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digital design: power. Here we also discuss methods for architectural power optimization in an FPGA. Relative to ASICs (application speci c integrated circuits) with comparable functionality, FPGAs are power-hungry beasts and are typically not well suited for ultralow-power design techniques. A number of FPGA vendors do offer lowpower CPLDs (complex programmable logic devices), but these are very limited in size and capability and thus will not always t an application that requires any respectable amount of computing power. This section will discuss techniques to maximize the power ef ciency of both low-power CPLDs as well as general FPGA design. In CMOS technology, dynamic power consumption is related to charging and discharging parasitic capacitances on gates and metal traces. The general equation for current dissipation in a capacitor is I V C f where I is total current, V is voltage, C is capacitance, and f is frequency. Thus, to reduce the current drawn, we must reduce one of the three key parameters. In FPGA design, the voltage is usually xed. This leaves the parameters C and f to manipulate the current. The capacitance C is directly related to the number of gates that are toggling at any given time and the lengths of the routes connecting the gates. The frequency f is directly related to the clock frequency. All of the power-reduction techniques ultimately aim at reducing one of these two components. During the course of this chapter, we will discuss the following topics:

As another option, one might argue that because in any realistic system the robot moves in discrete steps, those steps might be used to build a real-time objects approximation This choice is also hard to defend because the size and number of those steps may differ from one robot control system to the other What is left is to estimate the quality of the path itself that the algorithm generates A better measurement of algorithm ef ciency in the case with uncertainty is a function tied to the length of paths that the algorithm generates More precisely, the criterion measures the extent of the robot s wandering under a given algorithm: It assesses the maximum number of times, n, of the robot s retracing some segments of its path When comparing algorithms, this upper bound will actually.

Less rigorous ways may include, for example, a direct comparison of an algorithm s results with those of other existing algorithms, or with the performance of an average human traveler.

The impact of clock control on dynamic power consumption Problems with clock gating Managing clock skew on gated clocks Input control for power minimization

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be independent of the length of paths, in the following sense We can say, for example, that the algorithm A is better than the algorithm B because their n numbers are 2 and 35, respectively That is, under algorithm A the robot will visit the same piece of its path at most twice, whereas under algorithm B it can visit a piece of its path at most 35 times One inherent weakness in algorithms with incomplete information is that the problem dimensionality cannot be made arbitrarily high This drawback, again, comes from the nature of dealing with uncertainty, not from the lack of good algorithms Consider, for example, a point robot ying in the three-dimensional space, like a y If the robot meets an obstacle, it has an in nite number of possibilities for passing around it.

Given the robot s limited knowledge about the scene, its dif culty is unsurmountable: While good sensing will often help, in the worst case the robot may have to search an in nite number of paths to nd one acceptable path Luckily, for the cases of practical interest mobile robots moving on a 2D surface and 3D arm manipulators the situation is inherently easier The lack of information about the robot environment dictates a shift of emphasis in the SIM paradigm from objects geometry to their topology Relying on geometric properties of objects, as in the Piano Mover s model, would make SIM algorithms too brittle We will see that a more sensible approach is to rely on the scene s topological properties; this allows one to tolerate uncertainty in objects geometry Hence there is a corresponding shift in the SIM paradigm from computational geometry tools to those from topology.

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