Review of spacecraft trajectory optimization methods using discrete sets of pseudoimpulses

A review of new methods for continuous thrust spacecraft trajectory optimization is presented. The methods are based on a trajectory discretization by small segments and on a near-uniform discrete approximation of thrust directions by a set of pseudoimpulses with an inequality constraint for each segment. The optimization problem is to minimize the total characteristic velocity. The optimal impulse in each segment can be presented by the sum of non-zero pseudoimpulses with a constraint on the total characteristic velocities of the pseudoimpulses. The terminal conditions are presented as a linear matrix equation. A matrix inequality on the sums of the pseudoimpulses is used to transform the problem into a large-scale linear programming form. The continuous burns include a number of adjacent segments and a post-processing of the linear programming solutions is needed to form a sequence of the burns. An optimal number of the burns is automatically determined. The methods provide flexible opportunities for the trajectory computation in complex missions with various requirements and constraints. Summary of application examples of trajectory optimization for different spacecraft types is presented. Advantages of the methods are discussed.