Uncalibrated Visual Tracking Control for Networked Eye-in-Hand Robots by Adaptive Distributed Observer

This article investigates the problem of visual tracking of an unknown moving target by a network of robotic manipulators equipped with uncalibrated eye-in-hand cameras. The objective is to ensure that, for each robot, the target's projection is maintained at a specified position on the image plane, despite the uncalibrated camera parameters and uncertain, time-varying feature depths. The target's motion is assumed to be generated by a neutrally stable linear system, whose state and system matrix are not directly accessible to all robots. To address this problem, a distributed control scheme is developed in three steps. First, an adaptive distributed observer is introduced to estimate the motion of the moving target. Second, a novel image-space observer is designed for each robot to estimate the image-space position and to simultaneously provide the estimated image-space velocity, based on which the proposed distributed controller avoids using image-space velocity measurements. Third, by leveraging the linearly parameterized properties of the depth-independent image Jacobian matrix and the depth, adaptive laws are proposed to cope with uncertain parameters in cameras and robots. By using the Lyapunov stability theory, a rigorous analysis is provided to show the stability of the closed-loop system and asymptotic convergence of the image-space tracking errors. The effectiveness of the proposed scheme is illustrated through simulation with a group of three-DOF robotic manipulators.