TABLE OF CONTENTS Operating in the real world, robots lack the perfect sensors and deterministic actions of many artificial worlds. Rather, robots are faced with various kinds of uncertainty. In this chapter we continue to discuss probabilistic frameworks for typical fundamental tasks of mobile robots such as localization, mapping, and simultaneous localization and mapping (SLAM). While the methods presented in this chapter employ the same iterative prediction-update process that is used in the Kalman filter (see chapter 8), they do not rely on the restrictive assumptions required by the Kalman filter. The methods described here can use nonlinear models for both robot motion and sensing. Most important, the resulting estimate may be an arbitrary distribution instead of a Gaussian. Throughout this chapter we present the key ideas of successful techniques together with a derivation of their mathematical foundations. We will also discuss ways to efficiently implement these approaches, since the capability to represent arbitrary distributions can lead to higher computational demands compared to Kalman filters.
In the previous chapter, we achieved localization by maintaining a distribution of the robot by iteratively estimating the mean and covariance matrix of a Gaussian distribution. This way of representing a belief about the location of the robot assumes that there is no "ambiguity" in the sense that the distribution is always unimodal or more specifically a Gaussian. One form of localization in which this assumption is often met is position tracking, which assumes that the initial configuration of the robot is (approximately) known and...
