Reentry trajectory optimization for hypersonic vehicle based on improved Gauss pseudospectral method

Over the past decade, Gauss pseudospectral method (GPM) has been widely used to deal with the reentry trajectory optimization problems for hypersonic vehicle. However, for the trajectory generated by GPM, all constraints can only be satisfied at each Gauss point. To overcome this problem, in this paper, an improved GPM is proposed. Two kinds of newly defined breaks are applied to divide the trajectory into multiple segments, based on the distribution character of the Gauss points; the waypoints are transformed into Gauss points and dense Gauss points can locate near the appointed areas such as the no-fly zones; in this way, all the positions can meet the requirements of all the complex constraints. Furthermore, because the function of the breaks is to alter the distribution of the whole Gauss points and the number of them does not increase, the convergence speed advantage of GPM is not changed. Simulation results demonstrate that the proposed method can rapidly generate a trajectory with high precision.

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