Enhancements on the Convex Programming Based Powered Descent Guidance Algorithm for Mars Landing

In this paper, we present enhancements on the powered descent guidance algorithm developed for Mars pinpoint landing. The guidance algorithm solves the powered descent minimum fuel trajectory optimization problem via a direct numerical method. Our main contribution is to formulate the trajectory optimization problem, which has nonconvex control constraints, as a finite dimensional convex optimization problem, specifically as a finite dimensional second order cone programming (SOCP) problem. SOCP is a subclass of convex programming, and there are efficient SOCP solvers with deterministic convergence properties. Hence, the resulting guidance algorithm can potentially be implemented onboard a spacecraft for real-time applications. Particularly, this paper discusses the algorithmic improvements obtained by: (i) Using an efficient approach to choose the optimal time-of-flight; (ii) Using a computationally inexpensive way to detect the feasibility/ infeasibility of the problem due to the thrust-to-weight constraint; (iii) Incorporating the rotation rate of the planet into the problem formulation; (iv) Developing additional constraints on the position and velocity to guarantee no-subsurface flight between the time samples of the temporal discretization; (v) Developing a fuel-limited targeting algorithm; (vi) Initial result on developing an onboard table lookup method to obtain almost fuel optimal solutions in real-time.

[1]  Stephen P. Boyd,et al.  Semidefinite Programming , 1996, SIAM Rev..

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

[3]  S. Ploen,et al.  A Powered Descent Guidance Algorithm for Mars Pinpoint Landing , 2005 .

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

[5]  Kenneth D. Mease,et al.  Fuel Efficient Powered Descent Guidance for Mars Landing , 2005 .

[6]  Kim-Chuan Toh,et al.  SDPT3 — a Matlab software package for semidefinite-quadratic-linear programming, version 3.0 , 2001 .

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

[8]  Bixiang Wang,et al.  IMPLEMENTATION OF INTERIOR POINT METHODS FOR SECOND ORDER CONIC OPTIMIZATION , 2003 .

[9]  James S. Meditch,et al.  On the problem of optimal thrust programming for a lunar soft landing , 1964 .

[10]  Richard W. Powell,et al.  Systems for pinpoint landing at Mars , 2004 .

[11]  I. Michael Ross,et al.  Direct Trajectory Optimization by a Chebyshev Pseudospectral Method ; Journal of Guidance, Control, and Dynamics, v. 25, 2002 ; pp. 160-166 , 2002 .

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

[13]  L. Berkovitz.  Convexity and Optimization in Rn , 2001 .

[14]  R. V. Dooren,et al.  A Chebyshev technique for solving nonlinear optimal control problems , 1988 .

[15]  I. Michael Ross,et al.  Direct trajectory optimization by a Chebyshev pseudospectral method , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[16]  Jiming Peng,et al.  Self-regularity - a new paradigm for primal-dual interior-point algorithms , 2002, Princeton series in applied mathematics.

[17]  Edward C. Wong,et al.  Autonomous guidance and control design for hazard avoidance aand safe landing on Mars , 2002 .

[18]  J. Betts.  Survey of Numerical Methods for Trajectory Optimization , 1998 .

[19]  D. Hull.  Conversion of optimal control problems into parameter optimization problems , 1996 .

[20]  Federico Najson,et al.  A Computationally Non-Expensive Guidance Algorithm for Fuel Efficient Soft Landing , 2005 .

[21]  W. Fleming,et al.  Deterministic and Stochastic Optimal Control , 1975 .

[22]  Ronald R. Sostaric,et al.  Powered Descent Guidance Methods For The Moon and Mars , 2005 .