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MOTION PLANNING INTRODUCTION
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(e) They are exceedingly complex computationally in more or less complex practical tasks. 2. Topological Approaches. Humans and animals rarely face situations where one can approach the motion planning problem based on complete information about the scene. Our world is messy: It includes shapeless hard-to-describe objects, previously unseen settings, and continuously changing scenes. Even if faced with a geometric -looking problem, say, nding a path from point A to point B in a room with 10 octagonal tables, we would never think of computing rst the whole path. We take a look at the room, and off we go. We are tuned to dealing with partial information coming from our sensors. If we want our robots to handle unstructured tasks, they will be thrown in a similar situation. In a number of ways, topological approaches are an exact opposite of the geometrical approaches. What is dif cult for one will be likely easy for the other. Consider the above example of nding a path from point A to point B in a room with a few tables. The tables may be of the same or of differing shapes; we do not know their number, dimensions, and locations. A common human strategy may look something like this: While at A, you glance at the room layout in the direction of point B and start walking toward it. If a table appears on your way, you walk around it and continue toward point B. The words walking around mean that during this operation the table is on the same side from you (say, on the left). The table s shape is of no importance: While your path may repeat the table s shape, algorithmically it is immaterial for your walk around it whether the table is circular or rectangular or altogether highly nonconvex. Why does this strategy represent a topological, rather than geometric, approach Because it relies implicitly on the topological properties of the table for example, the fact that the table s boundary is a simple closed curve rather than on its geometric properties, such as the table s dimensions and geometry. We will see in 3 that the aforementioned rather simplistic strategy is not that bad especially given how little information about the scene it requires and how elegantly simple is the connection between sensing and decision-making. We will see that with a few details added, this strategy can guarantee success in an arbitrarily complex scene; using this strategy, the robot will nd a path if one exists, or will conclude there is no path if such is the case. On the negative side, since no full information is available in this process, no optimality of the resulting path can be guaranteed. Another minus, as we will see, is that generalizations of such strategies to arm manipulators are dependent on the robot kinematics. Let us summarize the properties of topological approaches to motion planning: (a) They are suited to unstructured tasks, where information about the robot surroundings appears in time, usually from sensors, and is never complete. (b) They rely on topological, rather than geometrical, properties of space. (c) They cannot in principle deliver an optimal solution.
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BASIC CONCEPTS
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(d) They cannot in principle handle tasks of arbitrary dimensionality, and they require specialized algorithms for each type of robot kinematics. (e) They are usually simple computationally: If a technique is applicable to the problem in hand, it will likely be computationally easy.
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1.2 BASIC CONCEPTS This section summarizes terminology, de nitions, and basic concepts that are common to the eld of robotics. While some of these are outside of this book s scope, they do relate to it in one way or another, and knowing this relation is useful. In the next chapter this material will be used to expand on common technical issues in robotics. 1.2.1 Robot What Robot De ning what a robot is is not an easy job. As mentioned above, not only scientists and engineers have labored here, but also Hollywood and ction writers and professionals in humanities have helped much in diffusing the concept. While this fact will not stand in our way when dealing with our topic, starting with a decent de nition is an old tradition, so let us try. There exist numerous de nitions of a robot. Webster s Dictionary de nes it as follows:
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A robot is an automatic apparatus or device that performs functions ordinarily ascribed to humans, or operates with what appears to be almost human intelligence.
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Half of the de nition by Encyclopaedia Britannica is devoted to stressing that a robot does not have to look like a human:
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Robot: Any automatically operated machine that replaces human effort, though it may not resemble human beings in appearance or perform functions in a humanlike manner.
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These de nitions are a bit vague, and they are a bit presumptuous as to what is and is not almost human intelligence or a humanlike manner. One senses that a chess-playing machine may likely qualify, but a machine that automatically digs a trench in the street may not. As if the latter does not require a serious intelligence. (By the way, we do already have champion-level chess-playing machines, but are still far from having an automatic trench-digging machine.) And what about a laundry washing machine This function has been certainly ordinarily ascribed to humans for centuries. The emphatic automatic is also bothersome: Isn t what is usually called an operator-guided teleoperation robot system a robot in spite of not being fully automatic
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