Near-optimal guidance scheme for a Mars trajectory

Abstract

This paper deals with a near-optimal guidance scheme for a spacecraft flying from a low Earth orbit (LEO) to a low Mars orbit (LMO). The importance of guidance can be understood from the following consideration: a small error in the launch velocity at LEO can induce a very large position error on arrival at LMO due to error propagation associated with the large flight time and distance. Indeed, the uncertainties and errors in the thrust, system equations, and measurements constitute a special challenge to the designer of the guidance and control for a Mars mission. On account of the large changes in the gravitational field near a planet, the guidance design has three phases: near-Earth phase, interplanetary phase, and near-Mars phase. The focus of this paper is on guidance for the interplanetary phase. We assume that chemical engines are used and that the control is implemented by changing the magnitude and/or direction of the thrust via propellant consumption. A detector-predictor-corrector scheme is developed for guidance and control. The detector computes the spacecraft trajectory from the current measured state, estimating the trajectory error in the neighborhood of the low Mars orbit. The predictor is activated when the trajectory error exceeds a specified threshold. The task of the predictor is to generate a velocity correction, hence a thrust input, such that the target trajectory (the trajectory after the velocity correction) can rendezvous with the low Mars orbit. The corrector is a feedback control scheme to implement the control commands from the predictor. The key to the guidance design is the predictor. The maximum control margin concept is used in the predictor design to enhance the guidance robustness. Application of this concept means that the target trajectory for rendezvous with the low Mars orbit is to be achieved with minimum propellant consumption. The sequential gradient restoration algorithm (SGRA) is used in conjunction with system decomposition to achieve the real-time implementation of the guidance, and the target trajectory is computed via a two-step process, which includes target restoration followed by velocity restoration. The objective of the target restoration is to generate a trajectory leading from the current position to rendezvous with the low Mars orbit with the minimum velocity change w.r.t. the current velocity; the objective of the velocity restoration is to achieve the required velocity change via proper thrust input to the spacecraft. Considerable enhancement of SGRA for robustness, convergence, and speed can be achieved via this decomposition. Preliminary numerical results are encouraging. They show that the above detector-predictor-corrector scheme can achieve safely the rendezvous with the low Mars orbit, while containing the propellant consumption due to the errors and uncertainties in the thrust, system, and measurements.