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Tham khảo tài liệu 'sensing intelligence motion - how robots & humans move - vladimir j. lumelsky part 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 306 MOTION PLANNING FOR THREE-DIMENSIONAL ARM MANIPULATORS In particular in Section 6.3.1 we define the arm configuration Lj L j as an image of a continuous mapping from J-space to 3D Cartesian space i i3 which is the connected compact set of points the arm would occupy in 3D space when its joints take the value j. A real-world obstacle is the interior of a connected compact point set in i i3. Joint space obstacles are thus defined as sets of points in joint space whose corresponding arm configurations have nonempty intersections with real-world obstacles. The task is to generate a continuous collision-free motion between two given start and target configurations denoted Ls and Lt. Analysis of a J-space in Section 6.3.2 will show that a J-space exhibits distinct topological characteristics that allow one to predict global characteristics of obstacles in J based on the arm local contacts with that is sensing of obstacles in the workspace. Furthermore similar to the Cartesian arm case in Section 6.2 for all XXP arms the obstacles in J exhibit a property called the monotonicity property as follows For any point on the surface of the obstacle image there exists one or more directions along which all the remaining points of J belong to the obstacle. The geometric representation of this property will differ from arm to arm but it will be there and topologically will be the same property. These topological properties bring about an important result formulated in Section 6.3.3 The free J-space Jf is topologically equivalent to a generalized cylinder. This result will be essential for building our motion planning algorithm. Deformation retracts D of J and Df of Jf respectively are defined in Section 6.3.4. By definition Df is a 2D surface that preserves the connectivity of Jf. That is to say for any two points js jt G Jf if there exists a path pJ c Jf connecting js and jt then there must exist a path pD c Df connecting js and jt and pD is topologically equivalent to pJ in .
