# Trajectory Optimization with Dynamic Drivable Corridor-Based Collision Avoidance
## 4 Simulation Results and Discussion
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Average CPU Time (s)**} & **99 Percentile CPU** & **Solution Success** \\  & & **Time (s)** & **Rate** \\ \hline Planner 1 & 45.6180 & 170.6144 & - \\ \hline Planner 2 & 2.6950 & 3.8358 & 100\% \\ \hline This work (0.05 m resolution) & 1.1057 & 1.9922 & 100\% \\ \hline This work (0.1 m resolution) & 1.0422 & 1.7455 & 100\% \\ \hline This work (0.2 m resolution) & 1.0510 & 1.9564 & 100\% \\ \hline This work (0.3 m resolution) & 0.9909 & 1.7857 & 99\% \\ \hline This work (0.4 m resolution) & 1.0159 & 1.7268 & 100\% \\ \hline This work (0.5 m resolution) & 1.0071 & 1.7383 & 99\% \\ \hline This work (0.6 m resolution) & 1.0822 & 3.9333 & 98\% \\ \hline This work (1.0 m resolution) & 1.2533 & 4.8272 & 88\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of solution speed and success rate across different methods. Table 4 demonstrates that as the grid size increases from 0.05 m to 0.3 m, the average computation time shows a consistent decreasing trend. This observation indicates that, within this parameter range, reducing the resolution can effectively improve the solver's computational efficiency. However, when the grid size exceeds 0.5 m, not only does the success rate of the solver decrease, but the computation time also increases. The primary reason for this phenomenon is the significant increase in the optimizer's computation time, as illustrated in Figure 12: When the grid resolution is too low (i.e., grid sizes are large), although the number of grids representing environmental obstacles is reduced, the passable space is significantly compressed. This leads to a substantial deviation between the constructed DC and the initial solution. Such deviation directly increases the complexity of the search space during the optimization phase and may introduce additional nonlinearities or unfavorable local optima, thereby increasing the difficulty of solving the problem. Before obtaining the converged optimal trajectory (depicted by the blue curves in Figure 12), the optimizer must undergo multiple iterations, during which several intermediate trajectories (shown as black curves) are generated. This iterative process significantly increases the overall computation time. To further evaluate the performance of the proposed method, we designed an experimental scenario (c.f. Figure 13). Initially, a small number of obstacles were placed in the environment, and the optimization times of both Planner 2 and the proposed method were recorded. Subsequently, the number of obstacles was gradually increased from 1 to 8, and  
Figure 11: Scenario of invalid DC establishment in narrow areas: (**a**) initial path at 1 m resolution and (**b**) paved DCs at 1 m resolution. Figure 12: Four representative time-consuming scenarios requiring multiple iterations under a grid resolution of 1 m: (**a**) first scenario; (**b**) second scenario; (**c**) third scenario; and (**d**) fourth scenario. the optimization times of the two planners were measured. The results are summarized in Figure 14. As shown, with the increase in the number of obstacles, the optimization time of Planner 2 exhibits a continuously rising trend, whereas the optimization time of the proposed method remains within a relatively stable range without significant growth, demonstrating its superior scalability in complex environments. In summary, our approach significantly reduces the computational time compared to Planner 2 due to the following key reasons: First, in our approach, both the DC and the occupied grids representing obstacles are represented as AABBs. This representation allows the collision detection process to be performed via simple range comparisons, avoiding com  
Figure 14: Optimization time comparison under different numbers of obstacles.