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Certifying Guidance & Control Networks: Uncertainty Propagation to an Event Manifold

Sebastien Origer, Dario Izzo, Giacomo Acciarini, Francesco Biscani, Rita Mastroianni, Max Bannach, Harry Holt

TL;DR

This work utilizes three previously solved optimal control problems with varying levels of dynamics nonlinearity and event manifold complexity to perform uncertainty propagation on an event manifold for Guidance&Control Networks (G&CNETs), aiming to enhance the certification tools for neural networks in this field.

Abstract

We perform uncertainty propagation on an event manifold for Guidance & Control Networks (G&CNETs), aiming to enhance the certification tools for neural networks in this field. This work utilizes three previously solved optimal control problems with varying levels of dynamics nonlinearity and event manifold complexity. The G&CNETs are trained to represent the optimal control policies of a time-optimal interplanetary transfer, a mass-optimal landing on an asteroid and energy-optimal drone racing, respectively. For each of these problems, we describe analytically the terminal conditions on an event manifold with respect to initial state uncertainties. Crucially, this expansion does not depend on time but solely on the initial conditions of the system, thereby making it possible to study the robustness of the G&CNET at any specific stage of a mission defined by the event manifold. Once this analytical expression is found, we provide confidence bounds by applying the Cauchy-Hadamard theorem and perform uncertainty propagation using moment generating functions. While Monte Carlo-based (MC) methods can yield the results we present, this work is driven by the recognition that MC simulations alone may be insufficient for future certification of neural networks in guidance and control applications.

Certifying Guidance & Control Networks: Uncertainty Propagation to an Event Manifold

TL;DR

This work utilizes three previously solved optimal control problems with varying levels of dynamics nonlinearity and event manifold complexity to perform uncertainty propagation on an event manifold for Guidance&Control Networks (G&CNETs), aiming to enhance the certification tools for neural networks in this field.

Abstract

We perform uncertainty propagation on an event manifold for Guidance & Control Networks (G&CNETs), aiming to enhance the certification tools for neural networks in this field. This work utilizes three previously solved optimal control problems with varying levels of dynamics nonlinearity and event manifold complexity. The G&CNETs are trained to represent the optimal control policies of a time-optimal interplanetary transfer, a mass-optimal landing on an asteroid and energy-optimal drone racing, respectively. For each of these problems, we describe analytically the terminal conditions on an event manifold with respect to initial state uncertainties. Crucially, this expansion does not depend on time but solely on the initial conditions of the system, thereby making it possible to study the robustness of the G&CNET at any specific stage of a mission defined by the event manifold. Once this analytical expression is found, we provide confidence bounds by applying the Cauchy-Hadamard theorem and perform uncertainty propagation using moment generating functions. While Monte Carlo-based (MC) methods can yield the results we present, this work is driven by the recognition that MC simulations alone may be insufficient for future certification of neural networks in guidance and control applications.
Paper Structure (4 sections, 5 equations, 5 figures, 1 table)

This paper contains 4 sections, 5 equations, 5 figures, 1 table.

Table of Contents

  1. Results & Discussion
  2. Conclusion
  3. Drone racing model
  4. Optimal control problems values

Figures (5)

  • Figure A5: Training and validation loss of G&CNETs.
  • Figure A6: Relative error (Frobenius norm) between Monte Carlo- and Moment-Generating-Function -based covariance matrices versus polynomial order.
  • Figure A7: Proxy for convergence radius of each individual state as a function of polynomial order and Monte Carlo analysis.
  • Figure A8: Coordinate frames (Body x-axis points to the front of the drone) origer2023guidance.
  • Figure A4: From left to right: full G&CNET architectures for interplanetary transfer, asteroid landing and drone racing.