Core Concepts
This research paper introduces a novel method for certifying the robustness of Guidance & Control Networks (G&CNETs) by propagating uncertainty on an event manifold using Differential Algebra, addressing the limitations of traditional Monte Carlo simulations.
Stats
The target body for the interplanetary transfer is in a circular orbit of radius R with an angular velocity Ω = √(𝜇/R^3).
The interplanetary transfer spacecraft has a constant acceleration of magnitude Γ = 0.1 mm/s^2.
The radius of the sphere of influence for the target planet in the interplanetary transfer problem is R_SOI = 924,000 km.
The asteroid landing problem uses a rotating frame R with an angular velocity ω.
The drone racing problem uses two coordinate frames: an inertial world frame W and a body frame B attached to the drone.
The drone model has 16 states and 4 control inputs, with each control input u_i restricted within u_i ∈ [0, 1].
The G&CNETs for each problem have two hidden layers with 32 neurons each.
The interplanetary transfer and asteroid landing G&CNETs were trained on 400,000 and 300,000 optimal trajectories, respectively, generated using the Backward Generation of Optimal Examples (BGOE) technique.
The drone racing G&CNET was trained on 10,000 optimal trajectories solved individually using a direct method.
The polynomial expansions achieved 8th-order accuracy for the interplanetary transfer and asteroid landing problems and 7th-order accuracy for the drone racing problem.
The Monte Carlo analysis for the asteroid landing problem used 10,000 random perturbations per state.
The initial state uncertainty in spacecraft mass for the asteroid landing requirement is ±5%, uniformly distributed in m_0 ∈ [0.95m_0, 1.05m_0] ≈ [335, 370] kg.
Quotes
"Simply evaluating the neural network over countless Monte Carlo simulations is not only time-consuming, it also does not provide a rigorous answer to the question: 'Will my G&CNET behave as intended when presented with a state it has never seen before?'"
"Unless we revert back to a Monte Carlo-based approach, we cannot verify such a requirement by expanding the neural flow because the time at which the spacecraft will cross this boundary (defined as 1 km in altitude above the asteroid surface) is not known in advance and it is not an equilibrium point."
"This work is driven by the recognition that there is a need to increase confidence in neural network certification for future missions."