Reentry trajectory planning method based on Gauss pseudospectral with characteristics of trend partition

A new Gauss pseudospectral method based on the characteristics of trend partition which transformed continuous optimal problem into parallel nonlinear programming problem was presented in this work solving the problem of reentry trajectory planning with strong state constraints. Tradition pseudospectral method was hard to get convergent non smooth optimal control solutions with state constraint. So sobolev space was introduced to prove the convergence and consistency of partition parallel spectral method. Extraction method of non-continuous feature trend was then developed to solve the problem that non-continuous optimal control solution is difficult to convergence in the case of state constraint. This new method iteratively set the variable partition through analysis of discrete point collocation derivative. Then different partition dynamic allocation point number was computed using the derivative tendency. High-precision polynomial approximation with different orders was used to ensure the acquisition of feasible solution considering the multi constraint conditions. The computational efficiency is effectively improved by off-line partition state confirming. The final application in reentry trajectory planning shows the effectiveness of the proposed approach when facing uncertain accidence and terminal restricts condition and indicate that this method can accommodate 20% pneumatic bias and ensure the terminal precision.