Sensorimotor Model of Obstacle Avoidance in Echolocating Bats
[['Rhinolophidae are echolocating bats specialized in hunting for airborne prey among vegetation using echolocation .', 'To cope with clutter echoes returning from vegetation they employ a unique sensorial strategy for detecting prey .', 'They emit long narrow-band pulses and listen for frequency and amplitude shifts , so called glints , in the echoes caused by fluttering prey [1] .', 'Echoes from stationary obstacles do not contain these glints and do not interfere with the detection and localization of prey [2] .', 'While the sensorial adaptations of Rhinolophidae for prey detection have been extensively researched ( see [1] for a review ) , the cues supporting the ability of these bats to navigate and orient in cluttered environments have received much less attention .', 'Nevertheless , their ability to navigate small spaces [3–6] and their well-studied echolocation apparatus [1 , 7] makes them an interesting taxon to study how echolocating bats avoid obstacles in natural environments .', 'Indeed , as argued in the discussion , understanding the cues Rhinolophidae use to negotiate space is potentially informative about how other bats using frequency modulated pulses could avoid obstacles as well .', 'It would seem that Rhinolophidae , using long narrowband signals , lack both the bandwidth and the temporal resolution available to bats using short broadband signals .', 'Indeed , bats using broadband signals typically shorten their calls ( typically 1–3 ms [8] ) and increase the bandwidth when moving into cluttered spaces [8] .', 'Rhinolophidae , in contrast , negotiate cluttered space using much longer ( about 10–50 ms ) and narrowband signals that seem not particularly well suited for obstacle avoidance .', 'Indeed , while Rhinolophidae also shorten their calls and increase the bandwidth when moving into cluttered space [9 , 10] , their calls remain longer and more bandwidth limited than those of FM bats under the same conditions .', 'The characteristic cyclical pinna movements shown by Rhinolophidae [11 , 12] have been suggested to compensate for the lack of spatial cues available to bats relying on broadband calls .', 'Mogdans et al . [3] performed behavioural experiments to test specifically the role of these ear movements for obstacle avoidance based on Interaural Intensity Differences ( IIDs ) .', 'The hypothesis [3 , 10] that the moving ears generate changing IIDs encoding the reflector position in both the horizontal and the vertical plane was found by these authors to be in agreement with the results from their wire-avoidance experiments and put forward as a possible explanation for the bats’ obstacle avoidance ability .', 'Since then , simulation studies and robotic experiments have corroborated that these ear movements do indeed provide various localization cues that would allow localizing individual reflectors , such as prey items [13–15] .', 'However , natural environments encountered by bats are typically made up of objects that consist of many stochastic reflectors returning many overlapping echoes [16] .', 'Therefore , for 3D localization of reflectors , e . g . based on typical ear movement induced IID patterns , to be considered a plausible mechanism underlying the obstacle avoidance abilities of bats , it has to be proven first that such a localization capability is robust in the presence of multiple overlapping echoes .', 'Hence , while it has been shown that pinnae movements play a significant role in obstacle avoidance [3] , it is still not clear what information Rhinolophidae extract from such pinna movements to allow them to avoid natural ( and complex ) obstacles .', 'To complement behavioural experiments , we use the synthetic methodology , i . e . understanding natural systems by building artefacts [17–19] , computer simulations , in this case , to study bat obstacle avoidance behaviour .', 'In particular , we propose a sensorimotor system that does not rely on the bat reconstructing the 3D spatial layout of reflectors from the echoes , but instead relies on the dynamics of the bat-obstacle interaction to result in obstacle avoidance behaviour .', 'A similar approach is taken in ref .', '[20] for prey-catching behaviour in echolocating bats assuming that only a single reflecting target is present giving rise to a unique isolated echo .', 'This assumption is warranted in the case of prey-catching behaviour as the bat can choose to