A different approach to solving the PBVS control problem Adrian Burlacu Dept. of Automatic Control and Applied Informatics Gheorghe Asachi Technical University of Iasi Iasi, Romania email: aburlacu@ac.tuiasi.ro Daniel Condurache Dept. of Theoretical Mechanics Gheorghe Asachi Technical University of Iasi Iasi, Romania email: daniel.condurache@gmail.com Abstract—This paper offers a different approach to solving the position-based visual servoing control problem. If focuses on the development of a free of coordinates solution that allows the direct use of point features 3D position without the necessity of recovering the pose of the object. The proposed approach makes use of the rigid body motion parameterization techniques based on the properties of dual Lie algebras. Considering an imposed velocity field over the motion of a rigid body, our work gives an algebraic close form free of coordinates solution for the position based visual control law. This solution allows the motion control to be stable while keeping the image features in the field of view. Also, it provides a natural decoupling of the visual sensor motion on all six degrees of freedom. A comparison by simulations is conducted using different scenarios. The results show how the proposed solution copes with the problems of the classic servoing techniques. Index Terms—position based visual servoing, dual Lie algebra, rigid body motion. I. I NTRODUCTION The use of visual sensors for closing the feedback control loop is an important approach in multiple applications [1]–[3]. Visual servoing architectures can be designed using different control techniques: image based (IBVS) [4], 3D data based (PBVS) [4], 2 1/2D [5], hybrid [6], [7], partitioned or switched [8]. The IBVS and PBVS schemes are the most known techniques for the use of computer vision data in robot motion control. For an eye in hand setup, the task needed to be completed by a visual servoing system is to minimize the error between the features state in the current image in comparison with a desired one [9]. IBVS control is based on the principle of directly servoing using image features (points [4], lines [10], image moments [11], hole image [12]). This allows the following advantages: increased robustness to camera calibration and strong capa- bilities to ensure the target remains visible. However, IBVS controllers can generate excessive control action and transient response. A large initial error, mostly in the orientation part (in the vicinity of 180 degrees), can cause instability and generate commands that will have the target leave the field of view (FoV). Also, the resulting trajectories might not be physically valid or optimal. These disadvantages are induced by the nonlinearities and potential singularities associated with the transformation between the image space and the Euclidean- space [13]. In literature, PBVS is refereed with either position based or pose based denomination (Pose-based VS) [9]. The reason is that the considered feature is a pose estimated via image measurements [14]. In comparison to IBVS, Pose-based VS provides a better behavior to camera motions implying large translations and rotations. Pose-based VS is free of the im- age singularities, local minima, and camera-retreat problems specific to IBVS. Under certain assumptions, the closed- loop stability of Pose-based VS is robust with respect to bounded errors of the intrinsic camera-calibration and object model. However, Pose-based VS is more sensitive to camera and object 3D model errors than IBVS. The current Pose- based VS approaches are not designed with a mechanism for regulating the features in the image space. A feature- selection and switching mechanism would be necessary [15]. Because the current PBVS techniques are built of two steps, pose recovery and control design, feedback and estimation are more time consuming than IBVS. The relative pose must be estimated online, with accuracy depending on the system- calibration parameters, which can induce noisy results. In this paper we propose a different approach to PBVS, which does not need a prior 3D model of the object, thus pose estimation is removed. The proposed technique uses point features to provide a direct algebraic solution for the sensor velocity computation. The solution can be obtained with any number of point features, without the need of stacking data in large matrices. This asset comes from the properties of dual Lie algebras, especially the orthogonal dual tensors ensemble. Orthogonal dual tensors are a complete tool for computing rigid body displacement and motion parameters [16], [17], [18]. The use of this tool offers the advantages of a reduced number of algebraic equations and fewer variables. The main idea emerges from the analysis of the rigid body motion, where the instantaneous screw can be used to completely describe an imposed velocity field on a set of 3D point features. The proposed solution is free of coordinates and easy to implement. This approach to solving the PBVS control problem has multiple advantages in comparison with the classic methods. It induces minimum curvature image plane trajectories for the feature points while decoupling each degree of freedom in the visual sensor motion. This result generates stable and natural behavior of visual sensor in 3D  l -)))  Authorized licensed use limited to: Daniel Condurache. Downloaded on August 03,2020 at 19:16:09 UTC from IEEE Xplore. Restrictions apply.