Globally convergent visual-feature range estimation with biased inertial measurements

TL;DR

This paper presents a globally convergent observer for estimating feature point positions using only bearing measurements and biased inertial data, without requiring gravitational constant knowledge or strong observability conditions.

Contribution

It introduces a novel observer design that guarantees convergence under weaker conditions than traditional methods, applicable to visual inertial navigation.

Findings

Observer converges under weaker trajectory conditions

No need for gravitational constant in estimation

Applicable to visual inertial navigation

Abstract

The design of a globally convergent position observer for feature points from visual information is a challenging problem, especially for the case with only inertial measurements and without assumptions of uniform observability, which remained open for a long time. We give a solution to the problem in this paper assuming that only the bearing of a feature point, and biased linear acceleration and rotational velocity of a robot -- all in the body-fixed frame -- are available. Further, in contrast to existing related results, we do not need the value of the gravitational constant either. The proposed approach builds upon the parameter estimation-based observer recently developed in (Ortega et al., Syst. Control Lett., vol.85, 2015) and its extension to matrix Lie groups in our previous work. Conditions on the robot trajectory under which the observer converges are given, and these are strictly weaker than the standard persistency of excitation and uniform complete observability conditions. Finally, as an illustration, we apply the proposed design to the visual inertial navigation problem.