Task-Oriented Evaluation of the Feasible Kinematic Directional Capabilities for Robot Machining

Abstract

Performing the machining of complex surfaces can be a challenging task for a robot, especially in terms of collaborative robotics, where the available motion capabilities are greatly reduced in comparison with conventional industrial robot arms. It is necessary to evaluate these capabilities prior to task execution, for which we need efficient algorithms, especially in the case of flexible robot applications. To provide accurate and physically consistent information about the maximum kinematic capabilities while considering the requirements of the task, an approach called the Decomposed Twist Feasibility (DTF) method is proposed in this study. The evaluation of the maximum feasible end-effector velocity is based on the idea of decomposition into the linear and angular motion capabilities, considering a typical robot machining task with synchronous linear and angular motion. The proposed DTF method is presented by the well-known manipulability polytope concept. Unlike the existing methods that estimate the kinematic performance capabilities in arbitrarily weighted twist space, or separately in the translation and the rotation subspace, our approach offers an accurate and simple solution for the determination of the total kinematic performance capabilities, which is often highly required, especially in the case of robot machining tasks. The numerical results obtained in this study show the effectiveness of the proposed approach. Moreover, the proposed DTF method could represent suitable kinematic performance criteria for the optimal placement of predefined tasks within the robot workspace.

Toward Optimal Robot Machining Considering the Workpiece Surface Geometry in a Task-Oriented Approach

“…Similarly, as in [30], the Jacobian matrix is partitioned into two submatrices, i.e., the translational submatrix J T ∈ R 3×n and the rotational submatrix J R ∈ R 3×n :…”

“…For robot-to-workpiece placement for large-scale welding systems [24], the authors generated a kinematic performance map based on a kinetostatic condition index that was used to optimize robot configurations in a polishing application [25], introduced a custom index for robot-based placement optimization demonstrated in a trim application in shoe manufacturing [26], and optimized a workpiece placement for the robotic operation in challenging manufacturing tasks [27,28] and surface finishing [21,29]. An interesting new optimization approach was also introduced to maximize the available velocities of the end-effector during a task execution of path following in robot machining called the decomposed twist feasibility method [30].…”

“…However, the relation of the proposed measure to the relevant robot operational quantity, such as velocity, is unclear. An alternative to manipulability ellipsoids is presented by manipulability polytopes [30,[63][64][65][66][67][68], which can provide more accurate information about the operational space motion capability since they consider infinity norm metrics instead of Euclidean norm metrics. However, the problem of a dimensional non-homogeneous Jacobian matrix due to the unit inconsistency in robotics still presents a challenge since most approaches demonstrated limitations in terms of their physical interpretations, though task-oriented homogeneous Jacobians and associated performance indices showed some promising results and potential for further development [30,69].…”

“…However, all the manipulability-related performance indices above, and many others not mentioned, are based on the Jacobian matrix of the velocity kinematics description. In this paper, we focus on the problem of path following velocity performance in robot machining of a workpiece with complex geometry, similar to our previous work [30], where we considered a workpiece with a predefined path. Now, we propose a task-oriented robot kinematics description, which considers motion constraints imposed by the workpiece surface geometry explicitly; thus, a priori knowledge about the machining path is not required to evaluate the available velocity performance.…”

Toward Optimal Robot Machining considering the Workpiece Surface Geometry in a Task-Oriented Approach

“…For robot-to-workpiece placement for large-scale welding systems [24], the authors generated a kinematic performance map based on a kinetostatic condition index that was used to optimize robot configurations in a polishing application [25], introduced a custom index for robot-based placement optimization demonstrated in a trim application in shoe manufacturing [26], and optimized a workpiece placement for the robotic operation in challenging manufacturing tasks [27,28] and surface finishing [21,29]. An interesting new optimization approach was also introduced to maximize the available velocities of the end-effector during a task execution of path following in robot machining called the decomposed twist feasibility method [30].…”