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

摘要

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