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Safe Multi-agent Satellite Servicing with Control Barrier Functions

Deep Parikh, David van Wijk, Manoranjan Majji

TL;DR

This work tackles safe relocation of multiple TPODS satellite servicing modules on a tumbling RSO under pose uncertainty. It combines model-predictive trajectory following with ellipsoidal keep-out constraints, differentiable collision detection for polytopic hulls (DCOL), and control barrier function (CBF) based safety, including high-order extensions (HOCBFs) for relative-degree-two constraints. A hybrid framework toggles between DCOL and CBF/HOCBF approaches to balance fuel efficiency, safety guarantees, and computational load, further robustified by an MEKF-based pose estimator and covariance-driven uncertainty buffers. Monte Carlo simulations with 500 trials demonstrate high safety performance (97.6% success), highlighting the practical relevance for autonomous satellite servicing in uncertain, dynamic environments.

Abstract

The use of control barrier functions under uncertain pose information of multiple small servicing agents is analyzed for a satellite servicing application. The application consists of modular servicing agents deployed towards a tumbling space object from a mothership. Relative position and orientation of each agent is obtained via fusion of relative range and inertial measurement sensors. The control barrier functions are utilized to avoid collisions with other agents for the application of simultaneously relocating servicing agents on a tumbling body. A differential collision detection and avoidance framework using the polytopic hull of the tumbling space object is utilized to safely guide the agents away from the tumbling object.

Safe Multi-agent Satellite Servicing with Control Barrier Functions

TL;DR

This work tackles safe relocation of multiple TPODS satellite servicing modules on a tumbling RSO under pose uncertainty. It combines model-predictive trajectory following with ellipsoidal keep-out constraints, differentiable collision detection for polytopic hulls (DCOL), and control barrier function (CBF) based safety, including high-order extensions (HOCBFs) for relative-degree-two constraints. A hybrid framework toggles between DCOL and CBF/HOCBF approaches to balance fuel efficiency, safety guarantees, and computational load, further robustified by an MEKF-based pose estimator and covariance-driven uncertainty buffers. Monte Carlo simulations with 500 trials demonstrate high safety performance (97.6% success), highlighting the practical relevance for autonomous satellite servicing in uncertain, dynamic environments.

Abstract

The use of control barrier functions under uncertain pose information of multiple small servicing agents is analyzed for a satellite servicing application. The application consists of modular servicing agents deployed towards a tumbling space object from a mothership. Relative position and orientation of each agent is obtained via fusion of relative range and inertial measurement sensors. The control barrier functions are utilized to avoid collisions with other agents for the application of simultaneously relocating servicing agents on a tumbling body. A differential collision detection and avoidance framework using the polytopic hull of the tumbling space object is utilized to safely guide the agents away from the tumbling object.

Paper Structure

This paper contains 24 sections, 2 theorems, 28 equations, 15 figures, 2 tables.

Table of Contents

  1. Introduction
  2. System Dynamics
  3. Pose Estimation
  4. Optimal Relocation
  5. Collision Instances
  6. Safety Assurances
  7. Trajectory following with MPC
  8. Differentiable Collision Detection for Polytopic Hulls
  9. Planar Collision Avoidance
  10. Control Barrier Functions
  11. Multi-agent Collision Avoidance with CBFs
  12. Planar Collision Avoidance
  13. High-order Control Barrier Functions
  14. Multi-agent Collision Avoidance with HOCBFs
  15. TPODS-RSO Constraint
  16. ...and 9 more sections

Key Result

Theorem 1

Given a set $\mathcal{C}_{\rm S} \subset \mathbb{R}^n$ defined by eq:safeset$-$eq:safeset2 for a continuously differentiable function $h$, if $h$ is a CBF on $\mathcal{C}_{\rm S}$ then any locally Lipschitz continuous controller $k:\mathcal{X} \rightarrow \mathcal{U}$, $\boldsymbol{u}=k(\boldsymbol{ for all $\boldsymbol{x} \in \mathcal{C}_{\rm S}$ will render the set $\mathcal{C}_{\rm S}$ forward

Figures (15)

  • Figure 1: Scaffolding generation to enable servicing of RSO
  • Figure 2: TPODS module (right) and mothership satellite (left)
  • Figure 3: Architecture for safe module relocation on a tumbling RSO
  • Figure 4: Reference trajectories for optimal relocation and collision of TPODS
  • Figure 5: Collision avoidance using MPC and polytopic hulls
  • ...and 10 more figures

Theorems & Definitions (6)

  • Definition 1: Forward invariance
  • Definition 2: Control barrier function ames_2017
  • Theorem 1: ames_2017
  • Definition 3: Relative degree khalil2002nonlinear
  • Definition 4: High-order control barrier functions TanHOCBF_2022
  • Theorem 2: Thm. 1 TanHOCBF_2022