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below, show in this plane the outline of the sensing eld(s) for each point. The points ( 1 , 2 ) to check are, respectively: (90 , 0 ), (90 , 45 ), (90 , 90 ), (30 , 150 ), (30 , 135 ), (30 , 90 ) 3. Come up with an example of sensor-based motion planning for the prismatic prismatic (PP) arm manipulator algorithm (Section 5.4). The scene in the example shall feature nonconvex shapes of the arm link l2 and of obstacles in the workspace. Compare the results with the example in Figure 5.23. 4. Modify the sensor-based motion planning algorithm for the PP arm (Section 5.4), so as to incorporate in it a possibility of the rear end of link l2 to collide with obstacles. Connect this modi cation with the test for target reachability, and show that the modi ed algorithm converges. Provide an example where the arm goes through a local cycle.

Underconstrained: This is the at region near the bottom where the constraint was de ned to be less than 95 MHz. In this region, a compact implementation of the logic will run at approximately 95 MHz without any signi cant timing optimizations. Optimization region: The linear region between 95 MHz and 135 MHz that represents the range where increases in the timing constraints can be ful lled by corresponding optimizations in the logic implementation. In other words, the timing constraints in this region can be met by synthesizing higher speed (and correspondingly higher area) logic structures. Peak: The upper peak represents the maximum constraint that can be satis ed with improvements to the logic structure given the parallel architectures for the speci c design and the amount of space available in the FPGA. Overconstrained: This is the at region near the top where the constraint exceeds the maximum achievable frequency.

The robot is going to lose. Not by much. But when the nal score is tallied, esh and blood is going to beat the damn monster.

I was sure that they didn t actually have this much cash on them At this point their anger at each other was bound to turn into hurt and worry My head was spinning The losses in my trading account from that morning had faded away The situation here transfixed me Then Harvey.

This example helps to illustrate the problem associated with overconstraining a design. If the target frequency is set too high (i.e., greater than 15 20% above the nal speed), the design can be implemented in a suboptimal manner that actually results in a lower maximum speed. During the initial implementation, the synthesis tool will create logic structures based on the timing requirements. If during the initial timing analysis phase it is determined that the design is too

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6.1 INTRODUCTION We are continuing developing SIM (Sensing Intelligence Motion) algorithms for robot arm manipulators. The cases considered in 5 all deal with arm manipulators whose end effectors (hands) move along a two-dimensional (2D) surface. Although applications do exist that can make use of those algorithms for example, assembly of microelectronics on a printed circuit board is largely limited to a 2D operation most robot arm manipulators live and work in three-dimensional (3D) space. From this standpoint, our primary objective in 5 should be seen as preparing the necessary theoretical background and elucidating the relevant issues, before proceeding to the 3D case. Sensorbased motion planning algorithms should be able to handle 3D space and 3D arm manipulators. Developing such strategies is the objective of this chapter. As before, the arm manipulators that we consider are simple open kinematic chains. Is there a fundamental difference between motion planning for two-dimensional (2D) and 3D arm manipulators The short answer is yes, but the question is not that simple. Recall a similar discussion about mobile robots in 3. From the standpoint of motion planning, mobile robots differ from arm manipulators: They have more or less compact bodies, kinematics plays no decisive role in their motion planning, and their workspace is much larger compared to their dimensions. For mobile robots the difference between the 2D and 3D cases is absolute and dramatic: Unequivocally, if the 2D case has a de nite and nite solution to the planning problem, the 3D case has no nite solution in general. The argument goes as follows. Imagine a bug moving in the two-dimensional plane, and imagine that on its way the bug encounters an object (an obstacle).

far from achieving timing, the tool may give up early. If, however, the constraints are set to the correct target and not more than 20% above the nal frequency (assuming it does not make timing initially), the logic will be implemented with minimal area to achieve the speci ed timing and will have more exibility during timing closure. It is also important to point out that due to second order effects of the FPGA implementation, targeting a smaller design may or may not also improve timing depending on the particular circumstances. This issue is discussed in later sections.