The fuel-optimal control problem of soft landing becomes a significant challenge due to the highly irregular gravitational field of an asteroid. An indirect method is used to deal with this fuel-optimal control problem. The difficult bang-bang control problem caused by the indirect method is solved through an improved fast homotopic approach. To validate the advanced homotopic method, the landing site is selected in a region where the gravitational field is especially irregular. The results show that this method is effective for the fuel-optimal control problem in an irregular gravitational field. Moreover, the trajectory designed with the fuel-optimal control is taken as a nominal descent trajectory for a sliding mode control. Monte Carlo simulations show that the desired soft landing can be achieved by tracking the fuel-optimal trajectory.
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Yang et al. (2015) studied this question.
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