Optimization of Low-Thrust Many-Revolution Transfers and Lyapunov-Based Guidance

Paper number

IAC-08.C1.2.8

Author

Dr. Yang Gao, Academy of Opto-Electronics, Chinese Academy of Sciences, China

Coauthor

Mr. Xinfeng Li, Academy of Opto-Electronics, Chinese Academy of Sciences, China

Year

2008

Abstract

Compared to vehicles propelled by conventional chemical propulsion, spacecraft propelled by low-thrust solar electric propulsion can deliver more payload fraction. However, low-thrust propulsion usually results in long-duration transfers with hundreds or even thousands of revolutions. Due to this characteristic, optimization of low-thrust transfer trajectories has been considered a difficult optimal control problem. Furthermore, shadowing and perturbation effects might be taken into consideration if the spacecraft transfers through relatively low-altitude orbits, which makes the problem much harder to solve. Likewise, the volume of works on low-thrust guidance design is also somewhat limited. 

   Based on the orbital averaging method, a direct approach is developed to optimize low-thrust many-revolution transfers and a Lyapunov-based guidance with time-varying gains is proposed. Within each transfer revolution, a parameterized control law, called COV-based control derived from variation of calculus approach, is formulated in terms of a set of nonsingular equinoctial elements. A periapsis- and apoapsis-centered burn-coast structure is employed in order to efficiently solve fuel-saving orbital transfers. The parameters governing the COV-based control law and the burn-coast structure within each revolution are interpolated through a finite number of discrete nodes along the time axis. The optimal transfer problem is then converted to the parameter optimization problem that is solved by nonlinear programming, and multiple shooting is used to improve convergence robustness further. 

   Subsequently, a mapping between the COV- and Lyapunov-based control laws is revealed, based on which the optimality condition of Lyapunov control and a well-defined explanation for gain selection are obtained. Furthermore, the time-varying Lyapunov gains can be solved using trajectory optimization results. However, we found that the propoesed mapping may not guarantee that all gains are positive such that the Lyapunov-based guidance may not be strictly stable during the transfer. However, the Lyapunov-based guidance that is not strictly stable may still successfully guide a spacecraft with feedback mechanism. In addition, certain negative Lyapunov gains can be changed to appropriate positive values by trial-and-errors to warrant stability and achieve satisfactory performance. 

   Numerical examples of Earth-orbit transfers with thrust-to-weight ratios on the order of 10-5~10-4 are presented. Zonal harmonic perturbations and Earth shadowing are included. The feedback mechanism of the Lyapunov-based guidance is investigated. 

Abstract document

IAC-08.C1.2.8.pdf

Manuscript document

IAC-08.C1.2.8.pdf (🔒 authorized access only).

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