Optimal Multi-Gravity-Assist Trajectories Design with Likelihood Analysis

Abstract

A likelihood assisted optimization strategy for the complex mixed-integer nonlinear programming problem, Multiple Gravity Assist (MGA) trajectory design is proposed. In MGA design, both the total velocity ΔV and MGA sequence are considered, and possible transfers are incrementally built and explored at each planetary encounter. Dimension of searching subspace increases exponentially with the number of MGA. Traditional MGA design uses heuristic based branching and pruning techniques to reduce the computational cost due to the exponentially increased searching spaces. In this work, a new stochastic based searching strategy without branching-pruning operations is proposed instead. A stochastic type metric is introduced and used to measure similarity level of the spacecraft trajectory to the expected transfer orbit. Swing-by planets are sampled and new transfer arcs are generated with respect to the metric values. Log-likelihood of the orbital transfers is constructed, and put into the optimization as the constraint to be maximized. Based on the strategy, the MGA design problem is translated into a continuous non-linear optimization problem, and two algorithms for the MGA trajectory design are proposed. In the first algorithm, tuning parameters of the similarity function are put into the design space as extended parameters, while in the second algorithm, an adaptive update mechanism for the tuning parameters is designed. Tuning parameters are updated with population of the objective function values and prior data set of tuning parameters. Effectiveness of the algorithms are demonstrated through design optimization of MarcoPolo mission. Simulation results show that significant efficiency improvement of the searching process can be obtained.