Desensitizing the Minimum-Fuel Powered Descent For Mars Pinpoint Landing

This paper aims at reducing the sensitivity of the minimum-fuel powered descent trajectory on Mars in the presence of uncertainties and perturbations, using the desensitized optimal control methodology. The lander is modeled as a point mass in a uniform gravitational field, and the engine throttle is considered the control variable, which is bounded between two nonzero settings. Unlike the conventional practice of designing separately the nominal trajectory and a feedback tracking controller, desensitized optimal control strategy incorporates the two designs in synergy, delivering a superior performance. Sensitivities of the final position and velocity with respect to perturbed states at all times are derived and augmented onto the minimum-fuel performance index through penalty factors. The linear quadratic regulator technique is used to design the feedback control gains. To reduce the likelihood of the closed-loop throttle exceeding the prescribed bounds, a multiplicative factor is applied to the feedback gains. This reshapes the nominal trajectory from the well-known maximum-minimum-maximum structure in that the nominal throttle is encouraged to stay away from the prescribed bounds, leaving room for the feedback control. Monte Carlo simulations show that the occurrence of out-of-bound closed-loop throttles is significantly reduced, leading to improved landing precision.

[1]  Stephen Paschall,et al.  GN&C Technology Needed to Achieve Pinpoint Landing Accuracy at Mars , 2004 .

[2]  Shuang Li,et al.  Mars entry trajectory optimization using DOC and DCNLP , 2011 .

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

[4]  Mattia Mercolino,et al.  Flight of the Phoenix ESOC Supports NASA Mars Mission , 2008 .

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

[6]  Cheng-Chih Chu.  Development of advanced entry, descent, and landing technologies for future Mars missions , 2006, 2006 IEEE Aerospace Conference.

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

[8]  Richard W. Powell,et al.  Entry System Design Considerations for Mars Landers , 2001 .

[9]  A.M.S. Martin,et al.  Mars Science Laboratory: Entry, Descent, and Landing System Performance , 2007, 2007 IEEE Aerospace Conference.

[10]  W Powell Richard,et al.  Numerical Roll Reversal Predictor-Corrector Aerocapture and Precision Landing Guidance Algorithms for the Mars Surveyor Program 2001 Missions , 1998 .

[11]  David K. Geller,et al.  Apollo-derived Mars precision lander guidance , 1998 .

[12]  A. Charnes,et al.  Chance-Constrained Programming , 1959 .

[13]  Michael Nikolaou,et al.  Chance‐constrained model predictive control , 1999 .

[14]  Edward C. Wong,et al.  Guidance and Control Design for Hazard Avoidance and Safe Landing on Mars , 2006 .

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

[16]  Robert D. Braun,et al.  The Mars Surveyor 2001 Lander: A First Step Toward Precision Landing , 1998 .

[17]  C. Hargraves,et al.  DIRECT TRAJECTORY OPTIMIZATION USING NONLINEAR PROGRAMMING AND COLLOCATION , 1987 .

[18]  N. Sadegh,et al.  Minimum-time trajectory tracking of an underactuated system , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[19]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[20]  Robert D. Braun,et al.  Entry Descent and Landing Challenges of Human Mars Exploration , 2006 .

[21]  Arthur E. Bryson,et al.  Applied Optimal Control , 1969 .

[22]  Hans Seywald,et al.  Desensitizing the Pin-Point Landing Trajectory on Mars , 2008 .

[23]  I. M. Levitt.  Advances in astronautical sciences, vol.: edited by Horace Jacobs. 460 pages, illustrations, 612 × 934 in. New York, Plenum Press, Inc., 1959. Price, $8.00 , 1960 .