Abstract
The time-optimal control problem of a spacecraft equipped with reaction wheels has been studied, in which the spacecraft is constrained to sequentially assume a set of attitudes, whose order is not specified. This attitude scheduling problem has been solved as a multiphase mixed-integer optimal control problem in which binary functions have been introduced to model the choice of the optimal sequence of target attitudes and to enforce the constraint of adopting once and only once each attitude. Given the dynamic model of the spacecraft, the initial and final attitudes, and a set of target attitudes, solving this problem consists in finding the control inputs, the sequence of attitudes with the corresponding passage times, and the resulting trajectory of the spacecraft that minimize the time of the maneuver. The multiphase mixed-integer optimal control problem has been converted into a mixed-integer nonlinear programming problem first making the unknown passage times through the target attitudes part of the state, then introducing binary variables to discretize the binary functions, and finally applying a fifth-degree Gauss-Lobatto direct collocation method to tackle the dynamic constraints. The resulting problem has been solved using a nonlinear programming-based branch-and-bound algorithm.
Highlights
This paper focuses on time-optimal attitude scheduling of spacecraft
The time-optimal attitude scheduling of a spacecraft is formulated as a multiphase mixed-integer optimal control problem (MIOCP) which can be stated as follows: given the dynamic model of a rigid spacecraft and a set of target attitudes, find the control inputs that steer in minimum time the spacecraft from an initial attitude to a final one adopting all the target attitudes of the set and satisfying some constraints on the angular velocity of the spacecraft at the target attitudes
The multiphase MIOCP has been converted into a mixed-integer nonlinear programming (MINLP) problem first making the unknown passage times through the target attitudes part of the state, introducing binary variables to discretize the binary functions, and applying a fifth-degree Gauss-Lobatto direct collocation method [8] to tackle the dynamic constraints
Summary
This paper focuses on time-optimal attitude scheduling of spacecraft. This problem entails planning a sequence of slew maneuvers that join a set of attitudes of the spacecraft. The time-optimal attitude scheduling of a spacecraft is formulated as a multiphase mixed-integer optimal control problem (MIOCP) which can be stated as follows: given the dynamic model of a rigid spacecraft and a set of target attitudes, find the control inputs that steer in minimum time the spacecraft from an initial attitude to a final one adopting all the target attitudes of the set and satisfying some constraints on the angular velocity of the spacecraft at the target attitudes. To the best knowledge of the authors, the present paper is the first to employ and test this technique on this problem In this approach, the multiphase MIOCP has been converted into a mixed-integer nonlinear programming (MINLP) problem first making the unknown passage times through the target attitudes part of the state, introducing binary variables to discretize the binary functions, and applying a fifth-degree Gauss-Lobatto direct collocation method [8] to tackle the dynamic constraints.
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