Figure 8.

Stepping Model for Walking. The walker's state is specified by her global 2D position p_k and orientation θ_k. Each step of average length l is in the direction of the walker's current orientation, but the executed step v_k differs by the addition of noise in both the length (mean = l, variance = ${\sigma }_l^2$) and direction of the step (mean = β, variance = ${\sigma }_{\phi }^2$). By the end of each step, the walker's orientation has changed to point in the direction of the executed step. Initial orientation is a random variable across walks.