of the state space. Uncertainties in the initial conditions at re-entry and in the ballistic coefficient for three representative test cases are considered: a three-state and a six-state steep Earth re-entry and a six-state unguided lifting entry at Mars. The paper shows the comparison of the proposed method with Monte Carlo based techniques in terms of quality of the obtained marginal distributions and runtime as a function of the number of samples used.

[1]  Morten Bisgaard,et al.  AIAA Guidance, Navigation and Control Conference and Exhibit (2008) , 2008 .

[2]  Massimiliano Vasile,et al.  Sensitivity analysis and probabilistic re-entry modeling for debris using high dimensional model representation based uncertainty treatment , 2017 .

[3]  Joel Nothman,et al.  SciPy 1.0-Fundamental Algorithms for Scientific Computing in Python , 2019, ArXiv.

[4]  Ping Lu,et al.  Skip Entry Trajectory Planning and Guidance , 2007 .

[5]  Ashish Tewari.  Atmospheric and Space Flight Dynamics: Modeling and Simulation with MATLAB and Simulink , 2007 .

[6]  nasa,et al.  U.S. Standard Atmosphere, 1976 , 2015 .

[7]  T. Lips,et al.  Scarab -a Multi-Disciplinary Code for Destruction Analysis of Space-Craft during Re-Entry , 2005 .

[8]  Robert D. Braun,et al.  Extension and Enhancement of the Allen–Eggers Analytical Ballistic Entry Trajectory Solution , 2015 .

[9]  N. H. Kemp,et al.  Heat Transfer to Satellite Vehicles Re-entering the Atmosphere , 2012 .

[10]  Ya-Zhong Luo,et al.  A review of uncertainty propagation in orbital mechanics , 2017 .

[11]  Nicholas L. Johnson,et al.  The Object Reentry Survival Analysis Tool (ORSAT) ... , 2005 .

[12]  Pietro Marco Congedo,et al.  Space debris reentry prediction and ground risk estimation using a probabilistic breakup model , 2019 .

[13]  Ming-Jun Lai,et al.  The Multivariate Spline Method for Scattered Data Fitting and Numerical Solutions of Partial Differential Equations , 2006 .

[14]  P. Erdös,et al.  Interpolation , 1953, An Introduction to Scientific, Symbolic, and Graphical Computation.

[15]  Abhishek Halder,et al.  Dispersion Analysis in Hypersonic Flight During Planetary Entry Using Stochastic Liouville Equation , 2011 .

[16]  Ping Lu,et al.  Entry Guidance: A Unified Method , 2014 .

[17]  Herbert Edelsbrunner,et al.  Three-dimensional alpha shapes , 1992, VVS.

[18]  Carlos A. Coello Coello,et al.  Multi-objective Optimization Using Differential Evolution: A Survey of the State-of-the-Art , 2008 .

[19]  Hugh G. Lewis,et al.  Demisability and survivability sensitivity to design-for-demise techniques , 2018, 1910.06397.

[20]  R. Braun,et al.  Mars Pathfinder atmospheric entry - Trajectory design and dispersion analysis , 1996 .

[21]  Zachary R. Putnam,et al.  A Comparison of Two Orion Skip Entry Guidance Algorithms , 2007 .

[22]  C. A. Kluever,et al.  Entry Guidance Performance for Mars Precision Landing , 2008 .

[23]  Bruce G. Terrell,et al.  National Oceanic and Atmospheric Administration , 2020, Federal Regulatory Guide.

[24]  John C. Mather,et al.  A New Approach to Dynamical Evolution of Interplanetary Dust , 1997 .

[25]  C. Colombo,et al.  Interpolation and Integration of Phase Space Density for Estimation of Fragmentation Cloud Distribution , 2019 .

[26]  A. Eddington,et al.  Principles of Stellar Dynamics , 1943, Nature.

[27]  Robert E. Jones,et al.  Test Results for Entry Guidance Methods for Space Vehicles , 2004 .

[28]  Robert D. Braun,et al.  Feasibility of Guided Entry for a Crewed Lifting Body Without Angle-of-Attack Control , 2014 .

[29]  E. Mooij,et al.  Uncertainty propagation for statistical impact prediction of space debris , 2018 .

[30]  J. Balaram,et al.  Mars Science Laboratory Simulations for Entry, Descent, and Landing , 2006 .

[31]  Marek Teichmann,et al.  Surface reconstruction with anisotropic density-scaled alpha shapes , 1998, Proceedings Visualization '98 (Cat. No.98CB36276).

[32]  Camilla Colombo,et al.  A Density-Based Approach to the Propagation of Re-Entry Uncertainties , 2019 .

[33]  Mallory Lefland,et al.  Mars 2020 Entry, Descent, and Landing System Overview , 2019, 2019 IEEE Aerospace Conference.

[34]  L. J. Boya,et al.  On Regular Polytopes , 2012, 1210.0601.

[35]  Tristan van Leeuwen,et al.  Raising the order of multivariate approximation schemes using supplementary derivative data , 2010, ICCS.

[36]  Roberto Armellin,et al.  Atmospheric Entry Guidance Based on Differential Algebra for High Elevation Mars Landing , 2018 .

[37]  Luciano Anselmo,et al.  Re-Entry Predictions for Uncontrolled Satellites: Results and Challenges , 2013 .

[38]  Gaëtan Kerschen,et al.  Probabilistic Assessment of Lifetime of Low-Earth-Orbit Spacecraft: Uncertainty Propagation and Sensitivity Analysis , 2015 .

[39]  Harald Niederreiter,et al.  Random number generation and Quasi-Monte Carlo methods , 1992, CBMS-NSF regional conference series in applied mathematics.

[40]  Ping Lu,et al.  Verification of a Fully Numerical Entry Guidance Algorithm , 2017 .

[41]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[42]  Francesca Letizia.  Extension of the Density Approach for Debris Cloud Propagation , 2018, Journal of Guidance, Control, and Dynamics.

[43]  Erich Novak,et al.  High dimensional polynomial interpolation on sparse grids , 2000, Adv. Comput. Math..

[44]  Alireza Doostan,et al.  Satellite collision probability estimation using polynomial chaos expansions , 2013 .

[45]  F. Frances Yao,et al.  Computational Geometry , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[46]  P. Alfeld.  Scattered data interpolation in three or more variables , 1989 .

[47]  Mischa Schmidt,et al.  On the Performance of Differential Evolution for Hyperparameter Tuning , 2019, 2019 International Joint Conference on Neural Networks (IJCNN).

[48]  Ping Lu,et al.  Predictor-Corrector Entry Guidance for Low-Lifting Vehicles , 2007 .

[49]  Abhi Jain,et al.  DSENDS: Multi-Mission Flight Dynamics Simulator for NASA Missions , 2016 .

[50]  Arnold Neumaier,et al.  Introduction to Numerical Analysis , 2001 .

[51]  C. McInnes.  Autonomous ring formation for a planar constellation of satellites , 1995 .

[52]  Martin D. Buhmann,et al.  Radial Basis Functions: Theory and Implementations: Preface , 2003 .

[53]  Raktim Bhattacharya,et al.  Polynomial Chaos-Based Analysis of Probabilistic Uncertainty in Hypersonic Flight Dynamics , 2010 .

[54]  Hugh G. Lewis,et al.  Spacecraft design optimisation for demise and survivability , 2018, Aerospace Science and Technology.

[55]  Brian R. Hoelscher.  Orion Entry, Descent, and Landing Simulation , 2007 .

[56]  Robert D. Braun,et al.  Improving Lunar Return Entry Range Capability Using Enhanced Skip Trajectory Guidance , 2008 .