# Region-Based Approach for Machining Time Improvement in Robot Surface Finishing
###### Abstract
Introducing the workpiece surface constraint into the kinematic analysis provides a more accurate evaluation of the robot's available velocity capabilities in a reduced-dimensional space. The concept of manipulability, first introduced by [PERSON] [33], provides a qualitative method for assessing the ease with which a robot can move in its operational workspace. This concept is typically represented by the manipulability ellipsoid, derived from the robot's velocity kinematics description using the singular value decomposition of the associated Jacobian matrix [34]. However, traditional manipulability indices often suffer from physical inconsistencies due to the mixing of different units of linear and angular velocity [35]. To overcome these limitations, the author's work [32] introduces a task-oriented approach to robot kinematics, focusing on the surface constraints imposed by the workpiece geometry. The strategy involves the development of a task-specific augmented inverse Jacobian matrix, which incorporates motion constraints derived from the differential surface geometry of the workpiece. This matrix transforms the robot's task space into a two-dimensional surface tangent plane, effectively avoiding the physical inconsistencies associated with mixed linear and angular velocity units. The resulting manipulability analysis focuses solely on linear velocities, providing a more consistent and meaningful evaluation of the robot's motion capabilities. Building on this theoretical framework, our study employs clustering techniques, specifically K-means clustering [36], to segment the workpiece surface into regions with similar kinematic characteristics. Clustering the surface into manageable sections allows for more precise and optimized surface finishing strategies. An optimization algorithm determines the optimal machining directions and maximum feasible speeds for each region, which enables optimal surface finishing path planning concerning the machining time. The practical implications of this approach are demonstrated through numerical experiments involving semi-complex workpiece geometries. These experiments validate the effectiveness of the proposed method in enhancing the robot's machining time performance, while ensuring task feasibility within the constraints of the cobot's motion capabilities. By evaluating the robot's kinematic capabilities accurately and optimizing the machining paths, the proposed method improves the efficiency of the robot machining task significantly. In addition to improving the robot's machining performance, this approach addresses the critical issue of workpiece positioning. The optimal positioning of the workpiece is crucial for maximizing the robot's kinematic capabilities and ensuring that the machining tasks are performed efficiently. The proposed method uses an optimization algorithm to determine the best position for the workpiece, considering the robot's motion constraints and the geometry of the workpiece. This ensures that the robot can perform the machining taskswith maximum efficiency, thus additionally reducing the overall machining time. Reducing machining time is a measure of efficiency and a critical factor in enhancing production throughput and reducing operational costs. Lower machining times translate directly into faster cycle times, allowing for increased output within the same operational hours. This is particularly significant in MHP, where the process is time-consuming and can extend over several hours. Combining clustering techniques into the kinematic analysis represents a significant advancement in robot machining. The method allows for more detailed and precise kinematic evaluations by dividing the workpiece surface into regions. This segmentation enables the optimization algorithm to tailor the machining strategies to the specific characteristics of each region, ensuring that the robot operates at its maximum capability throughout the entire machining process.