Abstract: For the lunar surface trajectory design problem of hoppers, the fuel optimal trajectory for the whole hop process based on convex optimization was presented. Different from the typical method that the trajectory was designed separately firstly and then connected to a whole trajectory, it was assumed that the vertical ascent and descent time was fixed, then the constraints of the whole trajectory were divided into phases so that the constraints at each phase were convex according to practical engineering requirements. And the golden section method was used to search for the fixed ascent and descent time. The original fuel optimization problem was transformed into a second-order cone problem (SOCP) and the fuel optimal trajectory was obtained by solving this problem. In this way, an optimal solution was found for the whole trajectory design instead of a connected piecewise optimal one given by the classical method. As is shown in simulation results, when the piecewise constraints are satisfied, the fuel consumption of the piecewise convex optimization which adopts different vertical ascent and descent speed constraints is 25.7207kg and 25.3903kg respectively. On the other hand, the fuel consumption of the whole convex optimization method is only 24.9682kg, which is better than that of the piecewise convex optimization solution.

Key words: hop, trajectory design, convex optimization, second-order cone problem, fuel optimal