A Two-stage Improvement Method for Robot Based 3D Surface Scanning

As known that the surface of unknown object was difficult to measure or recognize precisely, hence the 3D laser scanning technology was introduced and used properly in surface reconstruction. Usually, the surface scanning speed was slower and the scanning quality would be better, while the speed was faster and the quality would be worse. In this case, the paper presented a new two-stage scanning method in order to pursuit the quality of surface scanning in a faster speed. The first stage was rough scanning to get general point cloud data of object’s surface, and then the second stage was specific scanning to repair missing regions which were determined by chord length discrete method. Meanwhile, a system containing a robotic manipulator and a handy scanner was also developed to implement the two-stage scanning method, and relevant paths were planned according to minimum enclosing ball and regional coverage theories.


Introduction
Aiming at measuring and recognizing the topography and contour of unknown object, the laser scanning was applied to collect 3D data as much as possible trying to reconstruct the surface. As a non-contact measurement technology, it owned many advantages, which had been widely applied in various engineering fields. To perform automatic 3D laser scanning application, recent studies mainly adopted the method of prediction estimation to plan the sampling points, the viewpoints and the scanning paths so as to obtain the complete 3D information of the surface. For example, to apply a mass vector chain to determine the exploration direction and the accurate position in the viewpoint planning of 3D model reconstruction [1] , to present a next-best-scan (NBS) approach to plan collision free path in order to completely scan unknown objects [2] , an adaptive sampling method presented to plan the measuring path according to the curvature feature of the fitted B-splines [3] , using a modelbased viewpoint planning method to inspect freeform surface [4] , and a new next-best-view (NBV) planning method proposed for reconstruction of unknown 3D model based on limit visual surface [10] , etc. However, the missing region determine errors, the sampling point arrangement errors, the viewpoint deviations and other problems still existed in unknown surface scanning in spite of these studies had been demonstrated in some experimental applications. Furthermore, some of scanning methods might consume amount of resources by algorithm operations in the process and the speed was quite slow in pursuit of the completeness of scanning. To improve the quality of 3D scanning with consideration of speed, the paper presented a two-stage scanning method including the firstly rough scanning and secondly specific scanning. The idea was to scan the object in a faster speed so as to obtain general 3D information of surface, which would reduce scanning time immensely, then to 2

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International Conference on Robotics and Mechantronics (ICRoM 2017) IOP Publishing IOP Conf. Series: Materials Science and Engineering 320 (2018) 012006 doi:10.1088/1757-899X/320/1/012006 analyse and to determine whether the collected data existed missing regions. If the missing regions were confirmed, one more detailed scanning seemed to be very necessary to complete the scanning process. In the laser 3D scanning, point cloud data was collected from the surface and was able to be converted to spatial data points. Then it needed to apply mathematics algorithms to confirm the locations and orientation of the missing regions. In the scanning path planning, the minimum enclosing ball (MEB) theory [5][6][7][8] was introduced, since MEB had been already applied in solving large data sets problem [5,8] and evaluating the barycentre error in large blade optimization process [6,7] . It represented a ball field with the minimum radius to enclose a set of spatial points availably, whose characteristics were suitable to solve the missing problem of 3D surface scanning and to make effective estimation of the area of missing regions. Combining 3D scanning constraints mainly based on limited dimensions in Euclidean space [11,12] and the visibility cone concept which was simply described as scanning vector visual area [13,14] , the sampling points and directions of scanning were determined, so that the specific scanning path was planned through computed points and directions. To implement this improvement scanning method, it required the assistance of an automatic platform in order to execute the operations, so that a robotic manipulator mounted with a handy 3D scanner was designed and applied, since its movement trajectories were accurate and the performances of scanning paths were also guaranteed.

