Odometry sensors

A final category will be given, which provides interesting examples of history-based sensor mappings, as defined for discrete state spaces in Section 11.1.1. Mobile robots often have odometry sensors, which indicate how far the robot has traveled, based on the amount that the wheels have turned. Such measurements are often inaccurate because of wheel slippage, surface imperfections, and small modeling errors. For a given state history, ${\tilde{x}_t}$, a sensor can estimate the total distance traveled. For this model, $Y = [0,\infty)$ and $y = h({\tilde{x}_t})$, in which the argument, ${\tilde{x}_t}$, to $h$ is the entire state history up to time $t$. Another way to model odometry is to have a sensor indicate the estimated distance traveled since the last stage. This avoids the dependency on the entire history, but it may be harder to model the resulting errors in distance estimation.

In some literature (e.g., [350]) the action history, ${\tilde{u}}_k$, is referred to as odometry. This interpretation is appropriate in some applications. For example, each action might correspond to turning the pedals one full revolution on a bicycle. The number of times the pedals have been turned could serve as an odometry reading. Since this information already appears in ${\eta}_k$, it is not modeled in this book as part of the sensing process. For the bicycle example, there might be an odometry sensor that bases its measurements on factors other than the pedal motions. It would be appropriate to model this as a history-based sensor.

Another kind of history-based sensor is to observe a wall clock that indicates how much time has passed since the initial stage. This, in combination with other information, such as the speed of the robot, could enable strong inferences to be made about the state.