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Moving beyond philosophical concerns, we return to the subject of learning. A mobile robot in an unknown environment has, as a primary concern, the need to develop a model of its environment. A map. Given a simplistic room like the one in Fig. 18-1, you would think it would be easy for a robot to learn the layout. One rst step is to try to tame the in nite spaces of this room. The robot has limited memory and we need to nd a way to store the layout of this room in it. One way is to lay a grid over the room (Fig. 18-2) and then record information in each grid square as we nd it. This grid layout mimics the memory structure of the computer and is easy to represent. As the robot wanders around the room, it notes what it nds in each grid square as it passes through it (Fig. 18-3). The robot has moved a long distance and it hasn t learned much about the room. What if we added the ability to see out to the sides of the robot There are optical sensors that can provide a type of visual bumper, returning
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CHAPTER 18 Advanced Control
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Fig. 18-1. Simplistic room.
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Fig. 18-2. Grid overlay.
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Fig. 18-3. Bumper hits in the room.
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the distance to an obstacle. Assuming we can see out to the sides of the robot by three squares, this same path may return more information, as shown in Fig. 18-4.
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ODOMETRY
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Mapping assumes that the robot has some way of knowing where it is as it travels. The simplest technique for this is dead reckoning, technically known as odometry, the measurement of distances traveled. The math behind odometry is surprisingly simple. It requires an accurate measurement of the distance each wheel has traveled. From this, it can calculate the change in position and rotation of the vehicle. Figure 18-5 illustrates the odometry math. The distance traveled by the left wheel is DL, and by the right wheel DR. The width of the robot, from where the left wheel touches the ground to where the right wheel touches the ground, is W. At time T 0 the robot is facing in the direction OT, which is speci ed in radians. If the robot turns during its travels, it ends up in a di erent
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CHAPTER 18 Advanced Control
Fig. 18-4.
Side sensors in the room.
Fig. 18-5.
Idealized robot for odometry.
orientation OT 1. This new orientation is calculated as a ratio of the wheel s relative motions with the robot s width: OT 1 OT DR DL W 18-1
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The straight-line distance the robot traveled is the average of the two wheels travel distance: D DL 18-2 DT R 2 The new position of the robot in the X,Y grid is then approximated by: XT 1 XT DT cos OT 1 18-3 YT 1 YT DT sin OT 1 The catch is that this motion is only a straight-line approximation of the actual curved path.
ODOMETRY ERRORS
Even if we used better, more complicated, math there would be errors recording the motion. The wheels don t contact the oor in a precise mathematical point so there is some error in W. If there is any slipping or shifting of the wheels, the measured distances do not match the actual distance traveled. Also, the sensor used to measure the wheel motion is not in nitely precise, which adds some uncertainty into each measurement. All of this adds up to errors, especially errors in calculating the robot s turns. There are also errors in the sensors, so they don t report the exact truth of the situation. Even if we blur the information returned from the sensors, the odometry errors can still put us out of the ballpark. Figure 18-6 represents this. This is a tricky diagram. The wide path is where the robot thinks it is going. The narrow path illustrates the actual path through the environment. The blurred sensor marks show how the robot s sense of the environment varies from the actual environment it is distorted and inaccurate. The more the robot travels, the more distorted its map becomes, until it s a useless blur. Researchers who use odometry spend a bunch of their time correcting for these built-in errors. One of the lessons to learned from this is that robotic tasks are never as simple as they seem at rst glance.
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