锚杆钻车串并联冗余机械臂的运动学研究

孙晓宇; 王恒升; 郭新平; 贺昕

doi:10.13433/j.cnki.1003-8728.20200621

锚杆钻车串并联冗余机械臂的运动学研究

doi: 10.13433/j.cnki.1003-8728.20200621

孙晓宇^1,,
王恒升^{1, 2, ,},
郭新平¹,
贺昕¹

1.
中南大学机电工程学院, 长沙 410083
2.
中南大学高性能复杂制造国家重点实验室, 长沙 410083

基金项目:

国家自然科学基金项目 51975587

详细信息

作者简介:
孙晓宇(1995-), 硕士研究生, 研究方向为机器人运动规划, 机器人控制技术, SunXYu163@163.com

通讯作者:
王恒升, 教授, 博士, whscsu@163.com

中图分类号: TP242
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- PDF下载量: 20
- 被引次数: 0
出版历程
- 收稿日期: 2021-05-31
- 刊出日期: 2023-04-25

Kinematics Study on Redundant Manipulator with Serial-parallel Hybrid Mechanism of Bolter-drilling Rig

SUN Xiaoyu^1
,,
WANG Hengsheng^{1, 2
, ,},
GUO Xinping¹,
HE Xin¹

1.
School of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China
2.
State Key Laboratory for High Performance Complex Manufacturing, Central South University, Changsha 410083, China

摘要

摘要: 锚杆钻车机械臂的自动定位打孔可进一步提高巷道支护工艺的自动化作业程度。本文针对某锚杆钻车的串并联混合8自由度冗余机械臂的逆运动学问题展开研究。该机械臂有两大特点, 一是串并联混合机构, 臂在整体上为串联开链机构, 但其大臂存在一个四边形的并联结构; 二是冗余自由度, 导致逆运动学存在无穷解。针对前者, 为便于使用D-H法建立运动学模型, 推导了并联结构的运动表达式, 将其用一个等效的串联结构来替代。针对后者, 详细分析了机械臂的结构与实际工况, 设置了逆解的3个条件: 1) 为保证推进器获得最大打孔行程, 设置定位油缸为最大伸长量; 2) 根据不同类型锚杆孔设定大臂四边形形状, 可实现姿态补偿; 3) 优先使用中臂进行位置补偿, 以尽量减少大臂的运动。在以上约束下提出基于位姿分离的逆运动学求解方案, 得到的逆解结果充分利用了机械臂的设计特点, 且兼顾人工操作过程的直观、方便性。为验证算法, 针对一个矩形巷道断面的锚杆孔设计, 通过计算机进行了逆解计算, 计算精度与速度均有满意的结果; 将算法部署到PLC上, 在模拟巷道自动打孔试验, 结果满足工程要求。
- 锚杆钻车 /
- 冗余机械臂 /
- D-H法 /
- 逆运动学 /
- 位姿分离
Abstract: The automatic positioning of the manipulator of the bolt-drilling rig is needed in the further implementing the automatic supporting process in the construction of mine laneway. This focus is to solve the inverse kinematics problem of a redundant manipulator with serial-parallel hybrid mechanism and 8 degree of freedom. The manipulator has two characteristics, one of which is the overall series-open-chain mechanism embedded with a partly-parallel quadrilateral mechanism in its base arm, and another of which is the redundant degrees of freedom which leads to infinite solutions for the inverse kinematics. For the former, in order to establish the kinematics model by using the Denavit-Hartenberg(D-H) method, the motion expression of the parallel structure is deduced, and the equivalent open chain structure is proposed to replace the parallel counterpart. For the latter, the structure of the manipulator and its actual work conditions are analyzed, in which three constraints are concluded for solving the inverse kinematics: 1) the positioning cylinder is set at its maximum elongation in order to ensure the maximum stroke of the propeller in actual drilling; 2) according to the types of bolt holes, the quadrilateral shape of the base arm is conditionally set to realize the proper compensation for orientation; 3) the length of the middle arm for position compensation is chosen in higher priority to keep the demand for the moving of the base arm as rarely as possible. Then an inverse kinematics algorithm based on the position-pose separation is proposed for the manipulator, and the results of the solution takes full advantages of the redundant characteristic of the manipulator and is in favor of the straight forward and convenient operation for human operator. For the validation of the algorithm, an example design of bolt-holes for a rectangular section of mine laneway is used; the simulations on a personal laptop show the satisfactory result of the algorithm in the precision and calculation speed; the algorithm is also deployed on a control Programmable Logic Controller (PLC) of a bolt-drilling rig, and the drilling test in a simulated mine laneway shows that the algorithm meets the needs of the practical application.
- bolter-drilling rig /
- redundant manipulator /
- D-H method /
- inverse kinematics /
- position-pose separation

