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Chapter 15
Image-based Visual Servo Control Design with
Multi-Constraint Satisfaction
Sophie Tarbouriech and Philippe Soueres
Abstract. This chapter presents an application of advanced control techniques to the
design of a multicriteria image-based controller for robotics application. The prob-
lem of positioning a 3 degrees of freedom (DOF) camera with respect to a mobile
visual target with unknown square integrable velocity is considered. The proposed
controller allows to stabilize the camera and determine the associated region of sta-
bility in spite of unknown values of the target points depth, bounds on admissible
visual features errors to guarantee visibility, and limits on the camera velocity and
acceleration. The description of the closed-loop system is based on a mixed poly-
topic and norm-bounded representation of uncertainties combined with an original
sector condition. With this representation, the unknown target velocity is consid-
ered as a disturbance limited in energy and linear matrix inequality (LMI)-based
optimization schemes are used to compute the feedback gain that leads to the max-
imization of the size of the region of stability associated to the closed-loop system.
Two applications of the method are studied and simulated by considering a model
of car-like robot equipped with proximity sensors and supporting a camera mounted
on a plan-platform. The interest of the control approach for linking dynamically a
sequence of sensor-based navigation tasks for a mobile robot is illustrated.
15.1
Introduction
Image-based visual servoing aims at controlling robotic systems by regulating fea-
ture errors directly in the camera image-plane. In order to deal with parameter un-
certainty, and take into account additional constraints such as visibility or actuators
limitation, the design of robust control schemes turns out to be essential [5]. As
shown in [14], uncertainty in the depth distribution of target points may strongly
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