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As can be seen in the waveforms, a transition within the boundaries of the setup and hold conditions means that the output could rise to a voltage level that is not valid for either logic value. If a ip- op contains an output buffer, the metastability may manifest itself as a spurious transition at the output as the internal signal settles. The amount of time the output can stay metastable is probabilistic, and it is possible for the output to remain metastable for the entire clock period. Thus, if this metastable value is fed into combinatorial logic, incorrect operations may occur depending on the thresholds of the logic gates. From a timing closure standpoint, the delay through the logic from one ip- op to another is assumed to be less than the minimum clock period, but with a metastable signal the duration of metastability will consume available path delay. Clearly, a metastable signal can cause catastrophic functional failures in a design and will be very inconsistent depending on the relationship of the clock edges.

A serious analysis of holonomic and nonholonomic systems requires more rigorous mathematical de nitions. These will be introduced later as needed. 1.2.6 Robot Programming A robot executes a given motion because it is programmed to do so. The meaning of the words robot motion programming is not dissimilar to what an adult does when teaching a child how to walk. One can distinguish between two basic approaches to robot motion programming:

Explicit robot motion programming when every robot con guration along the path is prescribed explicitly. One variation of this is when a set of con gurations is given explicitly beforehand, and the robot interpolates con gurations between the set points using some rule. Task-level robot motion programming in which contents-based subtasks are given, such as Grasp a part or Insert a peg in a hole, and the robot gures out further details on its own.

One important thing to note about the FPGA design ow is that simulating the effects of metastability can be very dif cult. Digital-only simulators will not check for setup and hold violations, and then propagate a logic-X (unknown) if the violation occurs. In an RTL simulation, no setup and hold violations occur, and thus no signal will ever go metastable. Even with gate-level simulations, that check for setup and hold violations, it may be a dif cult matter to simulate a condition where two asynchronous signals line up to cause a synchronization failure. This is especially dif cult when the design or veri cation engineer is not looking for the problem in the rst place. Thus, it is extremely important to understand how to design for reliability and avoid the need to uncover synchronization issues in simulation. There are a number of solutions to this problem, and these are discussed in the remainder of this chapter.

It helped put my feet back down on earth and my mind back into the present..

The subtask above can be a complex motion or procedure that has been programmed separately beforehand. For example, details of the task Grasp a part may differ from one task instantiation to the other, depending on the sensing data. Clearly, task-level programming is, in general, preferable to explicit programming. It is also signi cantly more dif cult to realize because it requires much beforehand knowledge on the part of the robot. The programming of a dancer or a gymnast is clearly closer to the task-level approach than to the explicit programming. The choreographer can, for example, say to the ballerina, Here you do a pirouette followed by an arabesque. A pirouette is a rather complex combination of little motions that the ballerina learned while at school. The motions have been programmed into her, so just naming it is suf cient for her to know what to do. The same is so for an arabesque. On the other hand, this does not mean the pirouette will be exactly the same at all times: For instance, the ballerina may slightly deviate from her usual pirouette when seeing another dancer backing up toward her. Another classi cation of robot motion programming is given by different types of robot teaching systems. A robot teaching system is a speci c technique for robot programming. The following list applies primarily to robot arm manipulators; the corresponding analogues for mobile robots are simpler and present a subset of this list: