Julio Sanchez's B-spline method speeds interplanetary trajectory design

In a new paper on arXiv (2607.23790), Julio C. Sanchez from an unspecified institution introduces a rapid preliminary design method for low-thrust interplanetary rendezvous trajectories. The technique uses clamped B-splines to parameterize heliocentric cylindrical coordinates, exploiting the differential flatness of low-thrust cylindrical dynamics. This allows the control acceleration to be derived algebraically from the shaped trajectory and its derivatives, eliminating the need for numerical propagation of equations of motion. The endpoint position and velocity constraints are satisfied analytically, reducing the fixed-time, minimum-delta-v problem to a finite-dimensional nonlinear program in the free interior B-spline control points. Numerical quadrature is used only for objective function evaluation, drastically cutting computational cost.

The method was validated on four transfer scenarios: Earth to Mars, Mercury, near-Earth asteroid 1989 ML, and comet Tempel 1. Across fine-grid campaigns, the B-spline configurations consistently reduced the mean, median, and minimum accumulated velocity increment compared to the high-order hodographic shaping benchmark. A ten control-point quintic B-spline emerged as the optimal trade-off between solution quality and computational efficiency. Higher-dimensional parameterizations proved useful for refining specific transfers. The paper spans 38 pages with 18 figures and 4 tables, demonstrating significant promise for quick, fuel-efficient mission planning.