## 1 Introduction
An objective function is formed using the introduced or selected local, task based or global kinematic index and the objective function is then subject to minimization [8] or maximization [6; 7; 9; 10; 11; 12]. In all cases, the manipulator kinematics were at the core of the determination of the optimization process. Due to the complexity of the problem, the search method is usually based on soft AI techniques such as Genetic Algorithms [6; 7; 8; 10]. However, most of these proposed methods are applied offline and the results presented by the authors are based on simulations rather than experimental verification. From the presented works, only [12] is verified using a physical system. As such, these results represent the upper limit of the ones expected from the physical system. One such simplification is that when kinematic tasks are simulated, the dynamics of a manipulator are either not considered or simplified to a degree that their influence is negligible. The present work presents a method for the optimal placement of a kinematic robotic task inside the workspace of a manipulator. The presented approach presents similarities to previous work by the authors such as [7]; however, its novelty is based on two respective points. Firstly, the optimal location of a kinematic task within the workspace takes into consideration the minimum singularity free paths that the manipulator's end effector may utilize in its motion between different task points in the respective sequence that describes the task. This was not considered previously, and singularity avoidance was assumed on the basis of the index value at the considered task points. As such, there was no guarantee that the manipulator would not reach a singular posture during its motion between consecutive points. The consideration of the minimum singularity free paths allows for the derivation of a solution ensuring the execution of the task under the certainty that during the end effector motion the manipulator will not reach any singular configuration. This consideration was first presented in [12]; however, in a global fashion. In this paper, the avoidance of singular postures during the end effector motion is conducted in a task-based fashion. Moreover, the simulation results for the optimal task placement are experimentally verified in order to provide an insight on the validity of the computational results of the proposed method, i.e., the execution of a kinematic task under constant increases kinematic performance. The main aim of the method presented is to allow the designer to derive the optimal location of a kinematic task within the robot's workspace, so as the required joint speeds for the generation of the required end effector velocity will be minimized. As a process is proposed to develop task-based kinematic indices base on well-established local indices, such as the Manipulator Velocity Ratio [5; 7]. In order to achieve the prescribed aims, the methodology presented aims for the maximization of the minimum value of the developed task-based kinematic performance indices. Given the computational results from the application of the proposed method, a physical experimental workcell is setup and the examined tasks are executed. Two types of robotic tasks are considered--a pick and place and a path-following task. The experimental workcell setup utilizes a UR-5 serial manipulator [13]. Additionally, in order to determine the validity of the method both the optimal results as well as the results for a considered \"bad\" task placement location are utilized for the experiments, and in both cases end effector velocity and joint speeds along with the required time for task execution are measured. The experimental results for both the \"bad\" and \"best\" task placements are evaluated in contrast to examine the validity of the proposed method.