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Chance-Constrained Control for Safe Spacecraft Autonomy: Convex Programming Approach

Kenshiro Oguri

TL;DR

This work addresses safe spacecraft path planning under uncertainty by formulating an output-feedback chance-constrained control problem and solving it via convex programming. The method linearizes dynamics, propagates state statistics, and leverages a Kalman-filtered, Markovian structure to obtain affine expressions for state and control statistics, enabling tractable optimization with probabilistic constraints. Key contributions include (i) a rigorous chance-constrained formulation for orbit control under multiple uncertainty sources, (ii) a convex reformulation with deterministic surrogates for path and terminal constraints, and (iii) demonstration on safe autonomous rendezvous and NRHO station-keeping with results showing safety under $99\%$ confidence and bounded $\Delta V_{99}$. The approach supports onboard execution of computed maneuvers, offering a practical framework for robust autonomous space operations under estimation, execution, and model uncertainties $\big(\text{Kalman filtering}, \text{Gates model}, \text{stochastic dynamics}\big)$.

Abstract

This paper presents a robust path-planning framework for safe spacecraft autonomy under uncertainty and develops a computationally tractable formulation based on convex programming. We utilize chance-constrained control to formulate the problem. It provides a mathematical framework to solve for a sequence of control policies that minimizes a probabilistic cost under probabilistic constraints with a user-defined confidence level (e.g., safety with 99.9% confidence). The framework enables the planner to directly control state distributions under operational uncertainties while ensuring the vehicle safety. This paper rigorously formulates the safe autonomy problem, gathers and extends techniques in literature to accommodate key cost/constraint functions that often arise in spacecraft path planning, and develops a tractable solution method. The presented framework is demonstrated via two representative numerical examples: safe autonomous rendezvous and orbit maintenance in cislunar space, both under uncertainties due to navigation error from Kalman filter, execution error via Gates model, and imperfect force models.

Chance-Constrained Control for Safe Spacecraft Autonomy: Convex Programming Approach

TL;DR

This work addresses safe spacecraft path planning under uncertainty by formulating an output-feedback chance-constrained control problem and solving it via convex programming. The method linearizes dynamics, propagates state statistics, and leverages a Kalman-filtered, Markovian structure to obtain affine expressions for state and control statistics, enabling tractable optimization with probabilistic constraints. Key contributions include (i) a rigorous chance-constrained formulation for orbit control under multiple uncertainty sources, (ii) a convex reformulation with deterministic surrogates for path and terminal constraints, and (iii) demonstration on safe autonomous rendezvous and NRHO station-keeping with results showing safety under confidence and bounded . The approach supports onboard execution of computed maneuvers, offering a practical framework for robust autonomous space operations under estimation, execution, and model uncertainties .

Abstract

This paper presents a robust path-planning framework for safe spacecraft autonomy under uncertainty and develops a computationally tractable formulation based on convex programming. We utilize chance-constrained control to formulate the problem. It provides a mathematical framework to solve for a sequence of control policies that minimizes a probabilistic cost under probabilistic constraints with a user-defined confidence level (e.g., safety with 99.9% confidence). The framework enables the planner to directly control state distributions under operational uncertainties while ensuring the vehicle safety. This paper rigorously formulates the safe autonomy problem, gathers and extends techniques in literature to accommodate key cost/constraint functions that often arise in spacecraft path planning, and develops a tractable solution method. The presented framework is demonstrated via two representative numerical examples: safe autonomous rendezvous and orbit maintenance in cislunar space, both under uncertainties due to navigation error from Kalman filter, execution error via Gates model, and imperfect force models.
Paper Structure (33 sections, 7 theorems, 66 equations, 1 figure)

This paper contains 33 sections, 7 theorems, 66 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Orbital Mechanics under Control
  3. Generic Formulation
  4. Chance-Constrained Control Problem
  5. Uncertainty Modeling
  6. Initial state dispersion
  7. Maneuver execution error
  8. Stochastic acceleration
  9. Navigation uncertainty
  10. Nonlinear Stochastic System
  11. Orbit Control under Uncertainty
  12. Cost Function
  13. Path chance constraints
  14. Distributional terminal constraints
  15. State-triggered chance constraints
  16. ...and 18 more sections

Key Result

proposition 1

Under the filtered state dynamics eq:linEstProcess with the output-feedback control policy eq:SOClinPolicy, $\ols{\bm{x}}_k$, $\hat{P}_k^{1/2}$, $P_k^{1/2}$, and ${P}_{u_k}^{1/2}$ are affine in $\ols{\bm{U}}$ and $\mathbf{K}$, given by: where $\mathbf{S}^{1/2}$ is given by $\mathbf{S}^{1/2} = $.

Figures (1)

  • Figure 1: Safe autonomy framework based on chance-constrained control

Theorems & Definitions (13)

  • proposition 1
  • proof
  • lemma 1
  • proof
  • lemma 2
  • proof
  • lemma 3
  • remark 1
  • lemma 4
  • theorem 1
  • ...and 3 more