Semiparametric dynamic model identification for hyper-redundant manipulator based on iterative optimization and neural network compensation

Table 1. Hyper-redundant modular manipulator modified DH parameters
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Table 1. Hyper-redundant modular manipulator modified DH parameters
关节 $α$ a d offset
1 0 0 0.287 8 0
2 $π / 2$ 0 0 $π$
3 $π / 2$ 0 0.349 8 $π$
4 $π / 2$ 0 0 $π$
5 $π / 2$ 0 0.318 7 $π$
6 $π / 2$ 0 0 $π$
7 $π / 2$ 0 0.294 1 $π$
8 $π / 2$ 0 0 $π$
9 $π / 2$ 0 0.235 1 $π$

Table 2. Hyper-redundant modular manipulator joint motor parameters
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Table 2. Hyper-redundant modular manipulator joint motor parameters
关节额定功率/W 额定力矩 $K$ /（N·m）力矩系数
1 $410$ $2.3$ 0.21
2 $410$ $2.3$ 0.21
3 $430$ $1.43$ 0.13
4 $430$ $1.43$ 0.13
5 $270$ $0.74$ 0.106
6 $270$ $0.74$ 0.106
7 $155$ $0.27$ 0.057
8 $155$ $0.27$ 0.057
9 $155$ $0.27$ 0.057

Table 3. Hyper-redundant manipulator joint motion restriction
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Table 3. Hyper-redundant manipulator joint motion restriction
关节 $q_{i}$ ${\dot{q}}_{i m a x}$ ${\ddot{q}}_{i m a x}$
1，3，5，7，9 $\pm 180$ ° $30$ （°）/s $50$ （°）/s²
2，4，6，8 $\pm 90$ ° $30$ （°）/s $50$ （°）/s²

Table 4. Identification trajectory parameters for hyper-redundant manipulator

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Table 4. Identification trajectory parameters for hyper-redundant manipulator

关节	$a_{1}$		$a_{2}$		$a_{3}$		$a_{4}$		$a_{5}$
1	0.245 29		0.444 83		-0.001 05		-0.031 19		-0.060 6
2	0.044 78		0.133 35		-0.018 24		-0.008 73		-0.010 9
3	0.876 44		-0.407 96		-0.065 77		0.023 5		0.038 9
4	-0.162 60		-0.018 6		0.082 1		0.166 26		-0.126 6
5	-0.004 31		0.001 53		0.005 76		-0.076 11		0.046 79
6	-0.675 95		-0.007 46		-0.013 72		0.120 159		-0.043 8
7	-1.556 05		0.005 1		-0.001 08		0.004 55		0.059 06
8	-0.136 723		-0.007 7		-0.040 1		-0.065 0		0.062 78
9	0.048 681		-0.018 4		0.096 5		-0.062 2		0.006 03
关节	$b_{1}$	$b_{2}$		$b_{3}$		$b_{4}$		$b_{5}$		$q_{0}$
1	-0.165 46	0.039 0		-0.072 4		0.228 7		-0.121 86		0.180 81
2	0.829 112	-0.135 4		0.365 4		-0.171		-0.193 71		0.019 94
3	-0.143 53	-0.337 8		0.042 9		0.032 7		0.112 00		-0.341 0
4	0.659 13	-0.001 79		0.026 1		-0.173 5		-0.008 4		0.038 32
5	-0.012 79	-0.307 5		-0.068 4		-0.048 8		0.205 64		-0.633 6
6	0.029 90	0.006 17		0.009 37		-0.017 4		-0.000 58		-0.021 3
7	0.018 48	0.015 62		0.007 3		-0.023 7		0.004 85		0.104 79
8	0.211 18	0.019 83		0.027 69		-0.140 5		0.044 88		0.033 15
9	0.523 66	-0.044 77		-0.004 1		-0.028 3		-0.062 39		-0.107 19

Table 5. Identify torque residual root mean square （RMS） values by various methods

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Table 5. Identify torque residual root mean square （RMS） values by various methods

方法^2*	关节1	关节2	关节3	关节4	关节5	关节6	关节7	关节8	关节9	总和/ （ $N \cdot m$ ）
方法1	7.759 8	11.443 8	11.096 6	7.436 2	4.878 8	4.842 9	1.876 5	2.009 1	1.655 1	52.998 9
方法2	7.807 6	10.603 3	10.002 1	6.462 9	3.245 1	4.119 4	1.381 6	1.681 7	1.401 1	46.704 8
方法3	3.695 7	8.696 6	7.254 7	5.848 5	2.864 3	3.064 7	1.213 8	1.638 3	1.288 2	35.564 7
方法4	3.704 7	9.106 7	7.335 6	5.411 9	2.841 7	3.017 1	1.300 7	1.566 0	1.321 8	35.606 3
方法5	4.074 0	7.351 8	5.208 7	2.765 1	2.306 1	2.101 2	1.138 6	1.466 6	0.804 7	27.216 7

Table 6. Dynamic parameter identification results

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Table 6. Dynamic parameter identification results

参数	值	参数	值	参数	值	参数	值	参数	值
1	10.58	8	-2.182	15	0.842 8	22	8.956 9	29	-0.189
2	115.1	9	13.462	16	0.021 6	23	121.04	30	2.515
3	12.84	10	-0.042	17	0.047 8	24	1.552	31	0.668
4	-1.47	11	-6.812	18	1.295 4	25	0.898	32	-3.784
5	1.843	12	114.87	19	0.853 7	26	1.800	33	7.383
6	1.109	13	7.195 5	20	0.402 2	27	-0.284	34	64.954
7	1.190	14	-2.328	21	-0.025	28	-0.297	35	4.268

Table 6. Dynamic parameter identification results

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Table 6. Dynamic parameter identification results

参数	值	参数	值	参数	值	参数	值	参数	值
36	3.368	48	0.549 8	60	-0.181 3	71	-0.017 7	83	0.004 4
37	-0.291	49	-0.005 8	61	-0.059	72	-0.012 2	84	-0.036 6
38	-0.021	50	-0.000 7	62	-0.104	73	-0.096 7	85	0.072 67
39	0.344 5	51	-0.001 3	63	0.456 5	74	0.237 6	86	-0.029 3
40	0.025 2	52	0.556 4	64	0.055 1	75	-0.050 7	87	0.017 6
41	0.301 4	53	-0.052 7	58	-0.332	76	-0.434 5	88	1.616 7
42	-0.129 7	54	-1.764	65	-0.059 9	77	3.065	89	26.124
43	0.002 4	55	3.407	66	2.953 1	78	33.66	90	3.091
44	4.396 1	56	43.01	67	32.698	79	6.710	91	-0.203 7
45	126.84	57	6.842	68	5.125 4	80	-0.123
46	6.074 4	58	-0.332	69	0.228 9	81	-0.006
47	0.286 0	59	0.005	70	0.233 2	82	-0.003 1

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Yufei ZHOU, Zhongcan LI, Yi LI, Jingkai CUI, Shunfeng HE, Zhanyi SHENG, Mingchao ZHU. Semiparametric dynamic model identification for hyper-redundant manipulator based on iterative optimization and neural network compensation[J]. Optics and Precision Engineering, 2024, 32(2): 193

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