**5.2. Evaluation results**

We evaluate the performance and path solution of search-based algorithms in two scenarios: partially known and unknown 2D grid environment with uniform resolution. The total expanded cells are averaged based on total replanning processes on each simulation instance, with 95% confident. The path solution of each algorithm is counted as the total cells that the robot has traversed from corner to corner of the map. We decrease the suboptimal bound of AD\* for 0.1 per step the robot travels until the suboptimal bound reaches 1.0 (optimal path).

**Figure 16** shows the speedup result throughout the evolution from Replanning A\* to AD\* with different *ε* suboptimal bounds as well as the trade-off of AD\*. The environment is initially generated randomly obstacles that occupy 25% of the map. The initial map is then input to the robot. While the robot is moving, we randomly change the cell states that are 15% of the map, thus forcing the robot to replan its path whenever it detects environmental

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As can be seen, AD\* has the highest performance that has least total expanded cells in replanning process; the higher the suboptimal bound, the better the performance. The reason is AD\* is inflated its heuristic function to make it greedier in expanding cells towards goal. It is interesting that path solution of AD\* is not much longer than optimal path. As the scale of map is increasing, the path between map corner is longer to travel, and thus, the robot is given enough time to improve its solution (path ratio with *ε* = 6.0 is gradually converged to the one

D\*LR slightly improves the performance of D\* Lite; it is because D\*LR relies on computation differences between Replanning A\* and D\* Lite. In fact, the pitfall of D\* Lite rarely happens in scenarios that the robot detects changes near its position. Replanning A\* does not have

The data confirms the fact that AD\*, in average throughout the increasing map scale, improves 125% and 194% performance compared to D\* Lite with *ε* = 3.0 and *ε* = 6.0, respectively. The

**Figure 17.** Comparison between search-based algorithms on unknown environment with increasing map scale in terms

incremental property and thus uses the highest computation.

path produces by AD\* only 1% longer than optimal path in average.

changes.

*ε* = 3.0 at 1.016).

of computation and path solution.

**Figure 15.** Simulated environment on our framework.

**Figure 16.** Comparison between search-based algorithms on partially known environment with increasing map scale in terms of computation and path solution.

**Figure 16** shows the speedup result throughout the evolution from Replanning A\* to AD\* with different *ε* suboptimal bounds as well as the trade-off of AD\*. The environment is initially generated randomly obstacles that occupy 25% of the map. The initial map is then input to the robot. While the robot is moving, we randomly change the cell states that are 15% of the map, thus forcing the robot to replan its path whenever it detects environmental changes.

As can be seen, AD\* has the highest performance that has least total expanded cells in replanning process; the higher the suboptimal bound, the better the performance. The reason is AD\* is inflated its heuristic function to make it greedier in expanding cells towards goal. It is interesting that path solution of AD\* is not much longer than optimal path. As the scale of map is increasing, the path between map corner is longer to travel, and thus, the robot is given enough time to improve its solution (path ratio with *ε* = 6.0 is gradually converged to the one *ε* = 3.0 at 1.016).

D\*LR slightly improves the performance of D\* Lite; it is because D\*LR relies on computation differences between Replanning A\* and D\* Lite. In fact, the pitfall of D\* Lite rarely happens in scenarios that the robot detects changes near its position. Replanning A\* does not have incremental property and thus uses the highest computation.

The data confirms the fact that AD\*, in average throughout the increasing map scale, improves 125% and 194% performance compared to D\* Lite with *ε* = 3.0 and *ε* = 6.0, respectively. The path produces by AD\* only 1% longer than optimal path in average.

**Figure 17.** Comparison between search-based algorithms on unknown environment with increasing map scale in terms of computation and path solution.

**Figure 16.** Comparison between search-based algorithms on partially known environment with increasing map scale in

terms of computation and path solution.

**Figure 15.** Simulated environment on our framework.

84 Advanced Path Planning for Mobile Entities

**Figure 17** describes the evaluation case on unknown environment. The environment is initially generated with random obstacles that occupy 15% of the map. The robot does not know the initial conditions; it will replan its path whenever it detects obstacles that do not exist in its map.

**Author details**

United Kingdom

**References**

10.1.1.38.1387

\* and Than D. Le2

University, Hồ Chí Minh, Vietnam

\*Address all correspondence to: eeit2015\_an.lt@student.vgu.edu.vn

1 Department of Electrical Engineering and Information Technology, Vietnamese-German

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2 Faculty of Engineering, Bristol Robotics Laboratory, Bristol University, Bristol,

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10.1007/978-3-319-33581-0\_15

An T. Le1

For unknown environment scenario, D\*LR performs significantly better than D\* Lite as increasing map scale. The reason is that if the replanned path is much longer than the initial path, which is the common case in unknown environment, the replanning process of D\* Lite is also expensive. AD\* still has the least computation compared to old search-based algorithm; it reduces drastically the computation of D\* Lite with 845% better performance, in the case *ε* = 10.0, while still maintains good path solution.
