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Neural-Rendezvous: Provably Robust Guidance and Control to Encounter Interstellar Objects

Hiroyasu Tsukamoto, Soon-Jo Chung, Yashwanth Kumar Nakka, Benjamin Donitz, Declan Mages, Michel Ingham

TL;DR

This paper tackles the challenge of autonomously guiding and controlling a spacecraft to encounter fast-moving interstellar objects (ISOs) under large state uncertainty and limited onboard computation. It introduces Neural-Rendezvous, a framework that learns a near-MPC terminal guidance policy via a spectrally-normalized DNN (SN-DNN) and augments it with a pointwise min-norm tracking controller to obtain provable robustness. Theoretical results establish an exponential bound on the expected delivery error with finite probability by constructing a non-negative supermartingale, while practical validation shows delivery errors below 0.2 km for most ISO candidates and real-time computation compatible with onboard constraints. Extensions cover stochastic MPC, multi-agent setups, and online learning, and empirical tests on spacecraft simulators and UAV swarms demonstrate the approach’s broad applicability and safety-relevant guarantees for autonomous G&C in challenging nonlinear environments.

Abstract

Interstellar objects (ISOs) are likely representatives of primitive materials invaluable in understanding exoplanetary star systems. Due to their poorly constrained orbits with generally high inclinations and relative velocities, however, exploring ISOs with conventional human-in-the-loop approaches is significantly challenging. This paper presents Neural-Rendezvous -- a deep learning-based guidance and control framework for encountering fast-moving objects, including ISOs, robustly, accurately, and autonomously in real time. It uses pointwise minimum norm tracking control on top of a guidance policy modeled by a spectrally-normalized deep neural network, where its hyperparameters are tuned with a loss function directly penalizing the MPC state trajectory tracking error. We show that Neural-Rendezvous provides a high probability exponential bound on the expected spacecraft delivery error, the proof of which leverages stochastic incremental stability analysis. In particular, it is used to construct a non-negative function with a supermartingale property, explicitly accounting for the ISO state uncertainty and the local nature of nonlinear state estimation guarantees. In numerical simulations, Neural-Rendezvous is demonstrated to satisfy the expected error bound for 100 ISO candidates. This performance is also empirically validated using our spacecraft simulator and in high-conflict and distributed UAV swarm reconfiguration with up to 20 UAVs.

Neural-Rendezvous: Provably Robust Guidance and Control to Encounter Interstellar Objects

TL;DR

This paper tackles the challenge of autonomously guiding and controlling a spacecraft to encounter fast-moving interstellar objects (ISOs) under large state uncertainty and limited onboard computation. It introduces Neural-Rendezvous, a framework that learns a near-MPC terminal guidance policy via a spectrally-normalized DNN (SN-DNN) and augments it with a pointwise min-norm tracking controller to obtain provable robustness. Theoretical results establish an exponential bound on the expected delivery error with finite probability by constructing a non-negative supermartingale, while practical validation shows delivery errors below 0.2 km for most ISO candidates and real-time computation compatible with onboard constraints. Extensions cover stochastic MPC, multi-agent setups, and online learning, and empirical tests on spacecraft simulators and UAV swarms demonstrate the approach’s broad applicability and safety-relevant guarantees for autonomous G&C in challenging nonlinear environments.

Abstract

Interstellar objects (ISOs) are likely representatives of primitive materials invaluable in understanding exoplanetary star systems. Due to their poorly constrained orbits with generally high inclinations and relative velocities, however, exploring ISOs with conventional human-in-the-loop approaches is significantly challenging. This paper presents Neural-Rendezvous -- a deep learning-based guidance and control framework for encountering fast-moving objects, including ISOs, robustly, accurately, and autonomously in real time. It uses pointwise minimum norm tracking control on top of a guidance policy modeled by a spectrally-normalized deep neural network, where its hyperparameters are tuned with a loss function directly penalizing the MPC state trajectory tracking error. We show that Neural-Rendezvous provides a high probability exponential bound on the expected spacecraft delivery error, the proof of which leverages stochastic incremental stability analysis. In particular, it is used to construct a non-negative function with a supermartingale property, explicitly accounting for the ISO state uncertainty and the local nature of nonlinear state estimation guarantees. In numerical simulations, Neural-Rendezvous is demonstrated to satisfy the expected error bound for 100 ISO candidates. This performance is also empirically validated using our spacecraft simulator and in high-conflict and distributed UAV swarm reconfiguration with up to 20 UAVs.
Paper Structure (36 sections, 4 theorems, 53 equations, 20 figures, 6 tables, 1 algorithm)

This paper contains 36 sections, 4 theorems, 53 equations, 20 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Technical Challenges in ISO Exploration
  3. Autonomous terminal G&C for ISO encounter with formal guarantees
  4. Autonomous Guidance via Dynamical System-Based Deep Learning
  5. Model Predictive Control Problem
  6. Imitation Learning of MPC State and Control Trajectories
  7. Optimality Gap of Deep Learning-Based Guidance
  8. Deep learning-Based Optimal Tracking Control
  9. Desired State Trajectory with Zero Delivery Error
  10. Deep Learning-Based Pointwise Min-Norm Control
  11. Assumptions for Robustness and Stability
  12. Neural-Rendezvous: Learning-based Robust Guidance and Control to Encounter ISOs
  13. Robustness and Stability Guarantee
  14. Neural-Rendezvous
  15. Extensions
  16. ...and 21 more sections

Key Result

Lemma 1

Suppose that $u_{\mathrm{mpc}}$ is Lipschitz with its $2$-norm Lipschitz constant $L_{\mathrm{mpc}}\in\mathbb{R}_{> 0}$. If $u_{\ell}$ is trained using the empirical loss function node_empirical_loss of Remark remark_empirical_loss to have $\exists\epsilon_{\mathrm{train}}\in\mathbb{R}_{\geq 0}$ s.t then we have the following bound: where $r(x,\textit{\oe},t,\rho)$ is given by

Figures (20)

  • Figure 1: Above: Artist's illustration 1I/'Oumuamua (https://photojournal.jpl.nasa.gov/catalog/PIA22357). Below: 2I/Borisov near and at perihelion (https://apod.nasa.gov/apod/ap220305.html).
  • Figure 2: Illustration of cruise and terminal GNC. Neural-Rendezvous provides a verifiable delivery error bound under the large ISO state uncertainty and high-velocity challenges.
  • Figure 3: Numerical and experimental validation of Neural-Rendezvous to be discussed in Sec. \ref{['sec_simulation']} and Sec. \ref{['sec_experiment']}.
  • Figure 4: Left: SN-DNN imitating a desired control input (first term of (\ref{['node_loss']})). Right: SN-DNN imitating a desired state trajectory (second term of (\ref{['node_loss']})).
  • Figure 5: Illustration of the optimality gap (\ref{['sn_learning_error']}), where $\bm{\mathcal{S}_{\mathrm{train}}}$ denotes the training set in which training data $\bm{(\bar{x}_i,\bar{\textit{\ae}}_i,\bar{t}_i,\bar{\rho}_i) \in \Pi_{\mathrm{train}}}$ is sampled.
  • ...and 15 more figures

Theorems & Definitions (29)

  • Remark 1
  • Definition 1
  • Remark 2
  • Definition 2
  • Remark 3
  • Lemma 1
  • proof
  • Remark 4
  • Remark 5
  • Remark 6
  • ...and 19 more