Sources of uncertainty

Nature interferes with both the configuration transitions and with the sensor. Let $U = [0,2 \pi)$, which indicates the direction in ${\mathbb{R}}^2$ that the robot is commanded to head. Nature interferes with this command, and the actual direction lies within an interval of ${\mathbb{S}}^1$. As shown in Figure 12.45a, the forward projection (recall from Section 10.1.2) for a fixed action $u \in U$ yields a cone of possible future configurations. (A precise specification of the motion model is given using differential equations in Example 13.15.) The sensing model, shown in Figure 12.45b, was already given in Section 11.5.1. The nature sensing actions form a disc given by (11.67), and $y = q + \psi$, in which $q$ is the true configuration, $\psi$ is the nature sensing action, and $y$ is the observation. The result appears in Figure 11.11.

Figure 12.45: Nature interferes with both the configuration transitions and the sensor observations.