Continuous Thrust Orbit Transfer Optimization Using Large-Scale Linear Programming

Abstract

A new technique is developed to optimize continuous medium- and low-thrust orbit transfers. This approach combines large-scale linear programming algorithms with discretization of the trajectory dynamics on segments and a set of pseudoimpulses or control for each segment. The set is a discrete approximation with a small mesh width for a space of possible thrust directions. Boundary conditions are presented as a linear matrix equation. A matrix inequality on the sum of characteristic velocities for the pseudoimpulses is used to transform the problem into a linear programming form. The number of decision variables is on the order of tens of thousands. In modern linear programming methods there are interior-point algorithms to solve such problems. In the general case, the continuous burns include a number of adjacent segments and a postprocessing of the linear programming solutions is needed to form a sequence of the burns. An optimal number of the burns is automatically determined in the postprocessing. A maintenance of a 24-hour elliptical orbit, long-term transfer from a geo-transfer to geostationary orbit, and a one-revolution, medium-thrust transfer between two elliptical noncoplanar orbits are considered as application examples. In the last two examples an iterative solution method was used. The presented method can be used effectively for trajectory optimization in a wide range of space missions.