NEURAL NETWORK-BASED UNIVERSAL VARIABLE APPROXIMATION FOR LAMBERT’S PROBLEM

This study introduces a novel approach to solving Lambert’s problem by approximating the universal variable using a neural network. The primary contribution lies in leveraging neural networks to predict the universal variable based on the given geometry and time of flight. Once approximated, this universal variable is used to compute the initial and final velocities of the transfer trajectories. For cases requiring greater accuracy, the universal variable can be updated using Halley’s method, which efficiently updates the predicted universal variable with just 12 steps. Since the gravitational parameter of the central body can be normalized, the trained neural network model is applicable to any two-body system. This paper includes a brief overview of Lambert’s problem, a detailed analysis of model training and testing, and demonstrates the method’s efficiency through Porkchop plot validation and speed test.