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Pose estimation problem of an object in real time is an important issue for robotic visual servoing (RVS). Many pose estimation schemes in RVS rely on an extended Kalman filter (EKF) that provides good accurate estimation. However, it may cause the estimation to become unstable because of nonlinear modeling uncertainties. While, smooth variable structure filter (SVSF) is a new method that is more robust to disturbances and uncertainties. In this paper, a novel pose estimate method is developed based on the EKF and SVSF. It is combined the accuracy of the EKF and the robustness provided by the SVSF that will lead to more accurate state estimates and improve robustness to modeling errors and uncertainties. The resulting algorithms are called the EKF-SVSF. The simulation results are provided to demonstrate the robustness and accuracy. Introduction In computer vision, the problem of pose estimation is to determine the position and orientation of a camera with respect to the object coordinate frame using the camera image information, known as 3-D pose estimation. This estimation benefits many applications, such as object recognition and RVS [1]. The focus of this study will be on pose estimation for RVS where the relative pose between the camera and the object is used for real-time control .The control error can be calculated in the image space, Cartesian space, or hybrid spaces in RVS [2], while is required partial or full pose estimation vector to calculate image error of the desired image and the current image in image-based visual-servoing (IBVS) or Cartesian error of the relative pose between the endpoint and the object in the position-based visual-servoing (PBVS), and they also face difficulties of efficiency and robustness in pose estimation [3]. The solutions of 3-D pose estimation problem usually focus on using the camera projection includes only 2-D data from the 3-D between geometric features and their projections on the image plane. Although high-level geometric features, such as lines and conics, have been proposed, point features are typically used for pose estimation due to their ease of availability in many objects, the four noncollinear points demonstrates robust and accuracy as well as high-level features, and is recommended [4]. Extended Kalman filter (EKF) is applied on account of the filter measurement output model that is nonlinear in the RVS system states, in which the output equations are linearized about the current state estimates [5]. The use of EKF has several advantages in RVS which includes its recursive implementation, capability to statistically combine redundant information or sensors, temporal filtering. For instance, an EKF-based platform has been proposed in to apply on vision sensor for robust and accuracy pose estimation in RVS. It has been shown that, in practice, the EKF provides near-optimal estimation. There are some issues with the application of EKF to pose estimation in spite its advantages. First, the geometric 3-D model of the objects usually assumed to be available in RVS, there are still some limitations on the ability of the EKF. The statistics of the measurement and 1 system noise must be known prior to its application and they assume zero mean Gaussian noise. Although EKF can handle nonlinear estimation problems well, it introduces a number of instabilities. For example, the linearization process may overlook nonlinear modeling uncertainties, which may cause the estimate to become unstable, and which is poor resistance to uncertainty and modeling error. In an effort to increase its stability, the EKF has been combined with a SVSF. The SVSF is a relatively new method [6], which is based on sliding mode control and estimation concept, such that the estimate is forced by a switching gain to remain within an area of the true state trajectory that is referred to as the existence subspace. The SVSF also uses a smoothing boundary layer (SBL), which reduces the effects of high-frequency switching (referred to as chattering) across the true state trajectory [7,8]. This methodology has been shown to yield extremely robust and stable results to disturbances and uncertainties [9]. In this paper, pose estimate methods is developed based on the EKF and the SVSF .It is combined the accuracy of the EKF gain and the robustness provided by the SVSF chattering effect which will lead to more accurate state estimates and improved robustness to modeling errors and uncertainties [10]. The resulting algorithms are called the EKF-SVSF [11]. The paper is organized as follows. In Section II , the modeling of the system is described In Section III, EKF-SVSF estimation strategy is proposed .In Section IV, a number of filtering algorithms are applied and compared on pose estimation problem through simulation in RVS. In Section V, concludes the paper. System Configuration and Modeling The eye-in-hand (EIH) camera has been mounted on the robot's end-effector and it is defaulted that it has the same coordinate frame as robot's end-effector. This camera always has a direct look at an object which can reduce unnecessary interference. The location and geometric shape of visual features on this object are known and easily identification. This object has a known pose with respect to the robot's end-effector. Having the camera and object, the relative pose of object with respect to EIH is to be estimated. A pin-hole camera model is used for the camera. Based on this model, a pinhole camera model is considered for the image projection [1]. Point features are exploited since they are simple to extract. A point in camera frame   , , , , = X T o i o i o i o i c c c c P Y Z and the pinhole camera model is used for each camera as follows: , , , , o i o i c c c c i i o i o i c c x y u v f z z            (1) where c i c c i i P u v      is the coordinates of this point mapped on the image plane, c i u and c i v are its coordinates. f is the camera focal length which is assumed to be one without losing the generality. The homogeneous transformation matrix is used for finding the relative pose of the point to each frame:   1 3 0 1 j j j i i i j i R T t            (2) where   j j i i R  (where j j j j i i i i          is the vector of Euler angles with roll, pitch, and yaw elements) is the rotation and j j j j i i i i x y z t      is translation between two arbitrary i and j coordinate frames, respectively. Figure 1 shows the system with object ( o ) and EIH ( c ) camera. The relative pose of the target object with respect to the robot’s end-effector is desirable and is obtained separately for EIH cameras. e e c o c o T T T  (3) 2

Kalman and Smooth Variable Structure Filters for Pose Estimation in Robotic Visual Servoing