Optimization of Multiple Gravity Assist Trajectories with Deep Space Maneuver Using Evolutionary Algorithms

Abstract

Multiple gravity assist (MGA) trajectories represent a particular class of space trajectories in which a spacecraft makes use of gravity assist (GA) of one or more celestial bodies to alter its path or velocity vector, in order to reach high $\Delta V$ targets with low propellant consumption. The search for optimal transfer trajectories can be formulated as a global optimization problem. A simple MGA problem without any deep space maneuver (DSM) considers the departure epoch and the transfer times of the trajectories between two planets as the design variables for the objective function evaluation with constraint on minimum periapsis radius at each planet. The introduction of DSM in this problem during a trajectory leg makes the model more flexible, but also more complex. Apart from the design variables taken for MGA problem, the bounds on additional variables relating to spacecraft’s relative velocity at departure planet, the time instant at which each DSM takes place, the pericenter radius at each body and the turning angle of each hyperbola are considered for the objective function assessment. This paper evaluates some benchmark MGA mission problems with one DSM. The data of these problems are available under Global Trajectory Optimization Competition (GTOC) in European Space Agency (ESA) website. These problems are optimized using the evolutionary algorithms (EAs) like differential evolution (DE), genetic algorithm (GA), particle swarm optimization (PSO), and a comparison of the results are made.