arXiv subjects

Madhusudan Vijayakumar

Publications and source records attributed to Madhusudan Vijayakumar.

3 recordsLinked to original sources

arXiv2024

Sub-Optimal Fast Fourier Series Approximation for Initial Trajectory Design

The Finite Fourier Series (FFS) Shape-Based (SB) trajectory approximation method has been used to rapidly generate initial trajectories that satisfy the dynamics, trajectory boundary conditions, and limitation on maximum thrust acceleration. The FFS SB approach solves a nonlinear programming problem (NLP) in searching for feasible trajectories. This paper extends the development of the FFS SB approach to generate sub optimal solutions. Specifically, the objective function of the NLP problem is modified to include also a measure for the time of flight. Numerical results presented in this paper show several solutions that differ from those of the original FFS SB ones. The sub-optimal trajectories generated using a time of flight minimization are shown to be physically feasible trajectories and potential candidates for direct solvers.

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arXiv2024

Low Thrust Trajectory Design Using A Semi-Analytic Approach

Space missions that use low-thrust propulsion technology are becoming increasingly popular since they utilize propellant more efficiently and thus reduce mission costs. However, optimizing continuous-thrust trajectories is complex, time-consuming, and extremely sensitive to initial guesses. Hence, generating approximate trajectories that can be used as reliable initial guesses in trajectory generators is essential. This paper presents a semi-analytic approach for designing planar and three-dimensional trajectories using Hills equations. The spacecraft is assumed to be acted upon by a constant thrust acceleration magnitude. The proposed equations are employed in a Nonlinear Programming Problem (NLP) solver to obtain the thrust directions. Their applicability is tested for various design scenarios like orbit raising, orbit insertion, and rendezvous. The trajectory solutions are then validated as initial guesses in high-fidelity optimal control tools. The usefulness of this method lies in the preliminary stages of low-thrust mission design, where speed and reliability are key.

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arXiv2024

Design of Initial Guess Low Thrust Trajectories Using Clohessy-Wiltshire Equations

The commercial interest in producing low-cost space missions by exploiting the superior propellant management of low-thrust propulsion technology has become increasingly popular. Typical to such missions is the design of transfer trajectories between desired targets. This is a complex and computationally expensive process. Additionally, the optimal solvers used to generate these trajectories are extremely sensitive to initial guesses. One way to overcome this challenge is to use a reasonably approximate trajectory as an initial guess on optimal solvers. This paper presents a flexible approach to generating very low thrust trajectories. The initial guess is obtained from a flexible semi-analytic approach that can provide both planar and three-dimensional initial guess trajectories for various design scenarios like orbit raising, orbit insertion, phasing, and rendezvous. NASA's Evolutionary Mission Trajectory Generator (EMTG) and General Mission Analysis Tool (GMAT) are used as optimal solvers in this analysis. Numerical case studies are presented in this paper.

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