Performance Analysis of Base Rotational Joint Under Obstacle Crossing Condition for Transmission Line Inspection Robot

doi:10.12068/j.issn.1005-3026.2025.20230294

Abstract

Abstract:

One of the main factors affecting the obstacle crossing performance is the base rotation joint of the walking arms. To improve the walking performance of the robot under the obstacle crossing conditions， an active adjustment method of the base rotation joint was proposed. Firstly， a dual-inertia dynamic model of the base rotation joint was established， and a joint controller was designed based on linear quadratic regulator （LQR） control theory. Through comparison， it is found that the performance of the base rotation joint is mainly determined by the weight coefficient matrices Q_c and R_c. Genetic algorithm is used to optimize the parameters in the coefficient matrices of the joint controller， and the optimization results are compared and analyzed to find the best scheme to improve the walking performance of the robot under obstacle crossing condition. Finally， the obstacle crossing experiment of the multi-joint double-arm inspection robot is carried out， and the results showed that the joint controller with optimized parameters can better control the robot to complete obstacle crossing tasks.

Key words: dual-arm inspection robot, dynamic modeling, joint control, genetic algorithm, performance analysis

CLC Number:

TH 11.1

Xiao-peng LI, Hai-long LIU, Xing FAN, Bing SHI. Performance Analysis of Base Rotational Joint Under Obstacle Crossing Condition for Transmission Line Inspection Robot[J]. Journal of Northeastern University(Natural Science), 2025, 46(4): 52-60.

Figures/Tables 20

Fig.1 Multi-joint dual-arm inspection robot model

Fig.2 Obstacle crossing process

Fig.3 Model of simplified joint

Fig.4 Control flow chart of the base rotation joint

Fig.5 Structure of the LQR controller

Table 1 Parameters of the robot rotation joint

名称	符号	单位	数值
负载转动惯量	$J l$	$k g ⋅ m 2$	$625 × 10 - 4$
负载阻尼系数	$B l$	$N ⋅ s / m$	0.05
传动系统扭转刚度	K	$N ⋅ s / r a d$	1.3
传动系统扭转阻尼	C	$N ⋅ s / m$	0.05

Table 1 Parameters of the robot rotation joint

名称	符号	单位	数值
负载转动惯量	$J l$	$k g ⋅ m 2$	$625 × 10 - 4$
负载阻尼系数	$B l$	$N ⋅ s / m$	0.05
传动系统扭转刚度	K	$N ⋅ s / r a d$	1.3
传动系统扭转阻尼	C	$N ⋅ s / m$	0.05

Table 2 Parameters of Qc and Rc

序号	$η 1$	$η 2$	$ξ$
1	100	0.1	0.1
2	50	1	1
3	100	1	50
4	100	0.1	100

Table 2 Parameters of Qc and Rc

序号	$η 1$	$η 2$	$ξ$
1	100	0.1	0.1
2	50	1	1
3	100	1	50
4	100	0.1	100

Fig.6 Time domain response comparison of the rotary joint with different parameters

Fig.7 Flow chart of optimization based on genetic algorithm[18]

Fig.8 Evolutionary curve of GA

Table 3 Simulation results with different η1

$η 1$	$T s s$ /s	M_p/(°)	$a m a x$ /((°)·s^-2)	$η 1$	$T s s$ /s	M_p/(°)	$a m a x$ /((°)·s^-2)
10	4.524	0.090	6.437	60	3.092	0.179	10.92
20	3.668	0.127	8.050	70	3.035	0.176	11.41
30	3.537	0.167	9.036	80	2.932	0.177	11.79
40	3.456	0.173	9.769	90	2.830	0.178	12.22
50	2.770	0.165	10.39	100	2.696	0.181	12.53

Table 3 Simulation results with different η1

$η 1$	$T s s$ /s	M_p/(°)	$a m a x$ /((°)·s^-2)	$η 1$	$T s s$ /s	M_p/(°)	$a m a x$ /((°)·s^-2)
10	4.524	0.090	6.437	60	3.092	0.179	10.92
20	3.668	0.127	8.050	70	3.035	0.176	11.41
30	3.537	0.167	9.036	80	2.932	0.177	11.79
40	3.456	0.173	9.769	90	2.830	0.178	12.22
50	2.770	0.165	10.39	100	2.696	0.181	12.53

Table 4 Simulation results with different η2

$η 2$	$T s s$ /s	M_p/(°)	$a m a x$ /((°)·s^-2)	$η 2$	$T s s$ /s	M_p/(°)	$a m a x$ /((°)·s^-2)
0.01	2.770	0.165	10.39	0.5	3.234	0.158	10.30
0.1	3.035	0.202	10.38	0.6	3.184	0.154	10.30
0.2	3.037	0.197	10.36	0.7	3.316	0.149	10.29
0.3	2.747	0.155	10.34	0.8	3.254	0.146	10.27
0.4	3.309	0.161	10.32	0.9	3.203	0.141	10.24

