Interplanetary transfer optimization using cost function with variable coefficients

In this paper, the optimal interplanetary transfer including planetary escape and capture phases is investigated in the heliocentric frame. Based on primer vector theory, a modified cost function with variable coefficients is developed to reflect the gravitational effect more precisely. The necessary conditions as well as the transversality conditions of the new cost function are derived to search the optimal solution in fixed-time. By introducing the initial and final coasts, the optimal interplanetary transfer is extended to the time-free situation. Finally, the proposed method is applied to the Earth—Mars and Earth—Asteroid transfer. Comparisons with existing methods show that the proposed method can provide better transfer performances with high efficiency. The proposed method extends the application of primer vector theory and provides a fast and accurate reference for preliminary mission design in spacecraft planetary exploration.

[1]  Daniel J. Scheeres,et al.  Optimal transfers between unstable periodic orbits using invariant manifolds , 2011 .

[2]  G. Richardson,et al.  Using the Two-Burn Escape Maneuver for Fast Transfers in the Solar System and Beyond , 2010 .

[3]  Donald E. Kirk,et al.  Optimal control theory : an introduction , 1970 .

[4]  Richard Brusch,et al.  Trajectory optimization for the Atlas/Centaur launch vehicle , 1977, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[5]  Kathleen C. Howell,et al.  Time-free transfers between libration-point orbits in the elliptic restricted problem , 1992 .

[6]  Aude Rondepierre,et al.  A New Mixed Iterative Algorithm to Solve the Fuel-Optimal Linear Impulsive Rendezvous Problem , 2013, Journal of Optimization Theory and Applications.

[7]  F. Topputo.  On optimal two-impulse Earth–Moon transfers in a four-body model , 2013 .

[8]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[9]  Bruce A. Conway,et al.  Spacecraft Trajectory Optimization: Contents , 2010 .

[10]  Guo-Jin Tang,et al.  Hybrid planning for LEO long-duration multi-spacecraft rendezvous mission , 2012 .

[11]  Guo-Jin Tang,et al.  Interactive optimization approach for optimal impulsive rendezvous using primer vector and evolutionary algorithms , 2010 .

[12]  Derek F Lawden,et al.  Optimal trajectories for space navigation , 1964 .

[13]  L. Casalino,et al.  Global Search Capabilities of Indirect Methods for Impulsive Transfers , 2015 .

[14]  K. C. Howell,et al.  Transfers between libration-point orbits in the elliptic restricted problem , 1994 .

[15]  Kathryn E. Davis.  Locally optimal transfer trajectories between libration point orbits using invariant manifolds , 2009 .

[16]  Pingyuan Cui,et al.  Design of optimal impulse transfers from the Sun–Earth libration point to asteroid , 2015 .

[17]  D. J. Jezewski,et al.  An efficient method for calculating optimal free-space n-impulse trajectories. , 1968 .

[18]  Denílson Paulo Souza Santos,et al.  Application of a genetic algorithm in orbital maneuvers , 2015 .

[19]  Francesco Topputo,et al.  Global Optimization of Interplanetary Transfers with Deep Space Maneuvers Using Differential Algebra , 2012 .

[20]  Ying Nan,et al.  A survey of numerical algorithms for trajectory optimization of flight vehicles , 2012, Science China Technological Sciences.

[21]  Y. Kawakatsu,et al.  Orbit Transfer Optimization for Asteroid Missions Using Weighted Cost Function , 2015 .

[22]  M. Handelsman,et al.  Primer Vector on Fixed-Time Impulsive Trajectories , 1967 .

[23]  J. E. Prussing,et al.  Illustration of the primer vector in time- fixed, orbit transfer. , 1969 .

[24]  B. Conway.  Spacecraft Trajectory Optimization , 2014 .

[25]  Sang-Young Park,et al.  Hybrid optimization for multiple-impulse reconfiguration trajectories of satellite formation flying , 2009 .

[26]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[27]  Ya-zhong Luo,et al.  Optimal robust linearized impulsive rendezvous , 2007 .

[28]  Richard H. Battin,et al.  An elegant Lambert algorithm , 1983 .

[29]  Neal D. Hulkower,et al.  On the accessibility of near-earth asteroids. , 1987 .

[30]  Kaijian Zhu,et al.  Satellite scheduling considering maximum observation coverage time and minimum orbital transfer fuel cost , 2010 .

[31]  R. Brusch.  Constrained Impulsive Trajectory Optimization for Orbit-to-Orbit Transfer , 1979 .