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Region of Attraction Estimation for Free-Floating Systems under Time-Varying LQR Control

Lasse Shala, Shubham Vyas, Mohamed Khalil Ben-Larbi, Shivesh Kumar, Enrico Stoll

TL;DR

The paper addresses region-of-attraction estimation for free-floating space robots under Time-Varying Linear Quadratic Regulator (TVLQR) control to enable safe, multi-phase ADR/OOS maneuvers. It combines offline trajectory optimization to produce nominal, dynamically feasible paths with online TVLQR feedback to stabilize deviations, and introduces a probabilistic RoA estimation method to certify stability along time-varying funnels. The approach is demonstrated in two scenarios: a simulated multibody ADR detumbling context and onboard experiments on the ELISSA free-floating testbed, illustrating both the utility of RoA estimates and real-world applicability. The work advances practical stability certification and controller composition for complex in-orbit operations, supporting safe phase transitions throughout multi-phase maneuvers.

Abstract

Future Active Debris Removal (ADR) and On Orbit Servicing (OOS) missions demand for elaborate closed loop controllers. Feasible control architectures should take into consideration the inherent coupling of the free floating dynamics and the kinematics of the system. Recently, Time-Varying Linear Quadratic Regulators (TVLQR) have been used to stabilize underactuated systems that exhibit a similar kinodynamic coupling. Furthermore, this control approach integrates synergistically with Lyapunov based region of attraction (ROA) estimation, which, in the context of ADR and OOS, allows for reasoning about composability of different sub-maneuvers. In this paper, TVLQR was used to stabilize an ADR detumbling maneuver in simulation. Moreover, the ROA of the closed loop dynamics was estimated using a probabilistic method. In order to demonstrate the real-world applicability for free floating robots, further experiments were conducted onboard a free floating testbed.

Region of Attraction Estimation for Free-Floating Systems under Time-Varying LQR Control

TL;DR

The paper addresses region-of-attraction estimation for free-floating space robots under Time-Varying Linear Quadratic Regulator (TVLQR) control to enable safe, multi-phase ADR/OOS maneuvers. It combines offline trajectory optimization to produce nominal, dynamically feasible paths with online TVLQR feedback to stabilize deviations, and introduces a probabilistic RoA estimation method to certify stability along time-varying funnels. The approach is demonstrated in two scenarios: a simulated multibody ADR detumbling context and onboard experiments on the ELISSA free-floating testbed, illustrating both the utility of RoA estimates and real-world applicability. The work advances practical stability certification and controller composition for complex in-orbit operations, supporting safe phase transitions throughout multi-phase maneuvers.

Abstract

Future Active Debris Removal (ADR) and On Orbit Servicing (OOS) missions demand for elaborate closed loop controllers. Feasible control architectures should take into consideration the inherent coupling of the free floating dynamics and the kinematics of the system. Recently, Time-Varying Linear Quadratic Regulators (TVLQR) have been used to stabilize underactuated systems that exhibit a similar kinodynamic coupling. Furthermore, this control approach integrates synergistically with Lyapunov based region of attraction (ROA) estimation, which, in the context of ADR and OOS, allows for reasoning about composability of different sub-maneuvers. In this paper, TVLQR was used to stabilize an ADR detumbling maneuver in simulation. Moreover, the ROA of the closed loop dynamics was estimated using a probabilistic method. In order to demonstrate the real-world applicability for free floating robots, further experiments were conducted onboard a free floating testbed.
Paper Structure (4 sections, 4 equations, 2 figures)

This paper contains 4 sections, 4 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Background
  3. Equations of Motion
  4. Trajectory Optimization

Figures (2)

  • Figure 1: Coupling of kinematics and dynamics, adopted from xu1993. For manipulators fixed to the ground, there is no significant motion of the base link, when moving individual joints. The contrary holds for manipulators mounted on a spacecraft.
  • Figure 2: Composition of a multi-phase ADR scenario using funnels in the spirit of burridge1999. Each funnel represents the stabilizing closed-loop dynamics during a given phase of ADR. Stability over the entire maneuver can be achieved by ensuring that states at the outlet of a preceding funnel are a subset of the states of the subsequent one.