From Low Thrust to Solar Sailing: A Homotopic Approach

This paper describes a novel method to solve solar-sail minimum-time-of-flight optimal control problems starting from a low-thrust solution. The method is based on a homotopic continuation. This technique allows to link the low-thrust with the solar-sail acceleration, so that the solar-sail solution can be computed starting from the usually easier low-thrust one by means of a numerical iterative approach. Earth-to-Mars transfers have been studied in order to validate the proposed method. A comparison is presented with a conventional solution approach, based on the use of a genetic algorithm. The results show that the novel technique has advantages, in terms of accuracy of the solution and computational time.

[1]  Bruce Conway.  Spacecraft Trajectory Optimization: Preface , 2010 .

[2]  E. Allgower,et al.  Introduction to Numerical Continuation Methods , 1987 .

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

[4]  Bernd Dachwald,et al.  Multiple near-Earth asteroid rendezvous and sample return using first generation solar sailcraft , 2005 .

[5]  Bruce A. Conway,et al.  Optimal Low-Thrust Orbital Maneuvers via Indirect Swarming Method , 2014, J. Optim. Theory Appl..

[6]  Thomas Haberkorn,et al.  Low thrust minimum-fuel orbital transfer: a homotopic approach , 2004 .

[7]  J. J. Moré,et al.  Levenberg--Marquardt algorithm: implementation and theory , 1977 .

[8]  E. Allgower,et al.  Numerical path following , 1997 .

[9]  H. B. Keller,et al.  NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (II): BIFURCATION IN INFINITE DIMENSIONS , 1991 .

[10]  Hexi Baoyin,et al.  Practical Techniques for Low-Thrust Trajectory Optimization with Homotopic Approach , 2012 .

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

[12]  Alessandro Antonio Quarta,et al.  Solar sail trajectories with piecewise-constant steering laws , 2009 .

[13]  G. Whitehead,et al.  Elements of Homotopy Theory , 1978 .

[14]  J. Stoer,et al.  Introduction to Numerical Analysis , 2002 .

[15]  John T. Betts,et al.  Practical Methods for Optimal Control and Estimation Using Nonlinear Programming , 2009 .

[16]  Sadri Hassani,et al.  Nonlinear Dynamics and Chaos , 2000 .

[17]  Bruce A. Conway,et al.  Particle Swarm Optimization Applied to Space Trajectories , 2010 .

[18]  John E. Prussing,et al.  Solar Sailing: Technology, Dynamics, and Mission Applications , 2000 .