Indirect optimization based on calculus of variations is used to develop an autonomous guidance scheme for low-thrust trajectories. This method is applied to a fixed-time Earth-Mars minimum-fuel orbit transfer. First, the nominal optimal control problem (OCP) is solved using indirect optimization, leading to a two-point boundary value problem (TPBVP) which is then solved using a single shooting method and extended logarithmic smoothing to obtain the optimal trajectory and open-loop control law. Then, an algorithm for determining updates to the nominal control in response to deviations from the nominal trajectory is presented. This method of obtaining the guidance control does not require approximating or linearizing the dynamics of the nominal OCP. Instead, the nominal solution and measurements of the current state are used to rapidly determine control updates by means of an algorithm which circumvents the need to guess costates or solve a new TPBVP.
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