hunt away from clutter [8] or take active measures to separate the echoes from the foreground prey item from the clutter background ones ( e . g . [21 , 22] ) .', 'In contrast , realistic obstacles , e . g . foliage and/or man-made structures , will always give rise to multiple overlapping echoes [16] .', 'The sensorimotor system we propose is intentionally kept as simple as possible .', 'It uses IID and time delay of the first echo onset in combination with alternating pinna movements to guide the bat .', 'In particular , it processes only the first millisecond of the echo train .', 'Furthermore , it does not need the right and left ear echo signals to be segmented into contributions from individual reflectors , as would be required by any approach that reconstructs the spatial layout of the bat’s surroundings .', 'While approaches that attempt to reconstruct the spatial layout of the environment first as a prerequisite for obstacle avoidance [23 , 24] , when successful , are clearly sufficient to explain such behaviour , we aim to show with the proposed sensorimotor system that such a reconstruction capability is not a necessary condition .', 'The main advantage of the proposed obstacle avoidance mechanism is that because of its simplicity as well as its reliance on the first millisecond of the echo train only it can react very rapidly to the relevant information contained in an otherwise very complex echo signal consisting of many overlapping echoes .', 'This allows the system to respond appropriately under hard real-time conditions independent of the complexity of the environment .', 'In this paper , we first present the environments used to simulate the echoes received by a bat moving through realistic , cluttered spaces .', 'Next , we propose a sensorimotor system that results in obstacle avoidance behaviour by extracting echo delay and IID information from the onset of the first echo in combination with alternating pinna movements .', 'Finally , we test the performance of the sensorimotor system in simulated 2D and 3D environments showing that despite its simplicity the system can avoid obstacles in a complex environment without the need to reconstruct the 3D spatial layout of the reflectors present .'], ['We tested the proposed sensorimotor system both in environments that were artificially generated and in environments derived from 3D laser scans of real bat habitats .', 'Below we discuss the construction of both types of test environments .', 'The intensity of the echo returning from each point reflector i was calculated for each call .', 'The intensity gi ( in dB ) of the echo received from reflector i is given by the sonar equation [31] ,', 'g i = g b a t + 40 · log 10 0 .', '1 r i + 2 · ( r i - 0 . 1 ) · a f + d ϕ i , p + s i + c ϕ i ( 1 ) In Eq ( 1 ) , gbat is the intensity of the call at 10 cm from the mouth , in this paper taken to be 120 dBspl [9] .', 'The parameters ri , af , dϕi , p , si give the range to reflector i , the atmospheric absorption at frequency f [35] , the directional sensitivity dϕi , p of the sonar apparatus of the bat for angle ϕi and pinnae position p ( see below ) , and the echo strength si of the reflector respectively .', 'Simon et al . [36] ensonified leaves for a range of aspect angles and found reflector strength to vary from −30 dB to −6 dB .', 'Therefore , variations in aspect dependent reflector strength si were modelled by choosing the reflector strength randomly from a uniform distribution over this interval for each call .', 'As stated above , for the regularly spaced artificial environments mimicking the wire avoidance tests of Mogdans et al , [3] the reflector strength si was fixed at −66 dB corresponding to the target strength of a wire with a diameter of 0 . 16 mm [29] .', 'In the torus environment , the reflector strength was chosen randomly from the interval −46 to −34 dB .', 'This corresponds to −40 dB , the approximate target strength of a sphere with diameter 5 cm [31] , plus and minus 6 dB .', 'In Eq ( 1 ) , cϕi denotes an additional attenuation reflecting changes in cochlear sensitivity for different frequencies .', 'The cochlea of Rhinolophidae is highly tuned to the species-specific constant frequency component of the call ( Reviewed in [1] ) .', 'While flying , these bats compensate the Doppler shift of the returning echoes by lowering the emission frequency .', 'In doing this , they effectively ensure that echoes return with a frequency very close to the frequency their cochlea is tuned to , i . e . the reference frequency .', 'However , the Doppler shift Δfϕi of an echo depends on the heading direction ϕi of reflector i as follows ,', 'Δ f ϕ i = f e m i s s i o n · 2 · v b a t v s o u n d · cos ϕ i ( 2 ) We were unable to find flight speed data for R . rouxii .', 'However , bats weighing about 10 grams were reported to commute with a speed of 6 ms−1 [37 , 38] .', 'Therefore , we modelled the maximum speed of R . rouxii as vbat = 6 ms−1 .', 'R . ferrumequinum is capable of drastically reducing its flight speed when near an obstacle .', 'Aldridge [4] reports a flight speed of about 0 . 