Tham khảo tài liệu 'sensing intelligence motion - how robots & humans move - vladimir j. lumelsky part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 186 MOTION PLANNING FOR TWO-DIMENSIONAL ARM MANIPULATORS robot around simple closed curves. The key property will then be deduced For a two-link arm no matter how complex the arm motion around an actual physical obstacle in W-space the corresponding virtual boundary in C-space presents a simple curve that is a curve with no self-intersections and double points. This will be shown to be true for each of the arms in Figure . With this property in hand by transforming the motion planning problem from W-space to C-space we will effectively make our problem similar to the one that was tackled in Chapter 3 for mobile robots. In fact on a certain level of generalization both problems look identical. The actual algorithms will differ due to a number of new issues that need to be worked out. Still understanding the Bug family algorithms from Chapter 3 will help one grasp the algorithms for robot arms that we are about to develop. We can now sketch the idea behind a motion planning algorithm for a planar robot arm manipulator. It is easier to describe the operation in C-space the actual operation in W-space proceeds accordingly. As one will notice the sketch sounds much like the algorithm Bug2 deviations and complexities will be added later. At the beginning the C-space arm image point moves along a simple M-line which is a desired path from point s to point T an equivalent of the straight-line M-line for the mobile robot Section . During this motion when in W-space some point of the arm body meets an obstacle in C-space this corresponds to the image of M-line intersecting the obstacle s virtual boundary. The point of intersection is said to define a hit point Hj where j is the running index enumerating such points. We will show below that the virtual boundary is a simple curve a curve with no self-intersections or double points. This being so at the hit point the arm has a simple choice to walk along the virtual boundary in one or the opposite direction along the .
