# Improving the Manipulability of a Redundant Arm Using Decoupled Hybrid Visual Servoing
## 1 Introduction
### Related Works  
Hybrid Visual Servoing was developed to combine the benefits of IBVS and PBVS while avoiding their drawbacks [16]. Switching approach is a hybrid visual servoing technique in which the controller alternates between IBVS and PBVS based on the efficacy of the system [17]. However, when switching occurs the controller suffers from discontinuities, particularly when the object is close to the image borders [18]. Task sequencing techniques provide a solution to fill such gaps [19], nevertheless sequencing techniques make the convergence time up [3]. Furthermore, two failures in IBVS (i.e., camera retreat and Chaumette Conundrum) could not be easily identified because image-Jacobian is not ill-conditioned in those configurations [12; 13]. As a result, switching between IBVS and PBVS can not resolve these issues. The Chaumette Conundrum could not be solved even by creating rotational motions around the camera optic axis, since they would cancel out each other [13].  
In [13], [PERSON] et al. proposed a visual servoing method that decouples the translation and rotation about \(Z\)-axis, from the image-Jacobian in order to address the Chaumette Conundrum and the camera retreat. However, expensive computation of the pseudo  
Figure 1: The automated process of sorting the dismantled EV battery components. The object tracking is carried out by the proposed VS method (DHVS) and the object is manipulated using a redundant manipulator arm.  
inverse is still challenging. To fix the Chaumette Conundrum and the camera retreat, a visual servoing method was proposed that decouples translation and rotation around the \(Z\)-axis from the image-Jacobian [13]. However, compensating for rotation errors in the picture plane about the \(X\) and \(Y\) axes also results in excessive motion for the robot joints which is undesirable [17]. By decomposing translations from rotations in 2 and 1/2D visual servoing methods, unnecessary motions are reduced [20]. These methods, however, are computationally intensive and necessitate homography construction, which is susceptible to image noise [13]. Another disadvantage of the 2 and 1/2D VS approach is that it necessitates the use of co-planar features in order to estimate the homography matrix. Otherwise, at least 8 visual features are required to make this estimation, while 4 features are sufficient in other methods [21]. The 2 and 1/2D VS approach also decomposes homography to remove rotational parameters associated with non-unique solutions [22]. In case of using static arm manipulators, issues like unfavourable configurations, joint limits, kinematic singularities and occlusions should be avoided.  
Redundant robots are preferable because adding redundancy to the robot increases the manipulability and versatility [23]. There are a number of studies that investigated the use of redundancy to define various types of constraints by integrating secondary tasks that express the constraints with the main task [24; 25; 26]. A global objective function is used in [27] to determine a balance between the main task and the secondary tasks by using the redundant DOFs of the robot with respect to the main task. However, significant perturbations may be occurred by the obtained motions which are generally incompatible with the main task. In another classical method [28], the authors employed a gradient projection method to solve the redundancy resolution; nonetheless, this approach necessitates that the main task will not constrain all DOFs of the robot. In such cases, the main Jacobian will gain full rank, and there would be no redundancy space left for projecting any constraint. This is a drawback of the traditional gradient projection technique. In [23], a projection operator for the redundant systems was proposed based on a task function specified as the norm of the usual error; in this approach, even if the main task is full rank, this projection operator allows the secondary tasks to be completed.