Comparison of Three Different Curves Used in Path Planning Problems Based on Particle Swarm Optimizer

Table 5

Best result of every curve.

Problems		Bezier curve	Ferguson curve	𝜂3 curve 𝑛=2	𝜂3 curve 𝑛=3
F1	Mean	14.7559	14.6720	14.8622	14.8915
	Std.	0.0087	3.065𝐸−5	0.2007	0.1053
	Min	14.6626	14.6626	14.6614	14.6599
	Max	15.0132	14.6830	16.9015	15.7512
F2	Mean	14.6486	14.6395	14.7317	14.7678
	Std.	0.0002	6.640𝐸−5	0.0902	0.0323
	Min	14.6242	14.6245	14.65536	14.6682
	Max	16.3361	14.6531	16.1707	15.5873
F3	Mean	14.9475	14.8069	15.8886	15.3092
	Std.	0.2976	0.0133	0.2801	0.7615
	Min	14.7240	14.6170	15.6068	14.7554
	Max	17.2080	15.2238	17.3939	17.1826
F4	Mean	14.7363	14.7361	15.8886	14.7421
	Std.	1.451𝐸−5	2.494𝐸−5	0.2801	6.941𝐸−4
	Min	14.7313	14.7291	15.6068	14.6988
	Max	14.7455	14.7497	17.3939	14.8068
F5	Mean	16.3361	16.8374	16.4134	16.3798
	Std.	0.0012	0.7757	1.865𝐸−4	0.0037
	Min	16.2827	16.3204	16.3787	16.3254
	Max	16.4123	17.8547	16.4457	16.6216
F6	Mean	15.2860	16.5777	16.0209	15.7087
	Std.	0.0103	0.3785	0.3553	0.32256
	Min	15.2400	15.6083	15.3031	15.2387
	Max	15.7535	17.9068	16.8915	16.7263
F7	Mean	15.1967	17.3071	15.6069	15.6007
	Std.	0.1794	15.6542	0.3488	0.3273
	Min	15.0355	15.0326	15.2917	15.0145
	Max	16.6090	28.4035	16.8491	16.7801
F8	Mean	14.6644	15.4485	15.0064	14.6521
	Std.	0.0003	0.0218	4.680𝐸−4	7.786𝐸−4
	Min	14.6291	15.1707	14.9863	14.6327
	Max	14.7046	15.7448	15.0621	14.7619