Improved Shaping Approach to the Preliminary Design of Low-Thrust Trajectories

This paper presents a general framework for the development of shape-based approaches to low-thrust trajectory design. A novel shaping method, based on a three-dimensional description of the trajectory in spherical coordinates, is developed within this general framework. Both the exponential sinusoid and the inverse polynomial shaping are demonstrated to be particular two-dimensional cases of the spherical one. The pseudoequinoctial shaping is revisited within the new framework, and the nonosculating nature of the pseudoequinoctial elements is analyzed. A two step approach is introduced to solve the time of flight constraint, related to the design of low-thrust arcs with boundary constraints for both spherical and pseudoequinoctial shaping. The solution derived from the shaping approach is improved with a feedback linear-quadratic controller and compared against a direct collocation method based on finite elements in time. The new shaping approach and the combination of shaping and linear-quadratic controller are tested on three case studies: a mission to Mars, a mission to asteroid 1989ML, a mission to comet Tempel-1, and a mission to Neptune.

[1]  Junichiro Kawaguchi,et al.  Powered Flight of HAYABUSA in Deep Space , 2006 .

[2]  Massimiliano Vasile,et al.  Optimizing low-thrust and gravity assist maneuvers to design interplanetary trajectories , 2011, ArXiv.

[3]  Michael Efroimsky,et al.  2 – Gauge Freedom in Astrodynamics , 2006 .

[4]  Angioletta Coradini,et al.  Dawn discovery mission to Vesta and Ceres: Present status , 2006 .

[5]  Dario Izzo,et al.  Lambert's Problem for Exponential Sinusoids , 2006 .

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

[7]  Bradley J. Wall,et al.  Shape-Based Approximation Method for Low-Thrust Trajectory Optimization , 2008 .

[8]  Massimiliano Vasile,et al.  On the optimality of a shape-based approach based on pseudo-equinoctial elements , 2006 .

[9]  Robert F. Stengel,et al.  Flight Control Design using Nonlinear Inverse Dynamics , 1986, 1986 American Control Conference.

[10]  Anastassios E. Petropoulos,et al.  Design and Optimization of Low-Thrust Trajectories with Gravity Assists , 2003 .

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

[12]  Anastassios E. Petropoulos,et al.  Automated Design of Low-Thrust Gravity-Assist Trajectories , 2000 .

[13]  Anastassios E. Petropoulos,et al.  Shape-Based Algorithm for Automated Design of Low-Thrust, Gravity-Assist Trajectories , 2004 .

[14]  David H. Lehman,et al.  Results from the Deep Space 1 technology validation mission , 2000 .

[15]  Bradley J. Wall,et al.  Shape-Based Approach to Low-Thrust Rendezvous Trajectory Design , 2009 .

[16]  J. Baumgarte.  Stabilization of constraints and integrals of motion in dynamical systems , 1972 .

[17]  D. Garcia Yarnoz,et al.  Trajectory design for the Bepi-Colombo mission to Mercury , 2006 .

[18]  Massimiliano Vasile,et al.  Preliminary Design of Low-Thrust Multiple Gravity-Assist Trajectories , 2006 .