# A Dynamic Multiple-Query RRT Planning Algorithm for Manipulator Obstacle Avoidance
## 5 Experiment
### Simulation-Platform  
The BG-RRT algorithm is inherited by C++ in ompl:base::planner to evaluate the efficiency of the proposed method in the simulation platform. The dynamic obstacle avoidance strategy is encapsulated as a ROS node to move_group interface. According to the uncertainty modeling [19], the \(CollisionObject\) function under the moveit_msgs class is used to plan the dynamic obstacle.  
The manipulator works in complex environments that include stationary obstacles and dynamic obstacles. Thus, the environments are set, as shown in Figure 12, compared with the ERRT algorithm [12] and the DRRT algorithm [13] to test the efficiency of the DBG-RRT algorithm with 100 simulation times in each map, as shown in Table 1. The difficulty of replanning from the map in Figure 12a to the map in Figure 12c is increasing. Although there are more obstacles in Figure 12b, the process of replanning is relatively simple. To experiment clearly, the manipulator's maximum speed and maximum accelerationare restricted to 30%. In addition, when the target is met, a one-second pause is established to indicate manipulator operation.  
As shown in Table 1, the ERRT algorithm does not perform well, because the waypoint cache method of the ERRT algorithm may directly grow to the goal with obstruction. That makes the ERRT algorithm cost a lot at some time. As for the manipulator, which has a complex joint space, the DRRT algorithm has a slower response, because of the replanning distance more than the DBG-RRT algorithm.The DBG-RRT algorithm maintains a high success rate in more complex environments. At the same time, the BG-RRT algorithm can also enhance the success rate. Therefore, the DBG-RRT algorithm has distinct advantages over other dynamic algorithms.  
The manipulator behavior is separated into six phases in Figure 13, once complete manipulator dynamic obstacle avoidance from the start to the objective has begun and next to the start in Map 3. In the beginning, the green dynamic obstacle is emerging in a manipulator workspace. In Figure 13b, the manipulator begins to execute the initial planning, and the dynamic obstacle is changing position. If the manipulator travels along the intended planning with the cyan line as depicted in Figure 13c, it will collide with the dynamic obstacle. Then, a new trajectory is planned, and the manipulator moves along with it, as shown in Figure 13d. After that, the manipulator arrives at the goal in Figure 13e and plans a trajectory to the start position in Figure 13f. As shown in Figure 14, the movement of the manipulator is gentle, and there is no abrupt change in the process of obstacle avoidance, plotted as \(p_{turn}\). The manipulator's joints move smoothly during obstacle avoidance.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Algorithm** & \begin{tabular}{c} **Avg. Initial** \\ **Planning Time** \\ \end{tabular} & \
\begin{tabular}{c} **Avg. Dynamic** \\ **Planning Time** \\ \end{tabular} &
\begin{tabular}{c} **Success Rate** \\ \end{tabular} \\ \hline \multirow{3}{*}{Map 1} & ERRT & 0.143 & 0.051 & 1.00 \\  & DRRT & 0.144 & 0.064 & 0.97 \\  & DBG-RRT & 0.018 & 0.017 & 1.00 \\ \hline \multirow{3}{*}{Map 2} & ERRT & 0.163 & 0.071 & 0.98 \\  & DRRT & 0.157 & 0.083 & 0.98 \\  & DBG-RRT & 0.018 & 0.022 & 1.00 \\ \hline \multirow{3}{*}{Map 3} & ERRT & 0.436 & 0.139 & 0.87 \\  & DRRT & 0.419 & 0.204 & 0.91 \\ \cline{1-1}  & DBG-RRT & 0.036 & 0.021 & 1.00 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The experiment data to test dynamic strategy.  
Figure 12: Experiment maps. In the workspace of the manipulator, (**a**) has no static obstacles, (**b**) has three static tables, and (**c**) has a static table. The start point is plotted in green, and the goal point is plotted in red.