Contribution of BAT Heuristic Optimization to Quaternion-Based Visual Servoing Marco Perez-Cisneros, Gerardo Garcia-Gil, Erik Cuevas, Daniel Zaldivar Abstract — Visual servoing (VS) refers to the use of a vision system to control the movement of a robot. The control information acquired from a camera that is mounted directly on a robot manipulator or a mobile robot, in which case the robot motion can be induced from the motion of the camera, on the other hand the camera may be fixed on the workplace with a stationary configuration (3D). Other configurations may be considered, for example have mounted cameras observing the movement of the robot. This study focuses on one of the most common schemes in VS called Eye-in-Hand (2D), which considers a camera mounted on the end effector of a robotic system. The control scheme is known as Image-based Visual Servoing (IBVS), under the control error reduction is performed directly on the image plane. Method IBVS or also called 2D Visual is known to be more robust with respect not only to the camera but also the robot calibration errors. However, the convergence is guaranteed only in a region (very difficult to determine analytically) around the desired position. Except in very simple stability analysis with respect to calibration errors appear impossible since the system is linear and non-coupled. [7], [8]. This is where BAT implement heuristic algorithm[], which is intended for use within a VS scheme, exhibits characteristics effective in solving nonlinear systems, and that relate to the context of 3D with a robotic system with 6 degrees of freedom (dof). The theme of the VS control schemes through optimization structures have been treated by many authors, especially by Corke [17] [18] and Chaumette [11]. The performance of heuristic algorithms in the VS system applied to object identification, tracking and restoration through artificial vision. VS is the goal of the use of visual information to control processing (position and orientation) automated actuator end, relative to a set of image characteristics of the object of interest. The author of this article believes that optimization schemes within VS systems can still provide significant improvement, which has led to this proposal. Index Terms—quaternion, visual servoing, BAT. I. INTRODUCTION. Visual servo control methods have been developer where the feedback signal is composed of pure image-space information. [7], [8], [9], [11], one significant advantage of homographic-based visual servo controllers is that singularities in the image-Jacobian are avoided. From a review of the three traditional approaches (see [10] for an in-depth discussion), (i.e., the image-Jacobian is typically upper triangular and invertible in homography-based approaches). However all of the previous homography- based visual servo controllers have been developed with the error system that containing trigonometric terms resulting from the Euler angle-axis representation of rotation matrix. A discussion is provided that explains how the singularity in the error system formulated via Euler angle-axis representation is manifested differently for various functions. Another difference between our approach and other more popular choices in the literature is in the use of quaternion representation, which eliminates the potential singularities introduced by rotational matrix representation[]. Motivated by the desire to eliminate the rotation singularity, an error system and visual servo regulation we using a quaternion formulation that a predictive model will be used formulated as solving on – line a nonlinear optimization problem. Based on the process model, the controller predicts the behavior of the system over a prediction horizon. The difference between the reference trajectory and the predicted model for quaternion behavior defines the cost function J to be minimized with respect to a control sequence. The optimization task will be performed by in a heuristic algorithm called BAT [5]. For the excellent characteristics that offer this algorithm in relation to other ones like the PSO [1], GA [2], DE [3]. Since the three decades, visual servoing has been largely developed from a theoretical viewpoint but also from a practical viewpoint. Many applications of visual servoing, among others things, for aerial, submarine or medical robots have been reported in the literature [4], [8], and [10]. The fundamental classification of visual servoing distinguishes three approaches: image-based control (2D), position-based control (3D) and a hybrid approach (2 1/2 D). Further details about visual servoing can be found in [5], [6]. Here, we focus our interest on Image-Based Visual Servoing (IBVS). In this context, the control task consists in determining the control input applied to the robotic system according to the error between the reference image and the current image from the camera. We consider a free-flying camera with six degree of-freedom (6 dof). The relationship between the camera velocity screw τ and the time variation of the visual features ݏ̇ is given by: ݏ̇ሺݐሻ= ௦ ሺݐሻ ሺͳሻ Where Ls is the interaction matrix related to s. The aim of visual servoing is to minimize the error e(t) between the reference features s∗, assumed to be constant, and the measured features s(t). It is defined by: ሺݐሻ= ݏሺݐሻ− ݏ* (2) In order to satisfy an exponential decay of the error (2), mathematically expressed by: ̇ሺݐሻ = −ሺݐሻ ݓݐℎ >Ͳ (3)