Robust Perturbed Multiple-Revolution Lambert Algorithm Based on Adaptive Homotopy

This study addresses the multirevolution perturbed Lambert problem, which is a nonlinear two-point boundary value problem with significant applications in spacecraft trajectory design. A robust perturbed multiple-revolution Lambert algorithm based on adaptive homotopy is proposed to overcome the limitations of traditional methods in handling long-duration transfers with complex perturbations. First, an adaptive step-size control homotopic iteration algorithm with dynamic parameter adjustment is developed to mitigate the initial-value sensitivity inherent in Newton’s iteration, and to enhance the computational efficiency and convergence range. Second, a Gaussian process-based nonlinear fitting approach is built, which can provide more accurate initial guesses than traditional Kepler solutions. The algorithm is validated through comparison with traditional methods such as the terminal position homotopy and acceleration homotopy. Numerical results with large-scale Monte Carlo tests involving 10,000 random cases show that the algorithm has superior performance in various perturbed Lambert scenarios, and that remarkable improvements in computational speed and convergence reliability are obtained.