The results of 100 replications (each consisting of 250 steps) of the 2D simulation using heterogeneously spaced reflectors.

<p>Movies illustrating the behaviour of the controllers in these environments are provided as supplementary material (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004484#pcbi.1004484.s001" target="_blank">S1</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004484#pcbi.1004484.s002" target="_blank">S2</a> Figs). (Left, a-c) Reflectors scattered in the horizontal plane (i.e. vertical reflectors). (Right, d-f) Reflectors scattered in the vertical plane (i.e. horizontal reflectors). (a) The median number of collisions for the default controller and the four variants (Df: Default controller; Fx: Fixed ears; rA: Random A; rB: Random B; Cs: Constrained). (b) The distribution of the distance (in m.) to the nearest obstacle for each of the controllers. Colours of the lines correspond to the colours in panel (a). (c) An example of the paths taken by each of the five controllers in a single environment. The light blue dots represent the reflectors. Black dots in panel (c) indicate locations where collisions occurred. (d-f) Similar, but for reflectors scattered in the vertical plane. (f) Side view of the simulation. All simulations are started in the centre of the arena. The grid squares are 5m by 5m.</p

The results of 100 replications (each consisting of 250 simulated calls) of the 2D simulations in environments with regularly spaced reflectors inspired by the wire avoidance experiments of Mogdans et al. [3].

<p>The reflectors are organized on a hexagonal grid and spaced 15 cm apart. (Left, a-c) Vertical wires. (Right, d-f) Horizontal wires (i.e. horizontal reflectors). (a) The median number of collisions for the default controller and the five variants (Df: Default controller; Fx: Fixed ears; rA: Random A; rB: Random B; Cs: Constrained; OA: Ears of axis). (b) The distribution of the distance to the nearest obstacle for each of the controllers. Colours of the lines correspond to the colours in panel (a). (c) A single example of the paths taken by each of the five controllers. The light blue dots represent the reflectors. Black dots in panel (c) indicate locations where collisions occurred. (d-f) Similar, but for horizontal wires. (f) Side view of the simulation. All simulations are started in the centre of the arena. The grid squares are 1m by 1m.</p

Parameters used to generate heterogeneous artificial environments mimicking the cluttered habitats of Rhinolophidae.

<p>Parameters used to generate heterogeneous artificial environments mimicking the cluttered habitats of Rhinolophidae.</p

The results for 100 replications of the 3D simulated environments.

<p>This figure is also provided as a MATLAB figure in the supplementary material (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004484#pcbi.1004484.s003" target="_blank">S3 Fig</a>). (a) The median number of collisions for each controller (Df: Default controller; Fx: Fixed ears; rA: Random A; rB: Random B; Cs: Constrained). (b) The distribution of the distance to the nearest obstacle. (c) Rendering of one replication of the 3D environment with the flight paths imposed. The right half of the environment has been cut away to reveal the flight paths. The grid size is 5m.</p

Results for the 3D scanned forest road.

<p>(a) The median number of collisions for 50 replications of the experiment (Df: Default controller; Fx: Fixed ears; rA: Random A; rB: Random B; Cs: Constrained). (b) The distribution of the distance to the nearest obstacle. (c-f) Renderings of the obstacles with a single example flight path overlaid. Colours indicate the different controllers. Each run consisted of 250 steps. The 3D rendering is also provided as a MATLAB figure in the supplementary material (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004484#pcbi.1004484.s006" target="_blank">S6 Fig</a>).</p

The distribution of the flight speeds in three different simulated environments.

<p>(a) Reflectors in the horizontal plane (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004484#pcbi.1004484.g005" target="_blank">Fig 5a-5c</a>). (b) Reflectors in the vertical plane (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004484#pcbi.1004484.g005" target="_blank">Fig 5d-5f</a>). (c) 3D reflectors (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004484#pcbi.1004484.g006" target="_blank">Fig 6</a>)</p

Summary of the equations governing the default controller (i.e boxes 5–7 in Fig 3).

<p>Line 2: The speed of the bat <i>V</i>_<i>bat</i> is set as a function <i>F</i> of the distance to the nearest obstacle <i>d</i>_<i>min</i> (using the curve depicted in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004484#pcbi.1004484.g001" target="_blank">Fig 1a</a>). Next (lines 3–14), the speed <i>V</i>_<i>bat</i> is used to set the rotations of the bat in azimuth (Δ<i>ϕ</i>) and elevation (Δ<i>θ</i>). The sign of the azimuth rotation depends on the relative strength of the echoes at the left (<i>g</i>_<i>l</i>) and the right ear (<i>g</i>_<i>r</i>) as given by <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004484#pcbi.1004484.e003" target="_blank">Eq (3)</a>. The sign of the elevation rotation depends on whether the ear with the weakest echo is pointing up or down.</p

This diagram describes the simulations and the controller investigated in this paper.

<p>(1) The simulation starts with the bat emitting a call. (2) Next, the echoes returning from all point reflectors are calculated. (3) While waiting for the first echo to arrive, the controller keeps the current flight direction. (4) Moreover, 50 ms is allowed to process the onset of the echo train (1 ms). Based on the IID the rotation direction (5) is determined. The magnitude (6) depends on the flight speed. The new flight speed itself is chosen based on the distance to the nearest obstacle (7). The controller applies the determined rotation angle and (8) moves in the new direction for the remainder of the interpulse interval (9). Finally, the controller swaps the position of the ears before emitting the next call (10).</p

Results of 25 replications in the tilted torus environment (each replication consists of 250 steps).

<p>This figure is also provided as a MATLAB figure in the supplementary material (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004484#pcbi.1004484.s004" target="_blank">S4 Fig</a>) (a) The median number of collision per replication corrected for distance travelled (b) Distribution of the distance to the nearest obstacle for each of the controllers (Df: Default controller; Fx: Fixed ears; rA: Random A; rB: Random B; Cs: Constrained). (c) Plots of the paths for 5 replications in the torus environment (not all replication were plotted for reasons of clarity). The torus is rendered as a transparent volume. The individual reflectors making up the torus are not plotted as they would obscure the flight paths. The grid size is 5m.</p

The results for 100 replications of <i>P. discolor</i> (an FM bat) flying in a heterogeneous artificial environment.

<p>(Left, a-c) Reflectors scattered in the horizontal plane (i.e. vertical reflectors). (Right, d-f) Reflectors scattered in the vertical plane (i.e. horizontal reflectors). (a) The median number of collisions for the default controller and the four variants. ‘Off-axis’ indicates the controller using an HRTF obtained by rotating the left ear downwards by 15 degrees and rotating the right ear upwards by 15 degrees (right column <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004484#pcbi.1004484.g012" target="_blank">Fig 12</a>). The ‘Constrained controller’ used the same ear configuration. In addition, the vertical rotation of this controller was constrained as before. All other controllers used the HRTF with the ears in the default position (left column <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004484#pcbi.1004484.g012" target="_blank">Fig 12</a>) (b) The distribution of the distance (in m.) to the nearest obstacle for each of the controllers. Colours of the lines correspond to the colours in panel (a). (c) An example of the paths taken by each of the five controllers in a single environment. The light blue dots represent the reflectors. (d-f) Similar, but for reflectors scattered in the vertical plane. (f) Side view of the simulation. All simulations are started in the centre of the arena. Black dots in panels (c) and (f) indicated locations were collisions occurred.</p