MOTION PLANNING FOR A MOBILE ROBOT in Visual Studio .NET

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Figure 3.25 Performance of algorithm VisBug-21 in the same scene (a) with a smaller radius of vision and (b) with a larger radius of vision. The smaller (worse) vision results in a shorter path!
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These examples demonstrate the variety of types of uncertainty. Notice another interesting fact: While the experienced hiker and experienced stock broker can make use of a probabilistic analysis, it is of no use in the problem of motion planning with incomplete information. A direction to pass around an obstacle that seems to promise a shorter path to the target may offer unpleasant surprises around the corner, compared to a direction that seemed less attractive before but is objectively the winner. It is far from clear how (and whether) one can impose probabilities on this process in any meaningful way. That is one reason why, in spite of high uncertainty, sensor-based motion planning is essentially a deterministic process.
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3.10 DISCUSSION The somewhat surprising examples above (see the last few gures in the previous section) suggest that further theoretical analysis of general properties of Class 2 algorithms may be of more bene t to science and engineering than proliferation of algorithms that make little difference in real-world tasks. One interesting possibility would be to attempt a meaningful classi cation of scenes, with a predictive power over the performance of various algorithmic schemes. Our conclusions from the worst-case bounds on algorithm performance also beg for a similar analysis in terms of some other, perhaps richer than the worst-case, criteria.
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This said, the material in this chapter demonstrates a remarkable success in the last 10 15 years in the state of the art in sensor-based robot motion planning. In spite of the formidable uncertainty and an immense diversity of possible obstacles and scenes, a good number of algorithms discussed above guarantee convergence: That is, a mobile robot equipped with one of these procedures is guaranteed to reach the target position if the target can in principle be reached; if the target is not reachable, the robot will make this conclusion in nite time. The algorithms guarantee that the paths they produce will not circle in one area an inde nite number of times, or even a large number of times (say, no more than two or three). Twenty years ago, most specialists would doubt that such results were even possible. On the theoretical level, today s results mean, to much surprise from the standpoint of earlier views on the subject, that purely local input information is not an obstacle to obtaining global solutions, even in cases of formidable complexity. Interesting results raise our appetite for more results. Answers bring more questions, and this is certainly true for the area at hand. Below we discuss a number of issues and questions for which today we do not have answers.
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Bounds on Performance of Algorithms with Vision. Unlike with tactile algorithms, today there are no upper bounds on performance of motion planning algorithms with vision, such as VisBug-21 or VisBug-22 (Section 3.6). While from the standpoint of theory it would be of interest to obtain bounds similar to the bound (3.13) for tactile algorithms, they would likely be of limited generality, for the following reasons. First, to make such bounds informative, we would likely want to incorporate into them characteristics of the robot s vision at least the radius of vision rv , and perhaps the resolution, accuracy, and so on. After all, the reason for developing these bounds would be to know how vision affects robot performance compared to the primitive tactile sensing. One would expect, in particular, that vision improves performance. As explained above, this cannot be expected in general. Vision does improve performance, but only on the average, where the meaning of average is not clear. Recall some examples in the previous section: In some scenes a robot with a larger radius of vision rv will perform worse than a robot with a smaller rv . Making the upper bound re ect such idiosyncrasies would be desirable but also dif cult. Second, how far the robot can see depends not only on its vision but also on the scene it operates in. As the example in Figure 3.24 demonstrates, some scenes can bring the ef ciency of vision to almost that of tactile sensing. This suggests that characteristics of the scene, or of classes of scenes, should be part of the upper bounds as well. But, as geometry does not like probabilities, the latter is not a likely tool: It is very hard to generalize on distributions of locations and shapes of obstacles in the scene. Third, given a scene and a radius of vision rv , a vastly different path performance will be produced for different pairs of start and target points in that same scene.
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