Image-based Visual Servo Control Design with Multi-Constraint Satisfaction

This chapter presents an application of advanced control techniques to the design of a multicriteria image-based controller for robotics application. The problem 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 stability 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 polytopic and norm-bounded representation of uncertainties combined with an original sector condition. With this representation, the unknown target velocity is considered 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 maximization 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.

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