tailieunhanh - Innovations in Robot Mobility and Control - Srikanta Patnaik et al (Eds) Part 12

Tham khảo tài liệu 'innovations in robot mobility and control - srikanta patnaik et al (eds) part 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 212 C. Castejón et al. Fig. . Normal in the point P estimation We define the lines Ộ and 0 as the horizontal and vertical scans respectively. And the 3D points image is defined as I 0 Ộ such as the value in each pixel is the depth p . In figure the normal vector is observed to be the normalized cross product of the tangent vectors to the lines Ộ and 0 called Pỳ and P9 . We mean -- --- A 0 ộ ĩpPĩp P A P with Sx x so Pfí Sy P - Sy SO ệ SỘ Sz Sz so sộ The surface orientation depends on the cross product sign the orientation is chosen such as NP goes always to the sensor direction. Mathematically the tangent vector is obtained when the curve in the point is derived. If a discretization is done and we apply digital image 6 Voronoi-Based Outdoor Traversable Region Modelling 213 processing techniques the continuous derivatives that appear in Pg and Pg are calculated by multiplying the mask and adding the elements. As can be seen in figure the slope is the angle between the normal vector in a point and the vector perpendicular to the XY situated in the robot base. The angle that defines the slope in the point P is calculated in the following equation NW inW cosệ where - . NW cos - __ in W and then Ẹ arccos - . NW n W1 1 1 This method gives the possibility to calculate the normal vector in each 3D point in a fast and easy way. It is suitable in unknown outdoor environments and non-structured because the operations are performed in a local neighbourhood. Besides the algorithm can be parallelized. Furthermore despite the slope values are not exact due to the filter applied its accuracy is enough for solving the navigation problem. In order to the robot physical restrictions basically the robot mass and its locomotion system a maximum and minimum slope that the robot can go up and go down exist. With the robot information the traversable slope analysis is performed as follows Definition 2. Given a three-dimensional points image I p ị Xị y ị zt