# Global Time-Varying Path Planning Method Based on Tunable Bezier Curves
## 6 Simulation
### Comparison of Different Methods  
For path planning of moving objects, traditional path planning methods used for obstacle avoidance cannot consider multiple conditions: (1) real-time obstacle avoidance; (2) global obstacle avoidance; and (3) obstacle avoidance under multiple obstacles. Up to now, a variety of path planning methods are proposed, and the comparison between these methods is summarized in Table 1.  
It can be seen from the table that most methods cannot take into account multiple-obstacle avoidance conditions at the same time. It can be seen from the simulation results that method [7] and method [9] not only cannot realize real-time path planning, but also the simulation time in the static path is longer than that in the present method. Although global real-time path planning can be achieved for multiple obstacles in paper [21], the PSO algorithm is adopted in the algorithm, which takes a certain amount of time to perform iterative operations in the process of solving the key points of the path. However, the path that meets multiple conditions can be solved without the help of an intelligent optimization solving algorithm in this method and the planned path is smoother. The distance between the robot arm and the obstacle is relatively close from 90 s to 100 s. During this period, path planning was performed through RRT, Q-RRT*[33], MDA+RRT [7] and GTVP to obtain Figures 10-13. In these four pictures, (a)-(f) are the corresponding simulation results of the six moments 90 s, 92 s, 94 s, 96 s, 98 s and 100 s, respectively. In the figure, the black solid part is the obstacle, the red line segment is the planned path and the black dot in Figure 13 is the feature point. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Methods** & **Real-Time** & **Global** & **Multi-Obstacle** & **Types of Path** & **Application Objects** \\ \hline Method 1 [7] & \(\times\) & \(\checkmark\) & \(\checkmark\) & RRT/ Straight path & Manipulator \\ Method 2 [9] & \(\times\) & \(\checkmark\) & \(\checkmark\) & VDSM/ Straight path & Manipulator \\ Method 3 [3] & \(\times\) & \(\times\) & \(\checkmark\) & Bezier curves & Wheeled mobile robot \\ Method 4 [20] & \(\times\) & \(\times\) & \(\checkmark\) & Bezier curves & Autonomous vehicles \\ Method 5 [21] & \(\checkmark\) & \(\checkmark\) & \(\checkmark\) & Bezier curves & Mobile robots \\ Method 6 [22] & \(\checkmark\) & \(\times\) & \(\checkmark\) & Bezier curves & Robot \\ Method 7 [23] & \(\checkmark\) & \(\times\) & \(\times\) & Bezier curves & Mobile robots \\ Method 8 [24] & \(\checkmark\) & \(\times\) & \(\times\) & Bezier curves & Robot \\ Method 9 [33] & \(\times\) & \(\checkmark\) & \(\checkmark\) & RRT & Robot \\ GTVP & \(\checkmark\) & \(\checkmark\) & \(\checkmark\) & Bezier curve & Manipulator \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Features of different algorithms. Figure 9: The closest distance between several key nodes and obstacles. Figure 11: Simulation results obtained by Q-RRT* [33]. (**a**) \(t=90\) s. (**b**) \(t=92\) s. (**c**) \(t=94\) s. (**d**) \(t=96\) s. (**e**) \(t=98\) s. (**f**) \(t=100\) s.  
As can be seen from Figure 10, the path planned by the RRT algorithm requires a small number of nodes, but the total length of each planned path is long and there are many turning points. When the manipulator moves along this path, the joint angle will exceed the limit of the deflection angle. As can be seen from Figures 11 and 12, the path length planned by the Q-RRT* algorithm or MDA+RRT algorithm is short, but the distance between the path and obstacles is close, and the planned path has uncertainty at any time. As can be seen from Figures 10-12, the path planned by other path planning methods has the following characteristics: (1) the distance between the path and the obstacle is relatively close, which cannot meet the conditions of obstacle avoidance by the manipulator;  
Figure 12: Simulation results obtained by MDA+RRT.