Using the Bees Algorithm for wheeled mobile robot path planning in an indoor dynamic environment

Figures & data

Figure 1. Configuration space.

Figure 2. Flowchart of the Bees Algorithm.

Figure 3. Proposed schema for path planning.

Figure 4. Generation of the initial population function.

Figure 5. Modified method to initiate population.

Figure 6. Local search process.

Figure 7. Flow chart of local search.

Figure 8. Sensors distribution.

Figure 9. There is no collision.

Figure 10. There is collision.

Figure 11. Modified local search.

Figure 12. Summary of the implementation of the proposed method in static case.

Figure 13. Evolution of the solution.

Table 1. The static environment

Figure	Optimal length	Modified method to initiate population	PRM result	Failure ratio of PRM
9(a)	8.59	×	17.7	0
9(b)	16.57	×	9.9	0
9(c)	14.2	×	14.2	0.5
9(d)	21.09	√	23.63	0.7

Figure 14. Static environment.

Figure 15. Failure examples of the PRM.

Table 2. The mean and the standard deviation

Map number	The traditional Bees Algorithm		The modified Bees Algorithm
	Mean	Standard deviation	Mean	Standard deviation
1	11.4943	0.0086	11.47	0.0082
2	14.6325	0.0169	14.62	0.0211
3	8.59	0.026	8.59	0.0360
4	13.3160	0.0224	13.28	0.0520
5	14.2	0.5924	13.97	0.0550
6	14.0594	0.0489	13.9424	0.0171
7	14.1136	0.3232	13.63	0.0046
8	13.5821	0.0838	13.45	0.0102
9	16.571	0.4869	16.16	0.1096
10	14.6951	0.7793	13.86	0.0233

Figure 16. The set of studied map.

Figure 17. Standard deviation of the results.

Figure 18. Case study 1 results.

Figure 19. Case study 2 results.

Figure 20. Case study 3 results.

Table 3. Comparision between the proposed method and GA

Figure	State	The proposed method	GA 1	GA 2	GA 3
20(a)	Static	22.22	22.42	22.42	22.72
20(b)	Dynamic	22.62	22.84	22.84	23.48
20(c)	Static	25.98	26.24	26.28	26.83
20(d)	Dynamic	27.6	27.86	28.40	28.96

Figure 21. Amigobot robot.

Figure 22. Collision avoiding of static obstacle.

Figure 23. Collision avoiding of moving obstacle.