Minimum-fuel powered descent guidance for soft landing on irregular-shaped asteroids

This work is concerned with the minimum-fuel power descent to a prescribed landing site on a irregular-shaped asteroid. With the small and complicated gravitational field taken into account, we present the equations of spacecraft motion in the asteroid-fixed Cartesian coordinate frame. To solve the minimum-fuel problem, we construct a performance index which links the minimum-fuel problem with the minimum-energy problem by a homotopy parameter. Based on the Pontryagin´s maximum principle and the numerical continuation method, we transform the optimal control problem into a series of two-point boundary-value problems. we solve the optimal problems by starting from a solution of the energy-optimal problem, which is obtained by the using of the pseudo-spectral method. We reduce the homotopy parameter by following a certain series and take the solution obtained in the current iteration as an initial guess for that in the next one. Finally, we obtain a minimum-fuel power descent trajectory for soft landing on a irregular-shaped asteroid with easy convergence and high precision.