Visual Feedback Control With an Input-to-State Safe Control Barrier Function

Abstract

In this paper, we present a visual feedback control method via an input-to-state safe control barrier function (ISSf-CBF). The control objective is that a camera-mounted mobile robot achieves the desired relative pose to a target object with avoiding any elliptic cylinder obstacles under input disturbances. First, we derive a visual feedback error system with visual motion observers to discuss stability via the Lyapunov method. Through the kinematic model for a relative rigid body, we design an ISSf-CBF for elliptic cylinder obstacle avoidance under input disturbances. Next, we present a control Lyapunov function (CLF) for the visual feedback error system. By using the ISSf-CBF and the CLF, we discuss a unified quadratic program formulation that connects the safety and the stability for pose control of a camera-mounted mobile robot under input disturbances. Finally, simulation and experimental results confirm the validity of the proposed ISSf-CBF control method compared to the other one which only achieves the desired pose.