An improved error estimation method for pseudospectral trajectory optimization

Error estimation is a crucial step for mesh refinement in pseudospectral trajectory optimization. In the classical error estimation method, the estimated results are susceptible to the influence of interpolation methods, and the reference trajectory does not satisfy the requisite dynamic constraints. To address these issues, an improved method for error estimation is proposed. A simplified optimal control problem is constructed near the originally solved trajectory and then transformed into linear equations through pseudospectral discretization. Finally, a modified trajectory with a reduced dynamic constraint violation is generated and regarded as a reference for error estimation. Numerical simulations verify that the improved method can robustly generate a modified trajectory with smaller differential gaps in an acceptable computation time. The modified trajectory serves as a superior reference for error estimation, facilitating accelerated convergence in practical mesh refinement.