3 ms−1 at the maximum turning rate for R . ferrumequinum .', 'Moreover , this bat starts reducing its speed from about 5 meters before landing [9] .', 'Hence , we model the flight speed of R . rouxii as 0 . 3 ms−1 and 6 ms−1 at 0 and 5 meter ( and more ) from the nearest obstacle respectively ( See Fig 1a ) .', 'We interpolate linearly between these points .', 'Notice that this implies that the simulated flight speed in the regularly spaced artificial environments ( see below ) where obstacles are spaced 15 cm apart is maximally about 0 . 47 ms−1 .', 'The details of how Rhinolophidae lower their emission frequency when faced with multiple reflectors with different Doppler shifts remain unknown .', 'Experiments using masking tones [39] suggest the bats lower their emission frequency such that the frequency of the maximally Doppler shifted echo is close to the reference frequency ( i . e . the frequency they are maximally sensitive to ) .', 'However , the compensation exhibited depends also on the intensity and delay of the echoes as well as the time constant of the feedback loop [39 , 40] .', 'As a first order approximation , we assumed that the synthetic bat lowers its emission frequency by about 2 . 6 kHz to compensate the Doppler shift for reflectors with heading ϕ = 0 ( at vbat = 6 m/s and femission = 75 kHz ) .', 'Lower flight speeds result in reduced Doppler shifts .', 'This implies that we assume that reflectors i with ϕi > 0 return echoes with frequencies between 0 and about 2600 Hz below the reference frequency .', 'Hence , in our simulations , we attenuate echoes for ϕi > 0 as bats are less sensitive to frequencies below the preferred frequency .', 'The attenuation cϕi for each echo as a function of the heading angle ϕi was determined based on data reported by Neuweiler [7] ( See Fig 1b ) .', 'It should be noted that this simple implementation of the Doppler compensation mechanism overestimates the loss in sensitivity due to Doppler shifts .', 'Indeed , we assume the maximum Doppler shift experienced ( and , hence the decrease in emission frequency ) is always equal to the hypothetical Doppler shift for an object with heading zero degrees—even if these echoes have large delays or low amplitudes .', 'In reality , bats lower their frequency to a lesser extent when echoes have low intensity and/or long delays [39 , 40] .', 'In the current simulations , we modeled the bat Rhinolophus rouxii which uses constant frequency calls in the range 73–79 kHz [5] .', 'We choose to approximate the call frequency using 75 kHz .', 'The atmospheric absorption af at 75 kHz was set to 2 . 4 dB/m [35] .', 'The directional sensitivity dϕi , p of the synthetic bat’s hearing and emission for 75 kHz was taken from previous simulation studies [13 , 14 , 41] .', 'The maximum gain of the head related transfer function was set to 4 . 5 dB at 75 kHz [42] .', 'As pointed out above , experimental results confirm that the typical ear movements of Rhinolophidae support obstacle avoidance [3] .', 'The continuous movement of the pinnae is approximated by modeling the directional sensitivity of the two extreme positions p of the ears .', 'This is warranted by the fact that the controller proposed in this paper ( detailed in the next section ) only processes the onset of the echoes , i . e . the first millisecond .', 'The available evidence [11 , 12 , 43] suggest that the pinnae are in the most extreme position at the onset of the echo and sweep to the inverse orientation while receiving the echo ( es ) .', 'Pinna movements are simulated by rigidly rotating the hearing spatial sensitivity pattern before combining it with the emission directivity to obtain the complete directional sensitivity ( see [13 , 14] for details ) .', 'Measurements have shown that the ears of Rhinolophidae do not undergo rigid rotations but instead