Kinematic study and implementation of a bio-inspired robotic fish underwater vehicle in a Lighthill mathematical framework

Robotics and Biomimetics

Table 1 Trajectory (geometric) points for mathematical oscillatory/undulatory propulsive waveforms

Node number	Oscillatory sin		LH quad		LH cubic		NURB quad
	xpos	ypos	xpos	ypos	xpos	ypos	xpos	ypos
1 (start point)	0.500000	0.029700	0.500000	0.029700	0.500000	0.029700	0.500000	0.029700
2	0.635240	0.160918	0.634913	0.159944	0.634781	0.159549	0.598402	0.046079
3	0.767541	0.245599	0.767169	0.245283	0.767018	0.245155	0.723631	0.204411
4	0.853758	0.283287	0.853553	0.283192	0.853471	0.283154	0.827144	0.270115
5	0.889791	0.296484	0.889726	0.296460	0.889699	0.296450	0.880214	0.292851
6	0.898802	0.299593	0.898791	0.299589	0.898787	0.299587	0.896969	0.298948
7	0.899911	0.299970	0.899910	0.299969	0.899910	0.299969	0.899745	0.299912
8	0.899994	0.299998	0.899994	0.299998	0.899994	0.299998	0.899982	0.299994
9 (end point)	0.900000	0.300000	0.900000	0.300000	0.900000	0.300000	0.900000	0.300000