MOTION PLANNING FOR TWO-DIMENSIONAL ARM MANIPULATORS in .NET

Maker PDF417 in .NET MOTION PLANNING FOR TWO-DIMENSIONAL ARM MANIPULATORS
MOTION PLANNING FOR TWO-DIMENSIONAL ARM MANIPULATORS
Scanning PDF-417 2d Barcode In Visual Studio .NET
Using Barcode Control SDK for .NET framework Control to generate, create, read, scan barcode image in VS .NET applications.
the sensing range will be a complex gure (Figure 5.16) that surrounds the arm and changes its shape as the arm links move relative to each other. In C-space the situation is somewhat closer to the mobile robot sensing range simply because in C-space the arm becomes a point. But that s where the similarity stops. Assume that the arm s sensing allows it to sense objects in W -space within some sensing range r (Figure 5.16). An obstacle will be detected when it is at a distance equal to or smaller than r from the point on the arm body closest to it. With this kind of proximity sensing, the robot s sensing range in C-space plane ( 1 , 2 ) is not a circle anymore. In fact, it is not even an entity with xed parameters. The sensing range image will look in C-space more or less like the one in Figure 5.17 (point C is the arm s current position). As the arm links move relative to the arm base and relative to each other, the joint angles ( 1 , 2 ) change accordingly. The sensing range C-space image then moves in the plane ( 1 , 2 ),
Paint PDF-417 2d Barcode In .NET
Using Barcode creation for .NET framework Control to generate, create PDF417 image in Visual Studio .NET applications.
C q2
PDF417 Decoder In Visual Studio .NET
Using Barcode reader for VS .NET Control to read, scan read, scan image in VS .NET applications.
q1 0
Barcode Drawer In .NET
Using Barcode drawer for Visual Studio .NET Control to generate, create barcode image in VS .NET applications.
C q1
Recognizing Bar Code In .NET
Using Barcode recognizer for Visual Studio .NET Control to read, scan read, scan image in .NET framework applications.
Figure 5.17 In C-space the sensing range of the revolute revolute arm has a shape similar to the one shown here. The point in the center of the gure corresponds to the values ( 1 , 2 ) of the arm s current position. As the arm moves in its workspace, this gure moves in C-space, with its shape and dimensions changing continuously.
Draw PDF-417 2d Barcode In Visual C#
Using Barcode generator for .NET Control to generate, create PDF-417 2d barcode image in Visual Studio .NET applications.
PLANAR REVOLUTE REVOLUTE (RR) ARM
PDF417 Creator In .NET
Using Barcode drawer for ASP.NET Control to generate, create PDF417 image in ASP.NET applications.
with its shape and dimensions shrinking and expanding from rectangle-like to ellipse-like, and with shapes in between like in Figure 5.17. Animation of this process makes for a wonderful movie: One sees a strange creature that is moving while constantly changing its shape according to some mystifying law. The extent of variability in the sensing range C-space image depends on the sensing range r and the arm s kinematics. Calculation of the sensing range C-space image is an interesting though rather involved task; there are many details and many special cases to attend to. With good equations for the sensing range, one could improve motion planning algorithms by providing a look-ahead optimization of the arm s next few steps, or attempt algorithms that take into account the arm dynamics, similar to the work we did in 4. To my knowledge, today there are no published analyses on this topic. As a rst approximation, one can start with a simpli ed model of the sensing range, presenting it as a circle whose radius changes as a function of the arm position ( 1 , 2 ). A conservative approximation would be to model the arm sensing by the maximum circle inscribed in the real sensing range. With this model the robot would be safe, but much sensing would be wasted: In some directions in the ( 1 , 2 ) plane the actual sensing will go much farther than the circular model will indicate. As the arm moves, its sensing range image in C-space breathes, shrinking and expanding as it moves in the plane ( 1 , 2 ). The extent of such changes depends on the motion. It is easy to see, for example, that if we x angle 2 and let angle 1 change, in C-space of Figure 5.17 the sensing range gure will move horizontally, and its shape will remain the same. This is because the motion does not involve any changes in the relative position of links l1 and l2 . Any motion involving a change in angle 2 will cause changes in the shape of the sensing range gure. Except for the added calculation due to the variable sensing range in C-space, incorporating proximity sensing in the arm motion planning algorithm is similar to the analogous process for mobile robots (Section 3.6). One can combine, for example, one of the VisBug algorithms for a mobile robot (Section 3.6) with the RR-Arm Algorithm developed in this chapter. The fact that the latter is noticeably more complex than Bug algorithms calls for a careful analysis. To date, there are no published results in this area, in spite of its signi cant theoretical and practical potential. How proximity sensing can affect the RR-Arm Algorithm performance can be seen in Figure 5.18. Here link l2 happens to be attached to link l1 not by its endpoint, as in some of our prior gures, but by some other point on the link. (This is a more realistic design; it often occurs in industrial arm manipulators.) Note how elegant and economical the arm s path becomes when the arm is provided with proximity sensing (Figure 5.18b), compared to its performance with tactile sensing (Figure 5.18a). In fact, the robot path in Figure 5.18b is almost the optimal path between the S and T locations; it could hardly be improved even by a procedure operating with complete information. This of course will
PDF-417 2d Barcode Printer In VB.NET
Using Barcode drawer for .NET Control to generate, create PDF417 image in VS .NET applications.
Code-128 Generation In Visual Studio .NET
Using Barcode encoder for .NET Control to generate, create USS Code 128 image in .NET framework applications.
UPC Symbol Creation In Visual Studio .NET
Using Barcode maker for Visual Studio .NET Control to generate, create UPC-A Supplement 5 image in .NET framework applications.
Generating Code 128 In Visual Basic .NET
Using Barcode generation for VS .NET Control to generate, create Code 128 Code Set A image in Visual Studio .NET applications.
Reading Barcode In Java
Using Barcode scanner for Java Control to read, scan read, scan image in Java applications.
Draw Code128 In .NET Framework
Using Barcode creator for ASP.NET Control to generate, create Code 128 image in ASP.NET applications.
Code 3/9 Creator In VB.NET
Using Barcode generator for .NET framework Control to generate, create Code 3/9 image in .NET applications.