# Motion Planning for Mobile Robot with Modified BIT+
## 4 Simulation
### Modified BIT* Planner
* Few obstacles with narrow channel: Figure 8 shows the environment with fewer obstacles and a narrow channel. The coordinates of the start point and the goal point are (0 m, 0 m) and (0 m, 5.5 m) respectively. The green solid line is the path generated by the global planner. From the map, we can see that there are two obstacle between start and goal, and the optimal path for mobile robot is to across the narrow channel between the obstacle. For sampling-based planning algorithm that uses a random sampling method like RRT*, the sampling points are rarely located in the narrow channel. So it is difficult to find an good path when iterations are not enough. In Figure 7(a), instead of passing through a narrow channel, the path found by RRT* after 3000 iterations bypasses the obstacles above to the goal. In addition, this path has unnecessary twists and turns, which is not suitable for mobile robots. Figure 7(b) shows the solution of BIT*. Compared with RRT*, BIT* successfully found a path through the narrow channel and it uses 1600 iterations. However, in our multiple tests, BIT* does not always find a solution as shown in Figure 7(b) and sometimes BIT* can only find a path around obstacles with 1600 iterations. The path from start to goal in Figure 7(c) shows the better performance of our proposed method. Benefit from the stretch method, the modified BIT* can find a shorter and smoother path through the narrow channel with less iterations.
* Multiple obstacles: In practical applications, mobile robots may need to plan a collision-free path in environment with multiple obstacles. Based on this requirement, we design an environment shown in Figures 9-11 with intensive obstacles to test the performance of the three planners. The coordinates of the start point and the goal point are (0 m, 0 m) and (-3 m, -2 m) respectively. Firstly, by observing the map, we can know that there are two kinds of good paths from the start to goal. One is to across the top left of goal, the other is through the top of the goal. So we show three different solutions for each planner to see that which kind of solutions these planners tend to select.  
In Figure 9, the paths found by RRT* with 3000 iterations are through top of the goal. However, the cost of these paths always are higher than those generated by the other two planners. Besides, some unnecessary turns occur in the path, resulting in relatively high cost, as shown in Figure 8(b),c. In Figure 10, with 1600 iterations, BIT* tend to find paths through the top left of the goal in most cases, which is shorter than paths found by RRT*. Modified BIT* can always find shorter path that is through the top left of the goal only with 800 iterations, much less than BIT* and RRT*, as shown in Figure 11. Compared to above two planners, the path found by modified BIT* is much smoother that is more suitable for mobile robot. Table 1 shows the average of the 10 planning results of the three planners in this scenario.  
Figure 8: The performance of three planner in a scenario with few obstacles and a narrow channel.  
Due to the simple stretch method, no matter in the environment with few obstacles or dense obstacles, our proposed modified BIT* always find shorter path than BIT* and RRT* with less iterations which is meaning faster converging rate.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Planner** & **Path Length (m)** & **Iterations** & **Computational Time (ms)** \\ \hline RRT* & 4.16 & 3000 & 106.3 \\ BIT* & 4.05 & 1600 & 90.6 \\ Modified BIT* & 3.92 & 800 & 64.2 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The average of ten results of three planners.  
Figure 11: Solutions of modified BIT* in a scenario with multiple obstacles, 800 iterations.  
Figure 9: Solutions of RRT* in a scenario with multiple obstacles, 3000 iterations.