Table 4 Simulation results with different η2

$η 2$	$T s s$ /s	M_p/(°)	$a m a x$ /((°)·s^-2)	$η 2$	$T s s$ /s	M_p/(°)	$a m a x$ /((°)·s^-2)
0.01	2.770	0.165	10.39	0.5	3.234	0.158	10.30
0.1	3.035	0.202	10.38	0.6	3.184	0.154	10.30
0.2	3.037	0.197	10.36	0.7	3.316	0.149	10.29
0.3	2.747	0.155	10.34	0.8	3.254	0.146	10.27
0.4	3.309	0.161	10.32	0.9	3.203	0.141	10.24

Table 5 Simulation results with different ξ

$ξ$	$T s s$ /s	M_p/(°)	$a m a x$ /((°)·s^-2)	$ξ$	$T s s$ /s	M_p/(°)	$a m a x$ /((°)·s^-2)
1	2.747	0.155	10.34	50	11.31	—	3.156
10	5.487	0.034	5.317	60	12.98	—	2.961
20	5.826	—	4.302	70	14.62	—	2.807
30	8.095	—	3.761	80	15.45	—	2.679
40	10.11	—	3.404	90	16.28	—	2.569

Table 5 Simulation results with different ξ

$ξ$	$T s s$ /s	M_p/(°)	$a m a x$ /((°)·s^-2)	$ξ$	$T s s$ /s	M_p/(°)	$a m a x$ /((°)·s^-2)
1	2.747	0.155	10.34	50	11.31	—	3.156
10	5.487	0.034	5.317	60	12.98	—	2.961
20	5.826	—	4.302	70	14.62	—	2.807
30	8.095	—	3.761	80	15.45	—	2.679
40	10.11	—	3.404	90	16.28	—	2.569

Fig.9 Influence curve of weight coefficient matrix parameters on the objective function

Table 6 Performance index after parameter

性能指标	$T s s$ /s			$M p$	$a m a x$
性能指标	$θ$	$θ ˙$	$θ ¨$	(°)	$(°) ⋅ s - 2$
GA-LQR	4.169 3	5.543 5	5.769 3	0.010 9	4.778 2

Table 6 Performance index after parameter

性能指标	$T s s$ /s			$M p$	$a m a x$
性能指标	$θ$	$θ ˙$	$θ ¨$	(°)	$(°) ⋅ s - 2$
GA-LQR	4.169 3	5.543 5	5.769 3	0.010 9	4.778 2

Table 7 Performance index comparison

性能指标		参数1	参数2	参数3	参数4
合计		33.35	32.38	9.493	9.732
$T s s$ /s	$θ$	-88.10	-73.31	57.56	65.76
	$θ ˙$	-59.16	-37.23	26.54	50.25
	$θ ¨$	-62.68	-32.16	21.85	43.99
$M p$ /(°)		91.20	92.04	—	—
$a m a x / ((°) ⋅ s - 2)$		78.82	52.67	-16.33	-33.87

Table 7 Performance index comparison

性能指标		参数1	参数2	参数3	参数4
合计		33.35	32.38	9.493	9.732
$T s s$ /s	$θ$	-88.10	-73.31	57.56	65.76
	$θ ˙$	-59.16	-37.23	26.54	50.25
	$θ ¨$	-62.68	-32.16	21.85	43.99
$M p$ /(°)		91.20	92.04	—	—
$a m a x / ((°) ⋅ s - 2)$		78.82	52.67	-16.33	-33.87

Table 8 Robot joint motion parameters

越障阶段	运行关节	运行时间/s	运行速度
后臂抬升	后臂抬升关节	10	5 mm/s
旋转越障	前臂基座旋转关节	20	9 (°)/s
旋转越障	后臂基座旋转关节	20	9 (°)/s
后臂下降	前臂抬升关节	10	5 mm/s

Fig.10 Inspection robot test prototype

Fig.11 Obstacle crossing test for robot

Table 9 Experimental results for different controller parameters

性能指标		GA-LQR	参数1	参数2	参数3
$T s s$ /s	$θ$	4.364	1.762	1.638	9.363
	$θ ˙$	4.765	2.635	3.396	8.254
	$θ ¨$	5.532	2.461	3.762	8.469
$M p$ /(°)		0.010	0.124	0.145	—
$a m a x / ((°) ⋅ s - 2)$		3.297	19.706	8.687	3.746
整体对比提升/%		—	31.87	29.53	24.36

Table 9 Experimental results for different controller parameters

性能指标		GA-LQR	参数1	参数2	参数3
$T s s$ /s	$θ$	4.364	1.762	1.638	9.363
	$θ ˙$	4.765	2.635	3.396	8.254
	$θ ¨$	5.532	2.461	3.762	8.469
$M p$ /(°)		0.010	0.124	0.145	—
$a m a x / ((°) ⋅ s - 2)$		3.297	19.706	8.687	3.746
整体对比提升/%		—	31.87	29.53	24.36

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