# Analysis and Simulation of Polishing Robot Operation Trajectory Planning
## 2 Materials and Methods
### Spiral Arc Trajectory Planning of Quintic Polynomial Interpolation Algorithm
This absence of any sharp or abrupt changes  
Figure 9: Terminal trajectory of the robot. (**a**) Quintic polynomial interpolation for end-effector trajectory of the robot. (**b**) Quintic B-spline interpolation for the end-effector trajectory of the robot. that the robot's movements are not only precise but also free from any jarring motions that could potentially damage the mechanical components or compromise the accuracy of the task being performed. Furthermore, the visualization in Figure 9 underscores the effectiveness of utilizing B-spline interpolation for trajectory planning by demonstrating the smooth and continuous motion path traced by the robot's end-effector. This seamless progression, devoid of any jerky movements, underscores the robustness and reliability of the planning method. The end position values presented in this figure serve as concrete evidence that the trajectory is not only well defined but also accurately executed, underscoring the high degree of control and predictability achieved through this approach. Additionally, the smooth motion trajectories generated by the B-spline interpolation algorithm are particularly advantageous in applications requiring precise and delicate manipulation, such as in surgical robotics, where even the slightest deviation or instability can have significant consequences. By ensuring that the robot moves smoothly and without any large vibrations, the use of this interpolation technique significantly enhances the safety and effectiveness of such operations. Thus, we believe that integrating the quintic B-spline interpolation algorithm into trajectory planning strategies serves as a valuable tool for achieving smooth and stable robot movements. As demonstrated in Figures 8 and 9, this approach not only ensures precision in the execution of complex trajectories but also minimizes the risk of mechanical stress and wear, thereby enhancing the overall performance and longevity of the robotic system. Moreover, the calculated MATLAB data were used to simulate the planning of a spatial spiral curve path for a space station polishing operation in RobotStudio 6.08, comparing three methods: no interpolation, quintic polynomial interpolation, and quintic B-spline interpolation. Enabling the simulation signal monitor in RobotStudio software, set up the signal monitor to record the total motor power and cumulative motor energy. Export the total motor power and cumulative motor energy for each of the three scenarios. Using Origin as an analytical tool, these data are processed and plotted on line charts as shown in Figures 10 and 11. Figure 10 compares the energy consumption of three interpolation methods: no interpolation, quintic polynomial, and quintic B-spline interpolation. It is observed that no interpolation consumes the least power, highlighting its efficiency despite the potential compromise in motion smoothness. Quintic polynomial interpolation, while providing smoother trajectories, requires significantly more power due to frequent dynamic adjustments in motor control. In contrast, quintic B-spline interpolation offers a balance, showing moderated energy consumption with improved trajectory smoothness. The data from Figure 11 shows that the energy consumption of the no-interpolation and quintic B-spline interpolation methods are comparable, highlighting that the advanced quintic B-spline interpolation achieves enhanced motion smoothness and accuracy without significantly increasing energy use compared to simpler or no-interpolation methods. This underscores the quintic B-spline's advantage of optimizing motion control while maintaining energy efficiency, making it an ideal choice for precision-demanding applications where both factors are crucial.