deform while rotating [44] .', 'However , current evidence leaves open the question whether the effects of this deformation on the hearing spatial sensitivity pattern is functionally relevant or not .', 'Ref .', '[45] discusses the validity of modeling the ear movements as rigid rotations .', 'The modeled head related transfer functions for the two pinna positions p are depicted in Fig', '2 . At the heart of the sensorimotor system responsible for obstacle avoidance behaviour we propose a biologically feasible controller that does not rely on explicit reconstruction of the 3D layout of individual reflectors to explore the possibility that Rhinolophidae can avoid obstacles without making use of a 3D model of the world .', 'The controller is illustrated in Fig', '3 . We assume that the flight parameters are updated after every call based only on the echoes of the last call .', 'Hence , the proposed controller constructs no internal model of the world and does not explicitly exploit changes in echo characteristics across calls .', 'Assuming otherwise would require us to specify a segmentation and grouping mechanism by which individual echoes from subsequent calls are assigned to so-called echo-streams corresponding one-to-one with particular objects .', 'The use of such echo-streams has been hypothesized [46] as a means for a bat’s perceptual system to organize acoustic information from complex environments .', 'However , no explicit computational mechanism capable of the required segmentation and grouping of complex echo signals has been put forward so far .', 'Also , while neurophysiological evidence [47 , 48] for an echo stream based representation for single reflector stimuli has been found , no multiple reflector stimuli have been experimented with yet .', 'Hence , until the possible use of an echo stream based representation in obstacle avoidance behaviour is further clarified we propose our reactive controller as a simpler and computationally explicit hypothesis .', 'The main advantage of a reactive approach is that it considers the world as its own best model [49 , 50] which is always exactly up to date and always contains every detail there is to be known [51] .', 'By avoiding the delay due to the reconstruction of a 3D model of the environment and/or planning a path , a reactive approach results in a highly responsive and robust controller [50] .', 'However , it should be noted that relying only on the echoes from the last call to determine the controller’s response does not make the proposed sensorimotor system memoryless .', 'Indeed , the dynamics of the interaction between the controller and its environment introduce an implicit memory of information extracted from previous call-echo pairs .', 'Put differently , the state of the controller , i . e . position and velocity , and latest call-echo pair jointly determine the bat’s next move , thereby ensuring that the perceptual history , i . e . previous call-echo pairs , and not just the last call-echo pair determine the controller’s response .', 'In the simulations , we assume the speed of the synthetic bat vbat to be a function of the time of flight of the first echo , i . e . the distance to the nearest object .', 'The range of speeds goes from 6 ms−1 to 0 . 3 ms−1 ( see above ) .', 'In addition to the speed , the flight direction also needs to be updated based on the echoes from each call .', 'For an obstacle avoidance algorithm based on sonar , desirable flight directions are characterized by low amplitude echoes .', 'Indeed , for the same reflector strength , weaker echoes imply obstacles that are further away or located more to the periphery .', 'A heuristic leading to weaker echoes is to turn towards the direction of the ear which receives the weakest echoes , e . g . turning right if the right ear receives the weakest echoes .', 'With stationary ears , moving in the direction of the ear receiving the weakest echo would only allow for updating the horizontal flight direction .', 'However , the ear movements of Rhinolophidae result in the main sensitivity axis of each ear to alternately point up and down .', 'The available evidence suggests that Rhinolophidae move one ear up and the other ear down while receiving echoes [11 , 12 , 43] .', 'The ears move in the other direction while receiving the next echo .', 'In this paper , we simplified the continuous movement of the pinnae by modeling only the two extreme positions of the ears ( see below and Fig 2 ) .', 'Considering the extreme positions of each ear results in the sonar system sampling four directions during each pair of successive calls .', 'Therefore , we propose our controller to turn left or right depending on which ear receives the weakest echo .', 'In addition , the controller steers up or down depending on whether the ear receiving the weakest echo is currently pointing up or down .', 'Echoes arriving earlier are reflected by more proximate obstacles .', 'Hence , the initial part of the echo signal is of greater importance to an obstacle avoidance sensorimotor system .', 'Therefore , we chose to take only the first millisecond of the echo into account ( i . e . the controller only uses the onset of the echo train ) .', 'We do not claim that the remainder of the echo has no function in obstacle avoidance , but we propose , as indicated by the results , that the onset of the echoes already contains sufficient information .', 'Rhinolophidae have their ears at extreme positions in between calls and move them into the opposing configuration while receiving echoes [12] .', 'Hence , by focussing on the onset of the echoes , we can further simplify the model and use only the extreme ear positions for each call .', 'Apart from the resulting simplifications to our model we argue that focussing on the onset of the echoes has advantages for bats as well .', 'Any mechanism that makes use of specific characteristics of the modulation pattern of the echo introduced by the complete pinna movement instead ( e . g . [13 , 14] ) , needs to control and/or to measure the ear movement in greater detail requiring a more complex and less robust system .', 'In our simulations , the echoes received at each ear t during the first millisecond after the arrival of the first echo are summed with randomized phase shifts .', 'The intensity gt , in decibels , of the summed echoes i received at ear t is given by ,', 'g t = 20 · log ( | ∑ i 10 g i 20 e j · φ i , t | ) ( 3 )', 'In Eq ( 3 ) , ϕi , t is a random phase angle ( between −π and π ) modeling the interference between narrowband echoes .', 'Note that this phase angle is randomized independently for each reflector i and ear t .', 'The hearing threshold was assumed to be 0 dBspl .', 'Therefore , echo amplitudes gi lower than 0 dBspl were set to 0 and did not contribute to intensity gt .', 'We propose the bat rotates in the direction of the ear receiving the weakest echoes , given by gt ( Fig 3 , box 5 ) .', 'If gl < gr , the bat turns left .', 'Conversely , if the right ear receives the weakest echoes ( gl > gr ) , the bat turns to the right .', 'Moreover , if gl < gr and the left ear is pointing up ( down ) the bat turns up ( down ) .', 'In addition to the direction of the turn , the controller also needs to specify the magnitude of the turn ( Fig 3 , box 6 ) .', 'In the proposed controller , the magnitude of the turn depends on the flight speed ( which in turn depends on the distance to the closest obstacle , Fig 3 , box 7 ) .', 'Jones and Rayner [6] report on the speed and angular rotation of Myotis daubentonii ( See Fig 1c ) .', 'We fitted a linear function to this data to obtain the following expression for angular rotation R in degrees per second as a function of flight speed , R = 665 − 116 × Vbat .', 'Values of R smaller than zero were set to zero resulting in the curve depicted in Fig 1c .', 'Incidentally , the turning rates thus obtained correspond largely to those reported by Holderied [38] .', 'Note that for low flight speeds the turning rate could be greatly increased .', 'For example , Aldridge [4] reports that R ferrumequinum is capable of turning with a curvature of up to 115 m−1 ( turning radius < 1 cm , angular rotation speed ∼ 1900 deg/s ) when suddenly faced with a barrier .', 'Nevertheless , as we did not aim at modeling such last minute avoidance manoeuvres , we opted for fixing the maximum turning rate to the conservative value of 665 degrees per second at Vbat = 0 .', 'In summary , the controller turns left or right depending on whether the left or the right ear received the loudest echoes .', 'In addition , it turns up or down depending whether the ear receiving the loudest echoes is currently pointed up or down .', 'The speed of the bat is determined by the closest ( detected ) obstacle ( Fig 1a ) .', 'In turn , the rotation speed is determined by the speed of the bat ( Fig 1c ) .', 'See Algorithm 1 for a listing of the computations and Fig 3 for a graphical