# A Nonlinear Observer for Free-Floating Target Motion using only Pose Measurements

## TL;DR

This paper introduces a nonlinear observer that estimates the pose and velocity of a free-floating satellite using only relative pose measurements, enhancing orbital robotic capture capabilities without direct velocity sensors.

## Contribution

It develops a model-based nonlinear observer on SE(3) that estimates pose and velocity solely from pose measurements, with proven stability and validation through simulations and experiments.

## Key findings

- Observer accurately estimates pose and velocity in noisy conditions.
- Stable error dynamics demonstrated through theoretical analysis.
- Validated with robotic experiments and Monte-Carlo simulations.

## Abstract

In this paper, we design a nonlinear observer to estimate the inertial pose and the velocity of a free-floating non-cooperative satellite (Target) using only relative pose measurements. In the context of control design for orbital robotic capture of such a non-cooperative Target, due to lack of navigational aids, only a relative pose estimate may be obtained from slow-sampled and noisy exteroceptive sensors. The velocity, however, cannot be measured directly. To address this problem, we develop a model-based observer which acts as an internal model for Target kinematics/dynamics and therefore, may act as a predictor during periods of no measurement. To this end, firstly, we formalize the estimation problem on the SE(3) Lie group with different state and measurement spaces. Secondly, we develop the kinematics and dynamics observer such that the overall observer error dynamics possesses a stability property. Finally, the proposed observer is validated through robust Monte-Carlo simulations and experiments on a robotic facility.