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vehicle navigation. Although robot arm manipulators are very important for theory and practice, little has been done for them until later, when the underlying issues became clearer. An incomplete list of path planning heuristics includes Refs. 28 and 47 52. Not rarely, attempts for planning with incomplete information have their starting point in the Piano Mover s model and in planning with complete information. For example, in heuristic algorithms considered in Refs. 47, 48 and 50, a piece of the path is formed from the edges of a connectivity graph resulting from modeling the robot s surrounding area for which information is available at the moment (for example, from the robot s vision sensor). As the robot moves to the next area, the process repeats. This means that little can be said about the procedures chances for reaching the goal. Obstacles are usually approximated with polygons; the corresponding connectivity graph is formed by straightline segments that connect obstacle vertices, the robot starting point, and its target point, with a constraint on nonintersection of graph edges with obstacles. In these works, path planning is limited to the robot s immediate surroundings, the area for which sensing information on the scene is available from robot sensors. Within this limited area, the problem is actually treated as one with complete information. Sometimes the navigation problem is treated as a hierarchical problem [48, 53], where the upper level is concerned with global navigation for which the information is assumed available, while the lower level is doing local navigation based on sensory feedback. A heuristic procedure for moving a robot arm manipulator among unknown obstacles is described in Ref. 54. Because the above heuristic algorithms have no theoretical assurance of convergence, it is hard to judge how complete they are. Their explicit or implicit reliance on the so-called common sense is founded on the assumption that humans are good at orienting and navigation in space and at solving geometrical search problems. This assumption is questionable, however, especially in the case of arm manipulators. As we will see in 7, when lacking global input information and directional clues, human operators are confused, lose their sense of orientation, and exhibit inferior performance. Nevertheless, in relatively simple scenes, such heuristic procedures have been shown to produce an acceptable performance. More recently, algorithms have been reported that do not have the above limitations they treat obstacles as they come, have a proof of convergence, and so on and are closer to the SIM model. All these works deal with motion planning for mobile robots; the strategies they propose are in many ways close to the algorithms studied further in 3. These works will be reviewed later, in Section 3.8, once we are ready to discuss the underlying issues. With time the SIM paradigm acquired popularity and found a way to applications. Algorithms with guaranteed convergence appeared, along with a plethora of heuristic schemes. Since knowing the robot location is important for motion planning, some approaches attempted to address robot localization and motion
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planning within the same framework.8 Other approaches assume that, similar to human and animals motion planning, the robot s location in space should come from sensors or from some separate sensor processing software, and so they concentrate on motion planning and collision-avoidance strategies. Consider the scene shown in Figure 2.22. A point robot starts at point S and attempts to reach the target point T . Since the robot knows at all times where point T is, a simple strategy would be to walk toward T whenever possible. Once the robot s sensor informs it about the obstacle O1 on its way, it will start passing around it, for only as long as it takes to clear the direction toward T , and then continue toward T . Note that the ef ciency of this strategy is independent of the complexity of obstacles in the scene: No matter how complex (say, ord-like) an obstacle boundary is, the robot will simply walk along this boundary. One can easily build examples where this simple idea will not work, but we shall see in the sequel that slightly more complex ideas of this kind can work and even guarantee a solution in an arbitrary scene, in spite of the high uncertainty and scant knowledge about the scene. Even more interesting, despite the fact that arm manipulators present a much more complex case for navigation than do mobile robots, such strategies are feasible for robot arm manipulators as well. To repeat, in these strategies, (a) the robot can start with zero information about the scene,
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Figure 2.22 A point robot starts at point S and attempts to reach the target location T . No knowledge about the scene is available beforehand, and no computations are done prior to the motion. As the robot encounters an obstacle, it passes it around and then continues toward T . If feasible, such a strategy would allow real-time motion planning, and its complexity would be a constant function of the scene complexity.
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One name for procedures that combine localization and motion planning is SLAM, which stands for Simultaneous Localization and Motion Planning (see, e.g., Ref. 55).
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