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摘要: 针对家庭服务机器人工作的非结构化环境, 本文设计了一种可以根据任务需求相应地调整连杆形状的可变形操作臂.该操作臂工作空间易于拓展、灵活度较高且成本低廉.但连杆形状的改变给操作臂的建模和控制带来了困难.首先, 可变形臂的运动学参数发生了巨大且无规律的变化, 使得固结在操作臂连杆上的关节坐标系可能脱离操作臂本体, 变得不可测量.其次, 为适应不同任务需求, 可变形臂的连杆形状需要经常改变, 而传统标定方法往往追求更高的标定精度而非标定效率.最后, 可变形臂的标定方法必须低成本且易于在家庭环境中实施, 而基于激光等传感器的标定方法设备价格昂贵, 对实验环境要求严格, 不便于在家庭中实施.因此, 一种廉价、快速、易于实施的标定方法是可变形臂应用的基础.本文分别基于Denavit-Hartenberg(DH)模型和旋量模型提出了基于视觉标志块间相对位姿测量的标定算法, 该算法在标志块处建立虚拟关节, 通过测量不同标志块间的相对位姿可快速、高效地获取可变形臂的运动学参数.实验说明了两种标定方法的有效性, 同时还表明旋量模型更适合可变形臂的建模.最后, 本文给出了利用可变形臂进行点触任务操作的实例, 展示出可变形操作臂在家庭使用中的优势.
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关键词:
- 可变形操作臂 /
- 运动学 /
- Denavit-Hartenberg表示法 /
- 旋量 /
- 操作臂标定
Abstract: The deformable manipulator can obtain relatively dexterous end-effector and extended workspace with fewer joints by bending its deformable links.However, frequent changes in links's shape may bring difficulties to the model and control of the manipulator.The reasons are as follows.First, the kinematic parameters experience drastic changes and become totally unknown.It is hard to measure the parameters directly.Second, the change is frequent.Thus a low-cost, less time consuming calibration method is the fundament of deformable manipulator for home service robots.In this paper, two calibration methods based on relative pose measurement of visual markers are developed for the Denavit-Hartenberg (DH) model and screw theory model, respectively.By introducing a virtual joint at the marker, the method can calculate the kinematic parameters quickly according to the relative pose of visual markers.Experimental results verify the effectiveness of the methods.It is shown that the screw model is more suitable for the deformable manipulator.Finally, two point touching tasks are conducted to demonstrate the advantage of the deformable manipulator.-
Key words:
- Deformable manipulator /
- kinematics /
- Denavit-Hartenberg (DH) /
- screw theory /
- calibration
1) 本文责任编委 侯增广 -
图 1 可变形连杆发生形变后对DH参数的影响
Fig. 1 The change in DH parameters caused by the deformable link
图 2 可变形连杆发生形变后对旋量参数的影响
Fig. 2 The change in screw parameters caused by the deformable link
图 4 可变形操作臂和传统刚性臂的工作空间与不同任务空间的重合度比较
Fig. 4 Comparison of the deformable and rigid manipulator facing two task spaces
图 5 具有两个可变形连杆的四自由度操作臂及其标定系统
Fig. 5 A deformable manipulator with four DOFs and two deformable links and its calibration system
图 7 第$k$个臂形下可变形操作臂DH模型示意图
Fig. 7 DH model of the deformable manipulator in\\ the $k$-th configuration
图 8 基于旋量理论的可变形操作臂运动学模型
Fig. 8 Kinematics model of the deformable manipulator based on screw theory
图 9 可变形操作臂参数标定的实验平台
Fig. 9 Experimental platform for parameters calibration of the deformable manipulator
图 10 可变形操作臂点触任务实验设置
Fig. 10 The experiments setup for the deformable manipulator in touching tasks
图 11 传统臂形下进行点触任务作业仿真实验
Fig. 11 The simulation of touching tasks by deformable manipulator in traditional configuration
表 1 可变形操作臂DH参数表
Table 1 DH parameters of the deformable manipulator
$i$ ${\alpha _{i - 1}}$ ${a_{i - 1}}$ ${\theta _{i}}$ ${d _{i}}$ 1 0 0 ${\theta _{1}}$ $d _{1}$ 2 $-\pi /2$ 0 ${\theta_{2}}+\Delta \theta _{2}$ $d _{2}$ 3 ${\alpha _2}$ ${a _2}$ ${\theta _{3}}+\Delta\theta _{3}$ $d _{3}$ 4 ${\alpha _3}$ ${a _3}$ ${\theta _{4}}+\Delta\theta _{4}$ $d _{4}$ $w$ 0 $L_w$ 0 0 
