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Information-Optimal Multi-Spacecraft Positioning for Interstellar Object Exploration

Arna Bhardwaj, Shishir Bhatta, Hiroyasu Tsukamoto

Abstract

Interstellar objects (ISOs), astronomical objects not gravitationally bound to the sun, could present valuable opportunities to advance our understanding of the universe's formation and composition. In response to the unpredictable nature of their discoveries that inherently come with large and rapidly changing uncertainty in their state, this paper proposes a novel multi-spacecraft framework for locally maximizing information to be gained through ISO encounters with formal probabilistic guarantees. Given some approximated control and estimation policies for fully autonomous spacecraft operations, we first construct an ellipsoid around its terminal position, where the ISO would be located with a finite probability. The large state uncertainty of the ISO is formally handled here through the hierarchical property in stochastically contracting nonlinear systems. We then propose a method to find the terminal positions of the multiple spacecraft optimally distributed around the ellipsoid, which locally maximizes the information we can get from all the points of interest (POIs). This utilizes a probabilistic information cost function that accounts for spacecraft positions, camera specifications, and ISO position uncertainty, where the information is defined as visual data collected by cameras. Numerical simulations demonstrate the efficacy of this approach using synthetic ISO candidates generated from quasi-realistic empirical populations. Our method allows each spacecraft to optimally select its terminal state and determine the ideal number of POIs to investigate, potentially enhancing the ability to study these rare and fleeting interstellar visitors while minimizing resource utilization.

Information-Optimal Multi-Spacecraft Positioning for Interstellar Object Exploration

Abstract

Interstellar objects (ISOs), astronomical objects not gravitationally bound to the sun, could present valuable opportunities to advance our understanding of the universe's formation and composition. In response to the unpredictable nature of their discoveries that inherently come with large and rapidly changing uncertainty in their state, this paper proposes a novel multi-spacecraft framework for locally maximizing information to be gained through ISO encounters with formal probabilistic guarantees. Given some approximated control and estimation policies for fully autonomous spacecraft operations, we first construct an ellipsoid around its terminal position, where the ISO would be located with a finite probability. The large state uncertainty of the ISO is formally handled here through the hierarchical property in stochastically contracting nonlinear systems. We then propose a method to find the terminal positions of the multiple spacecraft optimally distributed around the ellipsoid, which locally maximizes the information we can get from all the points of interest (POIs). This utilizes a probabilistic information cost function that accounts for spacecraft positions, camera specifications, and ISO position uncertainty, where the information is defined as visual data collected by cameras. Numerical simulations demonstrate the efficacy of this approach using synthetic ISO candidates generated from quasi-realistic empirical populations. Our method allows each spacecraft to optimally select its terminal state and determine the ideal number of POIs to investigate, potentially enhancing the ability to study these rare and fleeting interstellar visitors while minimizing resource utilization.

Paper Structure

This paper contains 16 sections, 1 theorem, 17 equations, 5 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Contributions
  3. Related Work
  4. Problem Formulation
  5. Technical Challenges in ISO Exploration
  6. Probability of ISO Encounter
  7. Multi-Spacecraft Positioning
  8. Conal Approximation of Field of View
  9. Cost Function Formulation
  10. Extensions to Stochastic Terminal Positions
  11. Numerical Simulations
  12. Simulation Setup and Results
  13. Probability of single spacecraft viewing the ISO
  14. Determining Optimal Number of Spacecraft
  15. Conclusion
  16. ...and 1 more sections

Key Result

Theorem 1

Suppose that we have uniformly bounded positive definite matrices $\underline{m}_c {\mathbb{I}} \preceq M_c(t) \preceq \overline{m}_c {\mathbb{I}}$ and $\underline{m}_e {\mathbb{I}} \preceq M_e(t) \preceq \overline{m}_e {\mathbb{I}}$ that satisfy the following contraction conditions: where $\alpha_c,\alpha_e,\underline{m}_c,\overline{m}_c,\underline{m}_e,\overline{m}_e\in{\mathbb{R}}_{> 0}$. Supp

Figures (5)

  • Figure 1: Conceptual illustration of the deputy spacecraft positioning using Theorem \ref{['thm_hierarchical_contraction']} and \ref{['eq_success']}.
  • Figure 2: Example of 5,000 POIs being sampled in an uncertainty ellipsoid.
  • Figure 3: A diagram with a conal FOV with an apex at the spacecraft position is labeled.
  • Figure 4: A diagram of the plane dividing the uncertainty ellipsoid into two hemispheres.
  • Figure 5: A diagram of the terminal positions of a five-spacecraft system and the POIs in view and not in view.

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Remark 1
  • Remark 2