Spacecraft Trajectory Optimization Based on Discrete Sets of Pseudoimpulses

Abstract

A brief review of new methods for continuous-thrust trajectory optimization is presented. The methods use discretization of the spacecraft trajectory on segments and sets of pseudoimpulses for each segment. Boundary conditions are presented as a linear matrix equation. A matrix inequality on the sum of the characteristic velocities for the pseudoimpulses is used to transform the problem into a large-scale linear programming form. Present-day linear programming methods use 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. The methods provide flexible opportunities for the trajectory computation in complex missions with various requirements and constraints. A systematic mathematical representation of these problems is considered. A summary of examples for orbit transfer, rendezvous, and moon ascent trajectories is presented. Application examples of lunar landing trajectories are examined. The examples represent a set of optimal unconstrained trajectories for different thrust-to-weight ratios and trajectories with safety descent profile, thrust level, and attitude constraints.