Joint-Smooth Toolpath Planning by Optimized Differential Vector for Robot Surface Machining Considering the Tool Orientation Constraints

The flexible robot has more advantages over the traditional machine tools in machining complex workpieces like the 3D-printed part which has less residual material for removal. In robot machining, the geometric smoothness of moving joints is vital for enhancing efficiency and accuracy and the tool orientation should be limited in certain regions considering the interfering requirements. As the robot has six DoFs at least, redundant DoFs are observed for robot surface machining, which can be employed to optimize the smooth machining process under the tool orientation requirements. In this paper, the tool posture differential vector along the tool-tip path curve is optimized firstly. The whole trajectory is numerically integrated by the optimized differential vector subsequently. In each step, the minimum 2-norm of the joints’ differential vector along the tool path curve is set as part of the optimization objective to ensure the minimal change of joints. Furthermore, a state-related optimization objective for the differential vector is established to keep the tool orientation away from the boundary of the feasible region. Combining with the two objectives, the tool posture differential vector along the tool-tip path is optimized and the whole machining process is obtained by the numerical integration method. As a case study, the joint trajectories for an inclined butterfly curve are planned by the algorithm and machined by the UR-5 robot with the ROS controller. In addition, a comparative experiment is also provided to verify the effectiveness and optimality of the proposed method.