Rough scanning
The general topography and contour information of object surface were quickly obtained by rough scanning. Through determining the information collected by 3D scanner and analysing the point cloud data of boundaries, it was able to provide necessary computational data support to path planning in specific scanning. From the perspective of discretization, transforming the 3D information of measured surface into point cloud data, the missing scanned regions were determined by the discretization algorithm [9] . As depicted in Figure 1, the original point cloud data was divided into several layers based on the values along Z axis and the data of each layer was projected onto the XOY plane. According to the accuracy of 3D scanner, the distance threshold of projected point cloud was defined by T. It also defined that adjacent projection points on the projection plane were P i (x i , y i ) and P i+1 (x i+1 , y i+1 ) respectively. If the Euclidean norm from P i to P i+1 satisfied the equation (1), it was determined that there was a missing region between P i and P i+1 , that was, 3D information was missing in this region. Meanwhile, P i and P i+1 represented the boundary points of the missing region. There also existed invalid scanning region which contained incomplete data in surface gridding process, reading and processing the 3D information of the triangular patches included in the region,

Specific scanning
In the specific scanning process, firstly sampling points of scanning was arranged in order to confirm the repair scanning centre and then scanning paths were planned

Sampling point arrangement
The MEB theory and the shrinkage optimization algorithm were introduced to enclosing compute the boundary point cloud of the missing regions. The MEB of missing region B r was obtained with the centre C 0 (x 0 , y 0 , z 0 ) and the radius R 0 as depicted in Figure 2(a). The ball centre C 0 was also treated as the geometric centre of missing region. Since the estimated value of the normal direction of missing region was N m , the plane Π was defined through the ball centre C 0 and perpendicular to the normal direction N m , so that the sampling points should be on plane Π. Defining arbitrary point C(x, y, z) on plane Π, then C 0 C(x-x 0 , y-y 0 , z-z 0 ), the plane Π was expressed by equation (3). The cross section of the plane Π and the MEB B r was the circle Π C with the centre C 0 and radius R 0 , as depicted in Figure 2 Figure 2(a) in grey. To ensure that all positions of missing regions of 3D surface were collected, the problem was converted to compute the minimum number of COVs Π Mi required to cover the circle Π C . Considering that the missing region was usually small, so that the difference between the radius of the circle Π Mi and the radius of the circle Π C was little, therefore, the minimum number of FOVs required to cover the MEB's cross section was computed by circumference division method and the spatial coordinates of the sampling points were arranged. Taking the diameter d of COV Π Mi as the chord length of circle Π C to equally divide the circumference of the circle Π C , defining that φ was the central angle corresponding to the string d and x was the number of required strings, the relationship between x and φ was expressed by x=[2π/φ+1], where [.] represented to be rounded down. According to the circumference division method, the number of strings x depends on the relationship between d and R 0 . When x>5, the missing region was relatively larger, which rarely appeared, so only

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International Conference on Robotics and Mechantronics (ICRoM 2017) IOP Publishing IOP Conf. Series: Materials Science and Engineering 320 (2018) 012006 doi:10.1088/1757-899X/320/1/012006 the situation when x<5 was considered. When x=1, the sampling point M i was the centre of the circle Π C , when x=3 or x=4, the number of sampling points was equal to the number of strings, and the sampling point M i was located at the midpoint of each chord of equally divided circumference. Since the missing region was quite small in most cases, it was usually required to arrange one sampling point.

Scanning path planning
On the theoretical basis of the 3D scanning constraints and the visibility cone concept, the scanning viewpoints were arranged and the scanning directions were confirmed, as depicted in Figure 2(b). In order to ensure that each position of the missing region was collected, the viewpoints S i were arranged on the axis parallel to the normal direction N m through the sampling point M i . The height of the viewpoint S i from the sampling point M i was between the near depth and the far depth of scanning vision and the scanning direction was C 0 N m . In specific scanning process, path planning was actually to determine the order of each scanning viewpoint, and then to confirm the corresponding movement trajectory of the scanner through the spatial position of each viewpoint. The procedure of scan path planning was described as following: • To determine the order of scanning viewpoints: connecting each viewpoint in the clockwise direction and scanning the viewpoint on the axis C 0 T in the end. • To plan the scanning path of adjacent viewpoints: applying the cubic spline interpolation method [15] to plan the trajectories between the two adjacent S i-1 and S i so as to ensure the stability of the whole scanning process. • To confirm the movement trajectory of scanner: establishing the relative spatial position relationship between the object and the scanner, transforming the planned path of viewpoints into the real trajectory of scanner, to complete the 3D scanning and surface reconstruction. In order to verify the effects of the two-stage scanning method, an experimental scanning system was set up as depicted in Figure 3(a). It consisted of a HandyScan300 3D scanner, a UR5 robotic manipulator, a Dell graphics processing station, a calibration board and other components. The main parameters of 3D scanner: the vision distance of was 300mm, the depth of field was 250mm, and the coverage area was 225mm x 250mm at the vision height. Since UR5 robot has six degrees of freedom,

