Rapid Optimization of Multiburn Rocket Trajectories Revisited

Abstract

This paper revisits the challenging problem of optimal rocket powered trajectory consisting of many burn and coast arcs in space. The problem is formulated as a series of N pairs of coast and finite-time burn arcs. The numerical solution to this problem is obtained by an analytical multiple shooting method. A major focus of this work is the treatment of constraints on the durations of the burn and coast arcs. These constraints arise from the requirements of non-negativeness of the flight time in each arc, upper bounds on burn times, and equality constraints on the sums of burns times across adjacent burn arcs. These constraints are treated as interior-point constraints on time. Unlike in previous work, analyses are conducted on the associated necessary conditions to determine applicable conditions without introducing additional unknowns or complexity. As a result, our algorithm has the notable ability to allow any number of arcs and conveniently handle the case when some of the durations of the arcs reduce to zero. Thus even without the knowledge of optimal number of arcs a priori in a problem, by starting with sufficiently large N ,o ur algorithm can converge to the optimal solution with correct number of arcs by nulling the unnecessary arcs. Numerical demonstrations in orbital transfer and ascent guidance are provided.