Autonomous Trajectory Redirection on Non-Linear Multi-Body Manifolds: A Moore-Penrose Gravitational Resolvent Approach to Orbital Keyhole Avoidance
Abstract
Autonomous trajectory redirection and kinetic deflection of hazardous orbital bodies and near-Earth asteroids demands real-time terminal guidance capable of operating within non-linear, perturbed multi-body gravitational fields without high-latency ground loops. We formulate a geometric guidance framework embedding the relative phase space into a discrete symplectic transition manifold and computing the discrete Laplace-Beltrami Green's function via the Moore-Penrose pseudoinverse L†. Monotonic descent toward terminal capture without local saddle trapping is established via the discrete Maximum Principle, with continuous terminal proportional closing governed by a dimensionally homogeneous quadratic Lyapunov function. Validated against the April 13, 2029 Earth close encounter of (99942) Apophis under full J2 and lunar tidal perturbations, the guidance law navigates a continuous Pareto frontier from a fuel-optimal cruise (Δv = 28.4 m/s) to an emergency sprint mode (18.5 min closure). We further formulate the dual-use extension to extra-atmospheric orbital asset defense, demonstrating autonomous, trap-free Collision Avoidance Maneuvers (CAM) and Active Debris Removal (ADR) for space stations and orbital infrastructure in vacuum.
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BibTeX
@misc{pirolo2026autonomous,
title = {{Autonomous Trajectory Redirection on Non-Linear Multi-Body Manifolds: A Moore-Penrose Gravitational Resolvent Approach to Orbital Keyhole Avoidance}},
author = {Andres Pirolo},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23461118},
url = {https://zenodo.org/records/23461118},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Autonomous Trajectory Redirection on Non-Linear Multi-Body Manifolds: A Moore-Penrose Gravitational Resolvent Approach to Orbital Keyhole Avoidance
AU - Andres Pirolo
PY - 2026
DA - 2026/10/19
PB - Zenodo
DO - 10.5281/zenodo.23461118
UR - https://zenodo.org/records/23461118
AB - Autonomous trajectory redirection and kinetic deflection of hazardous orbital bodies and near-Earth asteroids demands real-time terminal guidance capable of operating within non-linear, perturbed multi-body gravitational fields without high-latency ground loops. We formulate a geometric guidance framework embedding the relative phase space into a discrete symplectic transition manifold and computing the discrete Laplace-Beltrami Green's function via the Moore-Penrose pseudoinverse L†. Monotonic descent toward terminal capture without local saddle trapping is established via the discrete Maximum Principle, with continuous terminal proportional closing governed by a dimensionally homogeneous quadratic Lyapunov function. Validated against the April 13, 2029 Earth close encounter of (99942) Apophis under full J2 and lunar tidal perturbations, the guidance law navigates a continuous Pareto frontier from a fuel-optimal cruise (Δv = 28.4 m/s) to an emergency sprint mode (18.5 min closure). We further formulate the dual-use extension to extra-atmospheric orbital asset defense, demonstrating autonomous, trap-free Collision Avoidance Maneuvers (CAM) and Active Debris Removal (ADR) for space stations and orbital infrastructure in vacuum.
ER -