A Conceptual Framework for AI-Driven Autonomous Navigation and Debris Avoidance in Interplanetary Space Missions: Integrating CR3BP Dynamics, Stochastic Modeling, Bayesian Inference, and Physics-Informed Neural Networks

This conceptual paper presents a framework for interplanetary spacecraft navigation and debris avoidance, integrating Circular Restricted Three-Body Problem (CR3BP) dynamics with invariant manifolds, stochastic differential equations (SDEs) for perturbation modeling, global sensitivity analysis through Sobol indices, and Hamiltonian-preserving physics-informed neural networks (H-PINNs) with Proximal Policy Optimization (PPO) augmented by entropy regularization and recurrent neural networks (RNN/LSTM) for delayed Markov Decision Processes (MDPs) and interpretable decision-making. It includes Unscented Kalman Filters (UKF) with algorithmic details and Mars-specific applications, Approximate Bayesian Computation (ABC), multi-agent collision avoidance using B-plane parameters with collision probability gradients and game-theoretic coordination, solar radiation pressure modeling, structural uncertainty quantification distinguishing aleatoric and epistemic types using Gaussian Processes (GP) for discrepancy, and Fokker-Planck equations for probability evolution. Applications are tailored to Mars missions, including entry navigation with stochastic atmospheric density modeling, rover autonomy, and sample return; lunar missions with PINNs for trajectory prediction, thermal management with radiative heat transfer constraints, and low-thrust propulsion in CR3BP; asteroid missions for exploration and mining; and deep space missions such as asteroid exploration and outer planet probes. Validation uses NASA SPICE kernels integrated with CR3BP coordinate transformations, 10,000-run Monte Carlo simulations, Pareto optimality for trade-offs in Delta-v, arrival time, and collision risks, ensuring compliance with COSPAR planetary protection guidelines for Mars special regions. The framework is supported by mathematical derivations, including PINN loss functions for CR3BP with symplectic integration, non-spherical harmonics (J2/J3), Poincaré maps for stability, convergence proofs for PINNs under SDE noise, reproducible Python simulations, quantitative statistics, Popperian falsifiability criteria, computational complexity analysis for onboard RAD750 processors, Lyapunov stability for neural controllers, quantization error analysis in fixed-point arithmetic, Fisher information matrix for sensor sensitivity, stress testing for sensor failures, Yarkovsky effect on debris, and debris modeling as stochastic fluid.