Delay-dependent stability in uncalibrated image-based dynamic visual servoing robotic system

Abstract

This paper addresses the stability problem of uncalibrated image-based visual servoing robotic systems. Both the visual feedback delay and the uncalibrated visual parameters can be the sources of instability for visual servoing robotic systems. To eliminate the negative effects caused by kinematic uncertainties and delays, we propose an adaptive controller including the delay-affected Jacobian matrix and design an adaptive law accordingly. Besides, the delay-dependent stability conditions are provided to show the relationship between the system stability and the delayed time in order to obtain less conservative results. A Lyapunov-Krasovskii functional is constructed, and a rigorously mathematic proof is given. Finally, the simulation results are presented to show the effectiveness of the proposed control scheme.