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图 1 机械臂结构示意图

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图 2 大臂运动分析示意图

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图 3 机械臂D-H系示意图

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图 4 矩形巷道断面示意图

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图 5 竖直锚杆孔机械臂投影图

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图 6 水平锚杆孔机械臂投影图

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图 7 一般姿态锚杆孔机械臂投影图

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表 1 机械臂D-H参数

连杆	θ_i/(°)	d_i/mm	a_i/mm	α_i/(°)	关节变量范围
1	0	170	235	-90	(-0.26°, 42.75°)
2	90	0	0	90	(44.21°, 96.56°)
3	0	d₃	0	-90	(1 770, 2 370) mm
4	0	-100.5	165	90	(-6.56°+γ, 45.79°+γ)
5	0	d₅	0	0	(664, 1 164) mm
6	-90	0	0	-90	(-90°, 90°)
7	180	-278.5	0	-90	(90°, 270°)
8	90	d₈	374	0	(1 175, 2 225) mm

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表 2 锚杆孔相对于断面坐标系的位姿坐标

目标位姿	孔序
目标位姿	1	2	3	4	5	6	7	8	9
x_s/mm	0	0	0	0	0	0	0	0	0
y_s/mm	800	1 600	2 400	2 900	2 900	2 900	2 900	2 900	2 900
z_s/mm	4 150	4 150	4 150	3 950	3 150	2 350	1 550	750	150
α_s/(°)	90	90	90	90	90	90	90	90	90
β_s/(°)	-90	-90	-70	-15	0	0	0	0	15

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表 3 锚杆孔逆解结果

孔序	逆解结果
孔序	θ₁/(°)	θ₂/(°)	d₃/mm	θ₄/(°)	d₅/mm	θ₆/(°)	θ₇/(°)	d₈/mm
1	19.434 5	71.800 4	2 122.8	18.199 6	664	0	90	2 225
2	33.149 6	71.800 4	2 122.8	18.199 6	839.8	0	90	2 225
3	33.230 0	73.380 6	2 122.8	16.619 4	842.6	-16.933 0	100.802 7	2 225
4	9.197 9	47.115 3	2 178.3	42.884 7	1 164	-74.813 6	98.881 9	2 225
5	4.494 4	55.446 5	2 178.3	34.553 5	972.3	-90	94.494 4	2 225
6	4.494 4	78.296 8	2 147.0	11.703 2	664	-90	94.4944	2 225
7	4.494 4	64.020 1	2 147.0	25.979 9	836.3	90	265.505 6	2 225
8	4.494 4	86.176 6	2 107.0	3.823 4	664	90	265.505 6	2 225
9	9.197 9	87.443 6	2 098.2	2.556 4	664	74.813 6	261.118 1	2 225

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表 4 锚杆孔逆解误差分析

孔位	锚杆孔目标位置			偏差
孔位	x_s⁰/mm	y_s⁰/mm	z_s⁰/mm	Δx/10^-13 mm	Δy/10^-13 mm	Δz/10^-13 mm
1	3 000	260	2 893	-4.55	-2.27	0
2	3 000	1 060	2 893	-4.55	0	0
3	3 000	1 860	2 893	4.55	-821	0
4	3 000	2 360	2 693	4.55	50 791	0
5	3 000	2 360	1 893	0	13.64	0
6	3 000	2 360	1 093	0	13.64	0
7	3 000	2 360	293	0	9.09	-1.14
8	3 000	2 360	-507	4.55	9.09	-3.41
9	3 000	2 360	-1 107	0	50 787	-4.55

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