Solution for Ill-Posed Inverse Kinematics of Robot Arm by Network Inversion

Table 5

Estimated joint angles, calculated end-effector coordinates, and errors(a) with regularization $F_3$(x) and (b) without regularization for ill-posed problem of instability.

(a)

	Joint angles (${}^{°}$) ($\theta$ 1, $\theta$ 2, $\theta$ 3)	End-effector coordinates (x, y)	MSE of end-effector coordinates
1	(53.67, 152.29, 96.80)	(60.98, 12.08)	1.56
2	(50.75, 165.75, 117.70)	(70.11, 28.02)	12.69
3	(57.45, 178.11, 90.36)	(57.96, 33.22)	3.81
4	(55.85, 188.36, 104.63)	(59.33, 46.03)	12.38
5	(28.37, 168.91, 285.48)	(38.81, 48.39)	1.69
6	(37.31, 183.61, 248.99)	(36.31, 66.04)	12.45
7	(34.15, 195.49, 265.50)	(22.99, 60.86)	2.20
8	(42.89, 211.92, 230.95)	(12.31, 73.71)	11.75

(b)

	Joint angles (${}^{°}$) ($\theta$ 1, $\theta$ 2, $\theta$ 3)	End-effector coordinates (x, y)	MSE of end-effector coordinates
1	(53.67, 152.29, 96.80)	(60.98, 12.08)	1.56
2	(55.03, 163.23, 101.18)	(63.54, 23.65)	4.82
3	(59.11, 174.72, 92.30)	(58.02, 33.24)	3.87
4	(60.25, 182.58, 94.85)	(56.34, 41.34)	8.12
5	(66.21, 196.54, 75.65)	(43.78, 46.17)	3.89
6	(67.99, 208.19, 78.62)	(37.89, 54.92)	6.40
7	(71.44, 241.13, 61.29)	(18.38, 57.72)	3.50
8	(74.08, 253.47, 69.53)	(6.84, 63.03)	4.22