OPTIMAL RECONFIGURATION OF A TETRAHEDRAL FORMATION VIA A GAUSS PSEUDOSPECTRAL METHOD

This paper addresses the problem of determining a minimum-fuel maneuver sequence to reconfigure a tetrahedral formation. The objective of this work is to develop a single orbit, minimum-fuel reconfiguration strategy such that, after reconfiguration, the four spacecraft are able to return to an acceptable tetrahe-dral configuration in a region of interest near apogee for a period of three weeks without any required propulsive maneuvers. In the design considered here, an acceptable tetrahedron is obtained by satisfying several constraints on the shape and size of the tetrahedron. The optimal reconfiguration problem is posed as a nonlinear optimal control problem and is solved via direct trajectory optimization using a method called the Gauss pseudospectral method. The results obtained in this study provide insight into the structure of the optimal mission design and demonstrate the generality, computational efficiency, and accuracy of the Gauss pseudospectral method.

[1]  Emanuel Todorov,et al.  Optimal Control Theory , 2006 .

[2]  I. Michael Ross.  Hybrid Optimal Control Framework for Mission Planning , 2005, Journal of Guidance, Control, and Dynamics.

[3]  Ella M. Atkins,et al.  Optimization of a Tetrahedral Satellite Formation , 2005 .

[4]  David Benson,et al.  A Gauss pseudospectral transcription for optimal control , 2005 .

[5]  A. Rao,et al.  AAS 05-103 OPTIMAL CONFIGURATION OF SPACECRAFT FORMATIONS VIA A GAUSS PSEUDOSPECTRAL METHOD , 2005 .

[6]  F.Y. Hadaegh,et al.  A survey of spacecraft formation flying guidance and control. Part II: control , 2004, Proceedings of the 2004 American Control Conference.

[7]  L.M. Mailhe,et al.  Initialization and resizing of formation flying using global and local optimization methods , 2004, 2004 IEEE Aerospace Conference Proceedings (IEEE Cat. No.04TH8720).

[8]  P. Williams.  Jacobi pseudospectral method for solving optimal control problems , 2004 .

[9]  Yuichi Tsuda.  GLOBAL OPTIMIZATION OF MANEUVER SCHEDULE FOR MULTIPLE SPACECRAFTS FLYING IN FORMATION , 2004 .

[10]  Stuart A. Stanton,et al.  Optimal Orbital Transfer Using a Legendre Pseudospectral Method , 2003 .

[11]  Jonathan P. How,et al.  Distributed Control of Formation Flying Spacecraft Built on OA , 2003 .

[12]  David G. Hull,et al.  Optimal Control Theory for Applications , 2003 .

[13]  S. Ploen,et al.  A survey of spacecraft formation flying guidance and control (part 1): guidance , 2003, Proceedings of the 2003 American Control Conference, 2003..

[14]  Steven P. Hughes,et al.  Formation Tetrahedron Design for Phase I of the Magnetospheric Multiscale Mission , 2003 .

[15]  I. Michael Ross,et al.  DESIGNING OPTIMAL SPACECRAFT FORMATIONS , 2002 .

[16]  A. Rao,et al.  Performance Optimization of a Maneuvering Re-Entry Vehicle Using a Legendre Pseudospectral Method , 2002 .

[17]  Michael A. Saunders,et al.  SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization , 2002, SIAM J. Optim..

[18]  Frank H. Bauer,et al.  Preliminary Study for a Tetrahedron Formation: Quality Factors and Visualization , 2002 .

[19]  Michael A. Saunders,et al.  User’s Guide For Snopt Version 6, A Fortran Package for Large-Scale Nonlinear Programming∗ , 2002 .

[20]  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).

[21]  Oskar von Stryk,et al.  User's guide for DIRCOL (Version 2.1): a direct collacation method for the numerical solution of optimal control problems , 1999 .

[22]  I. Michael Ross,et al.  Costate Estimation by a Legendre Pseudospectral Method , 1998 .

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

[24]  P. Daly,et al.  Analysis methods for multi-spacecraft data , 1998 .

[25]  Gamal N. Elnagar,et al.  The pseudospectral Legendre method for discretizing optimal control problems , 1995, IEEE Trans. Autom. Control..

[26]  J. Betts,et al.  A sparse nonlinear optimization algorithm , 1994 .

[27]  James R. Wertz,et al.  Space Mission Analysis and Design , 1992 .

[28]  C. Canuto.  Spectral methods in fluid dynamics , 1991 .

[29]  R. Battin.  An introduction to the mathematics and methods of astrodynamics , 1987 .

[30]  T. A. Zang,et al.  Spectral methods for fluid dynamics , 1987 .

[31]  Anil V. Rao,et al.  Practical Methods for Optimal Control Using Nonlinear Programming , 1987 .

[32]  C. R. Hargraves,et al.  DIRECT TRAJECTORY OPTIMIZATION USING NONLINEAR PROGRAMMING AND COLLOCATION , 1986 .