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Paint surface estimation and trajectory planning for automated painting systems
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Abstract
This paper investigates the problem of paint surface estimation and trajectory planning for the automated painting process using a six-degree-of-freedom (6DOF) robot. We first present the kinematic model of the 6DOF articulated spraying robot and calculate the coordinate transformation of the robot's end effector relative to the base position. Then we design the size of the robot's joints to ensure sufficient spraying working space for the outer coverings of automobiles. Next, we stitch the acquired workpiece point cloud data (PCD) and perform noise reduction. The iterative closest point (ICP) algorithm integrates the workpiece PCD obtained from different locations into a unified coordinate system. Based on the features of the workpiece surface, we compute the normal vector for the point cloud. Then, the original point cloud data is segmented into several pieces by the different components of the normal vector on the coordinate axis. By slicing the segmented PCD evenly, we approximate the spraying paths of each surface of the car cover. Finally, we validate the effectiveness of our proposed algorithm through simulation.
Mathematics Subject Classification: Primary: 93-10; Secondary: 93-08.Citation: 
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Figure 1. Three coordinate systems: initial coordinate system $ O_i-X_iY_iZ_i $ (use $ \mathcal{O}_i $ for abbr.), intermediate coordinate system $ O_k-X_kY_kZ_k $(use $ \mathcal{O}_k $ for abbr.) and the coordinate system after transformation $ O_j-X_jY_jZ_j $ (use $ \mathcal{O}_j $ for abbr.). $ \mathcal{O}_k $ is obtained by translating $ \mathcal{O}_i $ along $ p_{ij} $. $ \mathcal{O}_j $ is obtained by rotating $ \mathcal{O}_k $ by $ \theta $ degrees around the $ z $-axis. The point $ p $ is any point in space
Figure 2. D-H coordinate system of adjacent linkage: $ Link $ $ i-1 $ and $ Link $ $ i $. The transformation here involves two translations and two rotations. The parameters of the transformation are $ {\alpha _i} $, $ {l_i} $, $ {d_{i}} $, $ {\theta _i} $
Figure 3. Spraying robot initial stance and the outer covering parts of the car to be sprayed. We will establish the coordinate system at each joint of the robot in this stance
Figure 4. Coordinate system established at each joint of the robot. $ l,d,\beta $ represent the values of the D-H parameters of the corresponding linkage. $ L $ represents the name of the linkage. $ X,Y,Z $ represent the coordinate system
Figure 5. Schematic diagram of point cloud slicing. The intersection plane is $ W_0 $ and the bandwidth is $ \partial $
Figure 6. Path generation process
Figure 7. Robot workspaces from different perspectives
Figure 8. Original point cloud
Figure 9. Registered point cloud
Figure 10. Point cloud segmentation results
Figure 11. Results of point cloud slices from different parts
Table 1. Spraying robot D-H parameter list
Linkage number $ {l_i} $ $ {\alpha _i} $ $ {d_{i}} $ $ {\theta _i} $ 1 0 0 0 $ {\theta _1} $ 2 0 -90 0 $ {\theta _2} $ 3 $ {l_3} $ 0 0 $ {\theta _3} $ 4 0 -90 $ {d_{4}} $ $ {\theta _4} $ 5 0 $ {\beta} $ $ {d_{5}} $ $ {\theta _5} $ 6 0 - $ {\beta} $ $ {d_{6}} $ $ {\theta _6} $ | Show Table
DownLoad: CSV
Table 2. The joint rotation range
Parameter $ {\theta _1} $ $ {\theta _2} $ $ {\theta _3} $ $ {\theta _4} $ $ {\theta _5} $ $ {\theta _6} $ Rotation range -160°-160° -90°-150° -60°-90° 0°-360° 0°-360° 0°-360° | Show Table
DownLoad: CSV
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References
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Figure 1.
Three coordinate systems: initial coordinate system
$ O_i-X_iY_iZ_i $ $ \mathcal{O}_i $ $ O_k-X_kY_kZ_k $ $ \mathcal{O}_k $ $ O_j-X_jY_jZ_j $ $ \mathcal{O}_j $ $ \mathcal{O}_k $ $ \mathcal{O}_i $ $ p_{ij} $ $ \mathcal{O}_j $ $ \mathcal{O}_k $ $ \theta $ $ z $ $ p $ -
Figure 2.
D-H coordinate system of adjacent linkage:
$ Link $ $ i-1 $ $ Link $ $ i $ $ {\alpha _i} $ $ {l_i} $ $ {d_{i}} $ $ {\theta _i} $ -
Figure 3.
Spraying robot initial stance and the outer covering parts of the car to be sprayed. We will establish the coordinate system at each joint of the robot in this stance
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Figure 4.
Coordinate system established at each joint of the robot.
$ l,d,\beta $ $ L $ $ X,Y,Z $ -
Figure 5.
Schematic diagram of point cloud slicing. The intersection plane is
$ W_0 $ $ \partial $ -
Figure 6.
Path generation process
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Figure 7.
Robot workspaces from different perspectives
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Figure 8.
Original point cloud
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Figure 9.
Registered point cloud
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Figure 10.
Point cloud segmentation results
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Figure 11.
Results of point cloud slices from different parts