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needed in order to fully utilize additional sensing capabilities. We will consider in detail two principles for provably correct motion planning with vision. As we will see, the resulting algorithms exhibit different styles of behavior and are not, in general, superior to each other. Third and very interestingly, while one can expect great improvements in real-world tasks, in general richer sensing has no effect on algorithm path length performance bounds. Algorithms that we are about to consider will demonstrate an ability that is often referred to in the literature as active vision [61, 62]. This ability goes deeply into the nature of interaction between sensing and control. As experimentalists well know, scanning the scene and making sense of acquired information is a time-consuming operation. As a rule, the robot s eye sees a bewildering amount of details, almost all of which are irrelevant for the robot s goal of nding its way around. One needs a powerful mechanism that would reject what is irrelevant and immediately use what is relevant so that one can continue the motion and continue gathering more visual data. We humans, and of course all other species in nature that use vision, have such mechanisms. As one will see in this section, motion planning algorithms with vision that we will develop will provide the robot with such mechanisms. As a rule, the robot will not scan the whole scene; it will behave much as a human when walking along the street, looking for relevant information and making decisions when the right information is gathered. While the process is continuous, for the sake of this discussion it helps to consider it as a quasi-discrete. Consider a moment when the robot is about to pass some location. A moment earlier, the robot was at some prior location. It knows the direction toward the target location of its journey (or, sometimes, some intermediate target in the visible part of the scene). The rst thing it does is look in that direction, to see if this brings new information about the scene that was not available at the prior position. Perhaps it will look in the direction of its target location. If it sees an obstacle in that direction, it may widen its scan, to see how it can pass around this obstacle. There may be some point on the obstacle that the robot will decide to head to, with the idea that more information may appear along the way and the plan may be modi ed accordingly. Similar to how any of us behaves when walking, it makes no sense for the robot to do a 360 scan at every step or ever. Based on what the robot sees ahead at any moment, it decides on the next step, executes it, and looks again for more information. In other words, robot s sensing dictates the next step motion, and the next step dictates where to look for new relevant information. It is this sensing-planning control loop that guides the robot s active vision, and it is executed continuously. The rst algorithm that we will consider, called VisBug-21, is a rather simpleminded and conservative procedure. (The number 2 in its name refers to the Bug2 algorithm that is used as its base, and 1 refers to the rst vision algorithm.) It uses range data to cut corners that would have been produced by a tactile algorithm Bug2 operating in the same scene. The advantage of this modi cation is clear. Envision the behavior of two people, one with sight and the
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other blindfolded. Envision each of them walking in the same direction around the perimeter of a complex-shaped building. The path of the person with sight will be (at least, often enough) a shorter approximation of the path of the blindfolded person. The second algorithm, called VisBug-22, is more opportunistic in nature: it tries to use every chance to get closer to the target. (The number in its name signi es that it is the vision algorithm 2 based on the Bug2 procedure.) Section 3.6.1 is devoted to the algorithms underlying model and basic ideas. The algorithms themselves, related analysis, and examples demonstrating the algorithms performance appear in Sections 3.6.2 and 3.6.3. 3.6.1 The Model Our assumptions about the scene in which the robot travels and about the robot itself are very much the same as for the basic algorithms (Section 3.1). The available input information includes knowing at all times the robot s current location, C, and the locations of starting and target points, S and T . We also assume that a very limited memory does not allow the robot more than remembering a few interesting points. The difference in the two models relates to the robot sensing ability. In the case at hand the robot has a capability, referred to as vision, to detect an obstacle, and the distance to any visible point of it, along any direction from point C, within the sensor s eld of vision. The eld of vision presents a disc of radius rv , called radius of vision, centered at C. A point Q in the scene is visible if it is located within the eld of vision and if the straight-line segment CQ does not cross any obstacles. The robot is capable of using its vision to scan its surroundings during which it identi es obstacles, or the lack of thereof, that intersect its eld of vision. We will see that the robot will use this capability rather sparingly; the particular use of scanning will depend on the algorithm. Ideally the robot will scan a part of the scene only in those speci c directions that make sense from the standpoint of motion planning. The robot may, for example, identify some intermediate target point within its eld of vision and walk straight toward that point. Or, in an unfortunate (for its vision) case when the robot walks along the boundary of a convex obstacle, its effective radius of vision in the direction of intended motion (that is, around the obstacle) will shrink to zero. As before, the straight-line segment (S, T ) between the start S and target T points it is called the Main line or M-line is the desirable path. Given its current position Ci , at moment i the robot will execute an elementary operation that includes scanning some minimum sector of its current eld of vision in the direction it is following, enough to de ne its next intermediate target, point Ti . Then the robot makes a little step in the direction of Ti , and the process repeats. Ti is thus a moving target; its choice will somehow relate to the robot s global goal. In the algorithms, every Ti will lie on the M-line or on an obstacle boundary. For a path segment whose point Ti moves along the M-line, the rstly de ned Ti that lies at the intersection of M-line and an obstacle is a special point called the hit point, H . Recall that in algorithms Bug1 or Bug2 a hit point would be
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