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Moving Obstacles. The model of motion planning considered in this chapter (Section 3.1) assumes that obstacles in the robot s environment are all static that is, do not move. But obstacles in the real world may move. Let us call an environment where obstacles may be moving the dynamic (changing, time-sensitive) environment. Can sensor-based planning strategies be developed capable of handling a dynamic environment Even more speci cally, can strategies that we developed in this chapter be used in, or modi ed to account for, a dynamic environment The answer is a quali ed yes. Since our model and algorithms do not include any assumptions about speci cs of the geometry and dimensions of obstacles (or the robot itself), they are in principle ideally suited for handling a dynamic environment. In fact, one can use the Bug and VisBug family algorithms in a dynamic environment without any changes. Will they always work The answer is, it depends, and the reason for the quali ed answer is easy to understand. Assume that our robot moves with its maximum speed. Imagine that while operating under one of our algorithms it does not matter which one the robot starts passing around an obstacle that happens to be of more or less complex shape. Imagine also that the obstacle itself moves. Clearly, if the obstacle s speed is higher than the speed of the robot, the robot s chance to pass around the obstacle and ever reach the target is in doubt. If on top of that the obstacle happens to also be rotating, so that it basically cancels the robot s attempts to pass around it, the answer is not even in doubt: The robot s situation is hopeless. In other words, the motion parameters of obstacles matter a great deal. We now have two options to choose from. One is to use algorithms as they are, but drop the promise of convergence. If the obstacles speeds are low enough compared to the robot, or if obstacles move more or less in one place, like a tree in the wind, then the robot will likely get where it intends. Even if obstacles move faster than the robot, but their shapes or directions of motion do not create situations as in the example above, the algorithms will still work well. But, if the situation is like the one above, there will be no convergence. Or we can choose another option. We can guarantee convergence of an algorithm, but impose some additional constraints on the motion of objects in the robot workspace. If a speci c environment satis es our constraints, convergence is guaranteed. The softer those constraints, the more universal the resulting algorithms. There has been very little research in this area. For those who need a real-world incentive for such work, here is an example. Today there are hundreds of human-made dead satellites in the space around Earth. One can bet that all of them have been designed, built, and launched at high cost. Some of them are beyond repair and should be hauled to a satellite cemetery. Some others could be revived after a relatively simple repair for example, by replacing their batteries. For long time, NASA (National Aeronautics and Space Administration) and other agencies have been thinking of designing a robot space vehicle capable of doing such jobs.
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Imagine we designed such a system: It is agile and compact; it is capable of docking, repair, and hauling of space objects; and, to allow maneuvering around space objects, it is equipped with a provable sensor-based motion planning algorithm. Our robot call it R-SAT arrives to some old satellite in a coma call it X. The satellite X is not only moving along its orbit around the Earth, it is also tumbling in space in some arbitrary ways. Before R-SAT starts on its repair job, it will have to y around X, to review its condition and its useability. It may need to attach itself to the satellite for a more involved analysis. To do this y around or attach to the satellite surface the robot needs to be capable of speeds that would allow these operations. If the robot arrives at the site without any prior analysis of the satellite X condition, this amounts to our choosing the rst option above: No convergence of R-SAT motion planning around X is guaranteed. On the other hand, a decision to send R-SAT to satellite X might have been made after some serious remote analysis of the X s rate of tumbling. The analysis might have concluded that the rate of tumbling of satellite X was well within the abilities of the R-SAT robot. In our terms, this corresponds to adhering to the second option and to satisfying the right constraints and then the R-SAT s motion planning will have a guaranteed convergence.
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Multirobot Groups. One area where the said constraints on obstacles motion come naturally is multirobot systems. Imagine a group of mobile robots operating in a planar scene. In line with our usual assumption of a high level of uncertainty, assume that the robots are of different shapes and the system is highly decentralized. That is, each robot makes its own motion planning decisions without informing other robots, and so each robot knows nothing about the motion planning intentions of other robots. When feasible, this type of control is very reliable and well protected against communication and other errors. A decentralized control in multirobot groups is desirable in many settings. For example, it would be of much value in a robotic battle eld, where a continuous centralized control from a single commander would amount to sacri cing the system reliability and fault tolerance. The commander may give general commands from time to time for instance, on changing goals for the whole group or for speci c robots (which is an equivalent of prescribing each robot s next target position) but most of the time the robots will be making their own motion planning decisions. Each robot presents a moving obstacle to other robots. (Then there may also be static obstacles in the workspace.) There is, however, an important difference between this situation and the situation above with arbitrary moving obstacles. You cannot have any beforehand agreement with an arbitrary obstacle, but you can have one with other robots. What kind of agreement would be unconstraining enough and would not depend on shapes and dimensions and locations The system designers may prescribe, for example, that if two robots meet, each robot will attempt to pass around the other only clockwise. This effectively eliminates
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