Sensing pointing angles and angular displacements.

The blue circle represents an idealized 360-degree visual sensor of the focal agent. Positions at time t are marked by x(t). The elongated shape of the neighbor agent leads to ambiguity in computing its kinematic parameters when using solely angular data. In contrast, for circular agent morphology, the angular data are sufficient to extract complete and exact kinematic data of the neighbor. (a) Angular velocity is computed from Δβ_j, i.e., from the change of the LOS direction. (b) Distance r_j to the neighbor j is estimated from the angle α_j subtended by the neighbor, using Eq 5. Different distances to the neighbor (green and purple lines) can have the same subtended angle α_j due to the different orientations of the neighbor with respect to the LOS. (c) A related source of ambiguity lies in the impossibility of computing the components of the neighbor’s velocity accurately when using only angular information from a single visual sensor. As shown: many different endpoints produce equal Δβ. (d) In contrast: when agents are circular, the angular information α_j and Δβ_j suffices for an exact computation of distance and velocity, because the distance r_j is uniquely obtained from α_j alone.