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

Table 4

Estimated joint angles, calculated end-effector coordinates, and errors with (a) regularization $F_1$(x) and (b) regularization $F_2$(x), for ill-posed problem of nonuniqueness.

(a)

	Joint angles (${}^{°}$) ($\theta$ 1, $\theta$ 2, $\theta$ 3)	End-effector coordinates (x, y)	MSE of end-effector coordinates
1	(0.00, 145.90, 284.08)	(65.11, 11.37)	3.10
2	(0.00, 170.03, 285.01)	(56.91, 24.69)	3.89
3	(0.00, 182.40, 282.07)	(52.48, 30.30)	2.40
4	(0.00, 199.61, 284.23)	(41.55, 34.99)	8.68
5	(0.00, 217.91, 264.82)	(37.45, 43.67)	5.51
6	(0.00, 234.76, 245.68)	(32.11, 50.37)	4.23
7	(0.00, 252.69, 225.30)	(24.85, 55.13)	5.24
8	(0.00, 281.08, 189.01)	(13.93, 57.62)	5.34

(b)

	Joint angles (${}^{°}$) ($\theta$ 1, $\theta$ 2, $\theta$ 3)	End-effector coordinates (x, y)	MSE of end-effector coordinates
1	(90.00, 85.51, 152.49)	(55.35, 11.76)	6.74
2	(90.00, 106.39, 132.56)	(54.48, 23.00)	4.94
3	(90.00, 123.27, 117.75)	(51.33, 31.93)	3.26
4	(90.00, 139.97, 103.46)	(46.13, 39.56	2.33
5	(90.00, 158.16, 89.18)	(38.85, 46.29)	2.57
6	(90.00, 177.82, 87.58)	(31.04, 57.57)	3.04
7	(90.00, 184.35, 90.19)	(27.63, 62.29)	6.82
8	(90.00, 121.83, 290.82)	(1.64, 64.02)	9.51