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表 2 第$k$个臂形下虚拟操作臂的DH模型参数表
Table 2 DH parameters of the virtual manipulator in the $k$-th configuration
$i^{\left(k\right)}$ ${\alpha _{i - 1}^{\left(k\right)}}$ ${a_{i - 1}^{\left(k\right)}}$ ${\theta _{i}^{\left(k\right)}}$ ${d _{i}^{\left(k\right)}}$ 1 0 0 ${\theta _{1}}$ $d _{1}$ 2 $-\pi /2$ 0 $\theta _2 + \underline {{\Delta \theta _{2}^{\left(k\right)}}}$ $\underline {{d _{2}^{\left(k\right)}}}$ 3 $\underline{{\alpha _{2}^{\left(k\right)}}}$ $\underline{{a _{2}^{\left(k\right)}}}$ $\theta _3 + \underline {{\Delta \theta _{3}^{\left(k\right)}} + {\theta _{M_3}^{\left(k\right)}}}$ $\underline {{d_{3}^{\left(k\right)}} + {d_{M_3}^{\left(k\right)}} } $ 4 $\underline {{\alpha _{3}^{\left(k\right)}}} $ $\underline {{a_{3}^{\left(k\right)}}} $ $\theta _4 + \underline {{\Delta \theta _{4}^{\left(k\right)}} - {\theta _{M_3}^{\left(k\right)}}} $ $\underline {{d_{4}^{\left(k\right)}} - {d_{M_3}^{\left(k\right)}} } $ $w$ 0 $L_w$ 0 0
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表 3 可变形操作臂第$k$个臂形的参数标定的初值的结果
Table 3 The raw calibration results of the deformable manipulator in the $k$-th configuration
$i^{\left(k\right)}$ ${\alpha _{i - 1}^{\left(k\right)}}$ ${a_{i - 1}^{\left(k\right)}}$ ${\theta _{i}^{\left(k\right)}}$ ${d _{i}^{\left(k\right)}}$ $1$ 0 0 ${\theta _{1}}$ $d _{1}$ $2$ $-90^{\circ}$ 0 $\theta _{2}+(\underline {{-2.81^{\circ}}})$ $\underline {-150.60}$ $3$ $\underline{-81.97^{\circ}}$ $\underline{269.46}$ $\theta _{3}+(\underline {-7.28^{\circ}})$ $\underline {-116.54} $ $4$ $\underline {138.73^{\circ}} $ $\underline {160.08} $ $\theta _{4}+(\underline {-109.26^{\circ}})$ $\underline {29.13} $ $w$ 0 $Lw$ 0 0
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表 4 可变形臂DH参数标定的初值的位姿误差
Table 4 Pose errors of the deformable manipulator based on raw calibrated DH parameters
误差类型 误差分量 位置误差(mm) $39.95 \pm 12.82$ $X$ $-13.54 \pm 13.41$ $Y$ $26.54 \pm 7.76$ $Z$ $19.17 \pm 16.57$ 欧拉角姿态误差$(^\circ)$ $4.66\pm 0.86$ $\alpha$ $-0.30 \pm 0.36$ $\beta$ $0.66 \pm 0.33$ $\gamma$ $3.61 \pm 0.62$
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表 5 可变形臂旋量模型参数标定的初值的位姿误差
Table 5 Pose errors of the deformable manipulator based on raw calibrated screw parameters
误差类型 误差分量 位置误差(mm) $39.57 \pm 22.31$ $X$ $-30.61 \pm 24.13$ $Y$ $4.21 \pm 14.83$ $Z$ $-4.88 \pm 17.31$ 欧拉角姿态误差$(^{\circ})$ $0.25 \pm 0.18$ $\alpha$ $0.09 \pm 0.17$ $\beta$ $0.05 \pm 0.08$ $\gamma$ $-0.03 \pm 0.04$
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表 6 传统臂形下进行点触任务作业仿真实验
Table 6 The simulation of touching tasks by deformable manipulator in traditional configuration
序号 点触目标点$\left({\rm mm}\right)$ 有效点触位姿点触角$\alpha$ $\left(^\circ \right)$ 1 $\left(-400.0, 280.0, -2.0\right)^{\rm T}$ 23.17 2 $\left(-400.0, 200.0, -80.0\right)^{\rm T}$ 17.77 3 $\left(-400.0, 160.0, 280.0\right)^{\rm T}$ 2.97 4 $\left(-400.0, 185.0, 200.0\right)^{\rm T}$ 18.17 5 $\left(-400.0, 230.0, 40.0\right)^{\rm T}$ 无解$\left(29.76\right)$ 6 $\left(-400.0, 290.0, -160.0\right)^{\rm T}$ 无解 7 $\left(-400.0, 340.0, 360.0\right)^{\rm T}$ 无解
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