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+ t 3 b + (3 b b )(1 t) + ( b 6 b + 12 b )

The fundamental problem with this approach was that a new HDL language had been invented that was no more easy to use than the standard languages for HDL Additionally, they required an extra synthesis step (sometimes automated, sometimes not) that could have been easily bypassed in the rst place The argument in favor of the cycle-based C language was that it could be compiled and run against other C models, but for the majority of HDL designers, this was unnecessary for most of their applications Although there are applications where this is a t, C-based design still has not caught on in the mainstream FPGA world because the EDA companies have not convinced the design community that there is a bene t or simpli cation of the design process with C-level design.

He was like my mother! He could see what I did at all times, he was Momnipresent No wonder this man had frightened me for 10 years A job-spanking for John Murphy, and possibly the loss of his cushy new corner-office location For me Maybe fired Maybe worse Gosh, I thought, I had even put Craig Taylor s job in jeopardy Maybe he was down there on Floor 31 getting beat down, and totally missing out on tasty pips from the FOMC interest rate decision What had the FOMC decided Maybe I should have checked that before I traded Craig said it could move 100 pips in one minute What about after that Would Anderson interview me for a job now How could I get myself out of this mess and back to looking at my trade My mind raced onward, toward nothing in particular.

Straight-Line Interpolation. Achieving a straight-line motion with the arm shown in Figure 2.12 may be tricky. The reason for that is that the arm s rotating joints move links endpoints on circular curves. This means that we cannot have an ideal straight line, and so we need to synthesize it from curves. The more those curves and the shorter they are, the better our straight-line approximation. To accomplish this, we will calculate a number of points along the desired straight line, and will force the arm endpoint through those points. Between those guaranteed points, the arm will move as it pleases; more precisely, the arm s own control will be linearly interpolating points between our speci ed points. The interpolation is done in terms of joint angles, or, as we call it, in the arm s joint space (or con guration space). To summarize, the straight-line interpolation of added points is to be done in Cartesian space, and the arm s own interpolation between those given points takes place in joint space. Assume, for example, that the 1 and 2 angles of points pa and pb in Figure 2.12 are pa = (0, ) and pb = ( , ). This corresponds, 6 3 2 respectively, to these Cartesian coordinates:

One of the primary bene ts of C-level design today is the ability to simulate hardware and software in the same environment Despite this, it is still important to understand where to divide the line between software and hardware implementation A few of the issues to consider are listed here Complexity: There are certain algorithms that simply lend themselves well to a software implementation over hardware Sophisticated algorithms that require recursion or a number of iterations that is not well de ned prior to executing the.

If we provide the robot with only starting and ending points (pa , pb ) of the desired straight-line path (pa , pc , pb ) (Figure 2.13), then, given the robot s joint space linear interpolation procedure, it will produce instead the curve (pa , pj , pb ). The midpoints of the joint and Cartesian paths indicate the extent of deviation of the actual path from the desired path: in Cartesian terms, pj = ( 23 l1 , ( 1 l1 + l2 )) 2 and pc = ( 3 l1 , ( 43 l1 + 1 l2 )). 4 2 A reasonable idea then is to further approximate the desired straight-line path by forcing the robot endpoint through more intermediate points along the straight line. This is called the bounded deviation paths technique [10]; the added points are called knots. The process starts with two knots, the initial and ending points.