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

TL;DR

This paper presents a method combining Time-Varying LQR control with probabilistic Lyapunov-based region of attraction estimation to enhance the stability analysis of free-floating systems, demonstrated through simulations and onboard experiments.

Contribution

It introduces a novel integration of TVLQR with probabilistic ROA estimation for free-floating systems, validated through simulation and real-world experiments.

Findings

Successful stabilization of ADR detumbling in simulation.

Probabilistic ROA estimates provide insights into system stability.

Experimental validation on a free-floating testbed confirms real-world applicability.

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.