Abstract
The growing complexity of modern space missions calls for guidance and targeting methods that are both robust and computationally efficient. This paper introduces a sample-based nonlinear guidance approach that combines GPU-accelerated trajectory propagation with Multivariate Polynomial Regression (MPR) to construct local polynomial dynamical maps that can be inverted through nonlinear least-squares for closed-loop control. Large ensembles of initial conditions are propagated in parallel using CUDAjectory, producing dense datasets approximated by polynomial maps and inverted to compute impulsive corrections without relying on linearization or Gaussian assumptions. This framework separates the guidance logic from the underlying dynamics while retaining nonlinear sensitivities embedded in the data. The method formulates weighted polynomial regression with fit quality assessed through coefficients of determination, and performs map inversion via nonlinear least-squares optimization to ensure numerical stability. Validation across different scenarios shows that first-order maps recover State Transition Matrix (STM) behavior, while higher-order maps capture nonlinear effects. The developed general-purpose GPU-enabled guidance tool achieves more than two orders of magnitude speedup through parallelization without sacrificing accuracy. Applications to lunar-flyby targeting and Earth–Sun heteroclinic escape demonstrate scalability, precision, and robustness to uncertainties, with second-order maps without constant terms offering the best balance between accuracy and conditioning, and a dynamics-agnostic alternative to STM schemes for rapid targeting.
Paolo Lunghi
Associate Professor of Space Systems
Aiming for autonomous Guidance, Navigation, and Control for spacecraft.