Estimation of Homography Dynamics on the Special Linear Group - Visual Servoing via Advanced Numerical Methods - page 127

Chapter 8
Estimation of Homography Dynamics on the
Special Linear Group

Ezio Malis, Tarek Hamel, Robert Mahony, and Pascal Morin

Abstract. During the last decade, a number of highly successful visual servo con-
trol and real-time image processing algorithms have been proposed that use the
homography between images of a planar scene as the primary measurement. The
performance of the algorithms depends directly on the quality of the homography
estimates obtained, and these estimates must be computed in real-time. In this chap-
ter, we exploit the special linear Lie group structure of the set of all homographies
to develop an on-line dynamic observer that provides smoothed estimates of a se-
quence of homographies and their relative velocities. The proposed observer is easy
to implement and computationally undemanding. Furthermore, it is straightforward
to tune the observer gains and excellent results are obtained for test sequences of
simulation and real-world data.

8.1 Introduction

Visual servo control schemes use visual information obtained by one or multiple
cameras as the primary measurement to regulate the motion of a robot [21, 11, 12, 6].
In the last decade, a number of visual servo control schemes have been proposed that
extract homography image transformations between images of a planar scenes and
use these as the primary visual information for a servo control problem [17, 7, 8].