# Path Planning under Force Control in Robotic Polishing of the Complex Curved Surfaces
## 4 Conclusions  
This paper presented a robotic polishing method for complex curved surfaces based on a combination of tool path planning, force control, and optimized polishing parameters. From the above results and discussions, the following conclusions could be drawn:  
(a) Robot polishing is a difficult task, in which the key considerations include: the surface area coverage, best-suited polishing parameters, the stable contact force, especially for complex surfaces, and the required surface quality (glossiness and uniformness). The presented method uses the divide-and-conquer strategy and is composed of four steps: workstation building, surface division, tool path generation, and tool path stitching. Based on the results of the tests on polishing eyeglass frames, this method was effective. It ensured the surface quality and avoided the robot running into singularities, joint limits, and jerks.  
(b) The surface division is important. It decomposes a complex surface into a number of plain or simple curved surfaces. For each piece of surface, the robot could move smoothly and speedily.  
Figure 23: Eyeglass frame: (**a**) before polishing and (**b**) after robotic polishing.  
Figure 22: Feed rate and time for selected polishing area on eyeglass frame at three different cycles.  
The main considerations in breaking a complex curved surface are edges of faces, variation in the orientation of surface normal vector, the robot joints limit, the curvature of the part surface, the size, and complexity of the surface.  
(c) Three major research directions in robotic polishing are new tool design, path planning, and force control between tool and surface. However, the correct selection of the input process parameters could increase the efficiency exponentially and could be implemented with all three improvement techniques. The optimization of the parameters in this study was achieved by using full factorial DOE (30 experimental runs). The optimized input polishing parameters for the eyeglass frame were _SFPM_ (3750), feed rate (45 mm/s), and no. of polishing cycles (2 cycles).  
Based on the experimental results on polishing eyeglass frames, the presented method could achieve a high-quality surface with an average roughness of 0.0185 \(\upmu\)m in 79 s. In addition, the entire surface was well covered and the average improvement in glossiness was 67 G, which was 88% improvement in just two polishing cycles. Moreover, all the scratches were eliminated successfully. It was believed that the presented method could be used on the shop floor directly.  
[PERSON], [PERSON], and [PERSON] contributed to the main idea of this paper; [PERSON] performed the experiments, analyzed the data and wrote the paper; [PERSON] is the project principal investigator; [PERSON] gave some system improvement suggestion and the paper structure, [PERSON] gave some data analysis and revision suggestions.  
This research was supported by Science and Technology Planning Project of Guangdong Province (2017B09014004) and CAS-HK Joint Laboratory of Precision Engineering. Author ([PERSON]) acknowledges CAS-TWAS President's Fellowship for sponsoring his Ph.D. at the University of Chinese Academy of Sciences, Beijing, 100049, China.  
The authors declare no conflict of interest.