A trajectory optimization method of hypersonic gliding vehicle based on differential flatness

A differential-flatness-based trajectory-optimization method was developed for hypersonic gliding vehicles to improve computational efficiency under multiple trajectory constraints. First, the lift force was decomposed using the bank angle, and the control variables were then reconstructed to achieve decoupling, and a flat-output parameterization of the dynamic model was established. Through this flatness-based mapping, which relates the states and control inputs to the flat outputs, the original problem was projected into the flat-output space, thereby reducing the dimensionality of the optimization variable space and yielding a constrained optimization problem wherein the differential constraints were implicitly satisfied. The flat outputs were then discretized using an improved piecewise Chebyshev pseudo-spectral method and interpolated using the Barycentric Lagrange interpolation algorithm, with good approximation properties. Analytical gradients were derived for two representative objective functions to enhance convergence and solution efficiency. The resulting nonlinear programming problem was solved using the open-source solver Interior Point Optimizer (IPOPT). Finally, two sets of numerical experiments were conducted, and their results were compared with those obtained using the conventional method. The numerical results confirmed the feasibility, convergence, and computational efficiency of the proposed method and verified that the flatness-based parameterization considerably improves solution efficiency and dynamic consistency while preserving trajectory accuracy.