Fast Solution of 6-axis Industrial Robot Workspace
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摘要: 由于机器人设计过程中需要反复计算机器人工作空间，提升工作空间的计算效率与精度具有重要意义。本文针对传统方法求解工作空间精度不高、速度慢的问题，提出了改进方法。用传统方法生成种子空间并离散为多个子空间，利用正态分布拓展工作空间点数量不足的子空间，并根据拓展后工作空间点的位置调整正态分布参数，得到可达工作空间。进一步，利用可操作度值评估机器人的灵活性，从可达工作空间筛选出灵活种子空间，利用可调参数的正态分布拓展灵活种子空间边界，得到灵活工作空间。以6轴机器人为对象，对本文方法进行仿真分析。结果表明，本文方法在保证求解精度的前提下可极大的提升求解效率，为后续的机器人优化设计提供了便利。Abstract: In the process of robot design, the robot workspace needs to be calculated repeatedly, so it is of great significance to improve the computational efficiency and accuracy of the workspace. An improved method to solve the problems of low precision and slow speed of the traditional method is proposed. The seed space is generated by the traditional method and discretized into multiple subspaces, the normal distribution is used to expand the subspace with insufficient number of workspace points, and the normal distribution parameters are adjusted according to the positions of the expanded workspace points to obtain the reachable workspace. Then, the operability value to evaluate the flexibility of the robot is used, the flexible seed space from the reachable workspace is filtered out, and the normal distribution of adjustable parameters to expand the boundary of the flexible seed space to obtain a flexible workspace is used. By taking the 6-axis robot as an example to simulate and analyze the improved method, the results show that the present method can greatly improve the solving efficiency on the premise of ensuring the solving accuracy, and provide convenience for the subsequent optimization design of the robot.
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Key words:
- 6-axis robot /
- workspace /
- monte-carlo method /
- manipulability
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表 1 6轴机器人D-H参数表
Table 1. 6-axis robot D-H parameter table
${{i} }$ ${ {{d} }_{ {i} } }/{\rm{mm}}$ ${ {{a} }_i}/{\rm{mm}}$ ${\alpha _{i} }/(^\circ )$ ${\theta _{i} }/(^\circ )$ 1 700 0 0 $ {\theta _{\text{1}}} $ 2 0 305 90 $ {\theta _{\text{2}}} $ 3 0 1110 0 $ {\theta _{\text{3}}} $ 4 1260 200 90 $ {\theta _{\text{4}}} $ 5 0 0 −90 $ {\theta _{\text{5}}} $ 6 245 0 90 $ {\theta _{\text{6}}} $ 
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表 2 6轴机器人关节运动范围
Table 2. Range of motion of 6-axis robot join
$ i $ 1 2 3 4 5 6 ${ {{q} }_{\max } }/(^\circ )$ + 185 + 140 + 168 + 350 + 125 + 350 ${ { {q} }_{ {{\rm{min} } } } }/(^\circ )$ −185 + 5 −120 −350 −125 −350
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表 3 改进蒙特卡洛法参数设置
Table 3. Improved Monte Carlo method parameter Settings
${{N} }$ ${{k} }$ ${{n} }$ $ \sigma $ $ \delta $ ${{n} }_{{f} }^{ {\text{max} } }$ ${ {n} }_{{l} }^{ {\text{max} } }$ 10000 20 × 20
× 20150 $\text{π}/3$ 1.5 5 300
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表 4 可达工作空间体积随工作空间点变化表
Table 4. Reachable workspace volume change table with workspace points
${{N} }$ $ 1 \times {10^5} $ $ 1 \times {10^6} $ $ 5 \times {10^6} $ $ 1 \times {10^7} $ $ 1.5 \times {10^7} $ $ 2 \times {10^7} $ $ V/{{\text{m}}^{\text{3}}} $ 64.422 72.524 74.358 74.856 75.166 75.238
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