Logarithmic Observation of Feature Depth for Image-Based Visual Servoing

Due to the robustness to robot modeling and camera calibration errors and avoidance of complete target geometry, image-based visual servoing has always been an important topic in the fields such as robotics, computer vision and so forth. When the image information obtained by the camera is mapped to the robotic task space to design the servoing control law, the resulting interaction matrix, which links the spatial velocity of the camera to the temporal variation of the selected image features, depends on the unknown feature depths. The use of inaccurate feature depths may influence the stability and robustness of the controller, and even cause the failure of the task. In this article, based on the perspective camera model, by employing the principle of reduced order observer, a novel logarithmic observer is presented for on-line recovery of feature depth. Compared with the typical observers now available, the presented observer offers several advantages: global convergence, a faster convergence rate of error structure than exponential error structure, a less restricted observability condition and greater robustness against measurements with noise. The comparison results of numerical simulations indicate the superiority of the presented observer, and real experiments with Kinect v2 sensor further validate the effectiveness of the presented observer in practical situation. Note to Practitioners—This article was motivated by the depth problem in the image-based visual servoing scheme, but it can also be used in other situations where the image depth information is needed, such as 3D reconstruction, robot navigation, etc. The existing depth acquisition methods include TOF sensors, stereo vision, depth observers and so on. However, TOF sensors are sensitive to light conditions, and the mounting space of stereo vision is slightly large, and there is contradiction between observation performance and computational complexity in most existing observers. In this article, a novel structure of logarithmic reduced order observer is described in detail, which can be utilized to estimate the depth information of images easily. The simulations and experiments verify the good performance of the observer. The limitations of the given observer are that the estimation accuracy is not very good under weak excitation, and the camera needs to be calibrated in advance. Future work will focus on overcoming these two limitations.