Constrained Reachability and Controllability Sets for Planetary Precision Landing via Convex Optimization

This paper presents a convex optimizations-based method to compute the set of initial conditions from which a given landing accuracy to a target can be achieved (constrained controllability set) and the set of states that can be reached from a given set of initial states (constrained reachability set) for a planetary landing vehicle with all the relevant control and mission constraints. The proposed method is based on the lossless convexification of the powered-descent landing guidance problem and methods of convex optimization and computational geometry. These techniques are used to generate approximations that can be arbitrarily close to the actual reachability or controllability sets. The quantification of these sets allows evaluation of the feasibility of a prescribed landing accuracy for a given vehicle and an expected set of dispersions from the parachute descent phase of a planetary landing mission. Since these sets are generated systematically and quickly, a wide range of design options can be eva...

[1]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[2]  Donald E. Kirk,et al.  Optimal Control Theory , 1970 .

[3]  Allan R. Klumpp,et al.  Apollo lunar descent guidance , 1974, Autom..

[4]  K. T. Tan,et al.  Linear systems with state and control constraints: the theory and application of maximal output admissible sets , 1991 .

[5]  Kim-Chuan Toh,et al.  SDPT3 -- A Matlab Software Package for Semidefinite Programming , 1996 .

[6]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[7]  Kuang-Yang Tu,et al.  Drag-Based Predictive Tracking Guidance for Mars Precision Landing , 1998 .

[8]  M. Alexander,et al.  Mars Transportation Environment Definition Document , 2001 .

[9]  Jos F. Sturm,et al.  Implementation of interior point methods for mixed semidefinite and second order cone optimization problems , 2002, Optim. Methods Softw..

[10]  Johan Efberg,et al.  YALMIP : A toolbox for modeling and optimization in MATLAB , 2004 .

[11]  Stephen J. Wright,et al.  Primal-Dual Interior-Point Methods , 1997 .

[12]  Mehran Mesbahi,et al.  Quadratically constrained attitude control via semidefinite programming , 2004, IEEE Transactions on Automatic Control.

[13]  Johan Löfberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .

[14]  Kenneth D. Mease,et al.  Computationally inexpensive guidance algorithm for fuel-efficient terminal descent , 2006 .

[15]  S. Ploen,et al.  Performance trades for Mars pinpoint landing , 2006, 2006 IEEE Aerospace Conference.

[16]  Richard W. Powell,et al.  Entry Configurations and Performance Comparisons for the Mars Smart Lander , 2006 .

[17]  A. Acikmese,et al.  A Convex Guidance Algorithm for Formation Reconfiguration , 2006 .

[18]  Alberto Bemporad,et al.  An Algorithm for Approximate Multiparametric Convex Programming , 2006, Comput. Optim. Appl..

[19]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[20]  R. Mitcheltree,et al.  Mars Science Laboratory entry, descent, and landing system , 2006, 2006 IEEE Aerospace Conference.

[21]  Aron A. Wolf,et al.  A Comparison of Powered Descent Guidance Laws for Mars Pinpoint Landing. , 2006 .

[22]  R. Manning,et al.  Mars Exploration Entry, Descent, and Landing Challenges , 2007 .

[23]  Kenneth D. Mease,et al.  Feasible Trajectory Generation for Atmospheric Entry Guidance , 2007 .

[24]  Behcet Acikmese,et al.  Convex programming approach to powered descent guidance for mars landing , 2007 .

[25]  Euler's polyhedron formula — a starting point of today's polytope theory , 2007 .

[26]  Ufuk Topcu,et al.  Minimum-Fuel Powered Descent for Mars Pinpoint Landing , 2007 .

[27]  D. Kipp,et al.  Mars Science Laboratory Entry, Descent, and Landing Triggers , 2007, 2007 IEEE Aerospace Conference.

[28]  A. Chen,et al.  Mars Science Laboratory Entry, Descent, and Landing System Overview , 2008, 2008 IEEE Aerospace Conference.

[29]  Craig A. Kluever.  Entry Guidance Using Analytical Atmospheric Skip Trajectories , 2008 .

[30]  Robert D. Braun,et al.  Guidance, Navigation, and Control System Performance Trades for Mars Pinpoint Landing , 2010 .

[31]  Behcet Acikmese,et al.  Minimum-Landing-Error Powered-Descent Guidance for Mars Landing Using Convex Optimization , 2010 .

[32]  Gavin F. Mendeck,et al.  Entry Guidance for the 2011 Mars Science Laboratory Mission , 2011 .

[33]  Stephen P. Boyd,et al.  CVXGEN: a code generator for embedded convex optimization , 2011, Optimization and Engineering.

[34]  Ping Lu,et al.  Autonomous Trajectory Planning for Rendezvous and Proximity Operations by Conic Optimization , 2012 .

[35]  R. Anderson,et al.  Mars Science Laboratory Mission and Science Investigation , 2012 .

[36]  Gurkirpal Singh,et al.  Powered Flight Design and Reconstructed Performance Summary for the Mars Science Laboratory Mission , 2013 .

[37]  Ales Bezdek,et al.  Matlab script for 3D visualizing geodata on a rotating globe , 2013, Comput. Geosci..

[38]  Behcet Acikmese.  Application of Lexicographic Goal Programming with convex optimization in control systems , 2013 .

[39]  Andrew E. Johnson,et al.  Flight testing of trajectories computed by G-FOLD: Fuel optimal large divert guidance algorithm for planetary landing , 2013 .

[40]  Behçet Açikmese,et al.  Lossless Convexification of Nonconvex Control Bound and Pointing Constraints of the Soft Landing Optimal Control Problem , 2013, IEEE Transactions on Control Systems Technology.

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

[42]  Jeffrey J. Biesiadecki,et al.  Mars Science Laboratory Flyaway Guidance, Navigation, and Control System Design , 2014 .

[43]  Behçet Açikmese,et al.  Lossless convexification of non-convex optimal control problems for state constrained linear systems , 2014, Autom..

[44]  Andrew E. Johnson,et al.  ADAPT demonstrations of onboard large-divert Guidance with a VTVL rocket , 2014, 2014 IEEE Aerospace Conference.

[45]  Jing Zhang,et al.  Automated Custom Code Generation for Embedded, Real-time Second Order Cone Programming , 2014 .

[46]  Behçet Açikmese,et al.  Finite-horizon controllability and reachability for deterministic and stochastic linear control systems with convex constraints , 2014, 2014 American Control Conference.

[47]  Behçet Açikmese,et al.  Maximum Divert for Planetary Landing Using Convex Optimization , 2014, J. Optim. Theory Appl..