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International Conference on Robotics and Mechantronics (ICRoM 2017) IOP Publishing IOP Conf. Series: Materials Science and Engineering 320 (2018) 012006 doi:10.1088/1757-899X/320/1/012006 strong load capacity and wide work range, it was applied with a customized gripper mounted on the end to carry the 3D scanner in the scanning process. The workflow of this robot based scanning system of the whole robot was depicted in Figure 3(b), and it was also applied with the two-stage scanning method. In the rough scanning, it required that to scan the surface of object at a faster speed to obtain the general point cloud data, which was able to increase the scanning efficiency with no need for high requirements of 3D information integrity. Similar to the motions of rough machining, the robot carried the scanner to perform alternating movements. In the process, the boresight axis of scanner was always vertically down, the scanning route interval was set to 150mm, and the speed of scanning was set to 0.3m/s, which was faster than the scanning speed by holding the scanner with hands. To roughly scan the object depicted in Figure 3(a), after processing 3D information collected by the scanner, relevant point cloud data was obtained, in which the total number of points was 1.31657E+5 and the superficial area after fitting was 3.858923E+4mm 2 . It was easily determined that the missing regions are M1 and M2 based on initial scanning results as depicted in Figure 4(a). Applying the shrinkage optimization method to enclosing compute the point cloud of boundaries of missing regions M1 and M2 respectively, the MEB centre of M1 was obtained at (72.86, -226.61, 188.22) and the radius was 8.12mm, similarly the MEB centre of M2 was at (23.35, -236.77, 198.62) and the radius was 16.07mm. Considering the geometric relationships in vision distance, depth of field, coverage area and other parameters of scanner, the radius of COV was computed to be 93.75mm. The radiuses of circles produced from the MEBs of M1 and M2 intersecting with respective Π planes were 8.12mm and 16.07mm respectively, and the ratios to the radius of COV were 0.09 and 0.17 respectively. The number of sampling points was set to 1 by the circumference division method. Therefore, the sampling points were arranged and the scanning viewpoints, the scanning directions and the scanning paths were all able to be planned. Then transforming the scan path into the movement trajectories of robot, guided the robot equipped with 3D scanner was guided to repair scanning the missing regions through specific sampling points and scanning directions, the complete point cloud data of object as depicted in Figure 4(b). After that, the number of points included in scanned point cloud data of object became 1.34053E+5 and superficial area after fitting became 3.93980E+4mm 2 , increased by 2396 and 808.77mm 2 respectively, compared to the obtained data in rough scanning, which meant that the quality of scanning was improved and the topography of object surface was completed in the end.

Conclusion
In order to pursuit the quality of scanning in a faster speed, a new two-stage method was presented in 3D laser surface scanning process for unknown object. In the first rough scanning, the general contour and topography of surface were obtained as point cloud data, and the missing regions were determined by using chord length method. In the second specific scanning, focusing on the missing regions, the exact sampling locations and the scanning paths were planned by MEB theory and regional coverage theory. The improvement method was implemented in a robot based scanning system which contained a robotic manipulator and a handy scanner, with the advantages of convenient operability and fast movability. Utilizing a robotic platform, it not only enhanced the stability of scanning, but also reduced the errors caused by shock and vibration in the scanner's movements. Finally, relevant experiments were carried out and the results were evaluated for the feasibility and effectiveness of this two-stage scanning method, and both of speed and quality of scanning were improved.