Adjoint estimation method for low-thrust multirevolution trajectory optimization

The homotopic approach solves the fuel-optimal problem of low-thrust trajectory by starting from the related and easier energy-optimal problem. However, suitable initial guesses of the adjoint variables should be provided to initialize the solving process of the homotopic method. This paper presents an adjoint estimation method, which would provide the approximate initial guesses for the optimization of low-thrust multirevolution trajectories. Originally, the initial adjoint variables are estimated by solving the optimal control problem of a simplified timeindependent dynamical model. The simplified time-independent dynamical model is then linearized around the nominal trajectory, through neglecting the thrust magnitude constraint and the transfer time constraint. Based on the initial adjoint variables analytically obtained, an algorithm is proposed to solve the fuel-optimal control problem of the original model. The effectiveness and efficiency of the proposed method are validated through a numerical simulation of the rendezvous mission from the Earth to the asteroid Dionysus.