analytical control laws for interplanetary solar sail trajectories with constraints
- Paper number
IAC-08.C1.5.4
- Author
Dr. Kenji Uchiyama, University of Strathclyde, United Kingdom
- Coauthor
Prof. Colin R. McInnes, University of Strathclyde, United Kingdom
- Year
2008
- Abstract
An indirect method is applied to derive an analytical control law for interplanetary trajectories using a solar sail whose thrust is subject to a constraint on its orientation with respect to the Sun. Trajectory optimization for solar sailing has been a focus of development activities as well as other forms of low-thrust propulsion. It is well known that the solar sail is superior to electric propulsion for long duration missions. However, the thrust magnitude generated by the solar sail has a boundary, due to range of sail steering angles and the fixed sail lightness number. If this constraint is not taken into account for analysis, this results in performance deterioration, i.e. it is not possible to realize a desired optimal orbit transfer. Almost all of optimal trajectories for such a constrained system have been derived by using mathematical programming. However, it is then difficult to update in real time an optimal trajectory subject to errors. In this study, an analytical control law is derived for the problem by using the barrier function method which is one of the penalty function method. The advantage of the method is to transform the optimal problem into an unconstrained optimal problem. We apply this method for the constrained system. A performance index which contains a logarithmic barrier function is defined to derive an analytical control law by solving a two-point boundary value problem. Lagrange multipliers used in the adjoint variables can be calculated by solving algebraic equations which are expressed by the boundary conditions. As a result, fast computation is possible even in the case with errors. Moreover, the steering angle and the thrust magnitude are controlled in its feasible region defined by the constraints. The proposed method is demonstrated for an Earth-Mars trajectory optimization problem and is compared with results of other optimal control methods.
- Abstract document
- Manuscript document
IAC-08.C1.5.4.pdf (🔒 authorized access only).
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