depiction of the complete controller .', 'We give the synthetic bat the same aerodynamic freedom in the horizontal ( left and right ) and vertical plane ( up and down ) .', 'This is; it can turn at the same rate without taking gravity into account ( but see below for a version of the controller taking into account the gravity vector ) .', 'Indeed , if the synthetic bat turns upwards/downwards for long enough , it might eventually fly upside down with respect to its initial orientation .', 'There are two reasons for modeling the vertical rotation in this way .', 'First , while it is well known that bats are very agile , to the best of our knowledge very little information is available about the aerodynamic constraints on climbing and ascending flight of the bat .', 'Second , and more importantly , by introducing the same constraints on both horizontal and vertical rotations , we can compare the sensorial performance of the algorithm in both the horizontal and vertical plane in the absence of differences in motor constraints .', 'Nevertheless , we are aware that having the same constraints for both turning rates is artificial .', 'Hence , we also test a variant of the controller that introduces a constraint on the maximum vertical rotation ( see ‘constrained’ controller below ) .', 'Both R . rouxii and R . ferrumequinum emit a pulse every 80 to 90 ms on average [5 , 52] .', 'For computational ease and to simulate a lower bound update rate , the synthetic bat was simulated to emit a pulse every 100 ms . On approaching a landing site , the pulse rate of R . ferrumequinum was found to increase to about 80 Hz ( i . e . about 12 ms interval ) [9 , 53] .', 'However , the informational update of 80 Hz might not translate into an ability of the bat to update its direction 80 times a second .', 'Rhinolophidae flap their wings at about 12 Hz ( i . e . about 80 ms interval ) irrespective of their air speed [54] .', 'Considering a wing beat as the minimal unit that allows changing the direction of the flight , would allow for an update rate of at most 12 Hz .', 'In the proposed controller , each pulse corresponds to a single update in the flight direction .', 'Hence , as 12 Hz is very close to the modeled pulse rate of 10 Hz , the interpulse interval was fixed at 100 ms . In the simulations , we account not only for the time needed for the echoes to arrive but also for the time required by a bat to process the echoes and produce a motor response .', 'Übernickel et al . [55] found a reaction time of about 50 ms to transient targets in the trawling bat Noctilio leporinus in accordance with a similar range of reaction times 47–63 ms found in ref .', '[56] .', 'Hence , we allowed for 50 ms to process the echoes .', 'In the interval between the emission of the call and the start of the turn , the current direction and speed of flight is maintained .', 'The interval between call and start of turn is given by ( 1 ) the time for the first echo to arrive , ( 2 ) 1 ms over which the echoes are summed and ( 3 ) 50 ms of processing time .', 'Note that as the duration of the turn is given by the fixed call period ( 100 ms ) minus the interval between call and start of turn , both the rotation speed R and the duration of the bat’s turn depend on the distance to the closest object .', 'As the time for the first echo to arrive gets shorter , the turn duration gets longer .', 'This increases the rotational gain of the controller even more for nearby obstacles .', 'The controller was tested in 2D and 3D environments .', 'The performance of the controller described above , referred to as the default controller from now on , was compared to that of five related controllers:', 'Fixed ears: This controller models a bat with static ears .', 'A single directional sensitivity is used for each ear .', 'As such , the directional sensitivity does not change from call to call .', 'The directionality used is depicted in the top row of Fig 2b .', 'The azimuthal rotation is updated as in the default controller .', 'However , the sign ( up/down ) of the elevation rotation was selected at random .', 'Off axis pinnae: This controller is identical to the default controller .', 'However , this controller consistently has the left ear pointing downwards and the right ear pointing upwards .', 'If the left ( right ) ear receives the weakest echoes , the bat turns downwards ( upwards ) .', 'The azimuthal rotation is updated as before .', 'Random A: The controller differs from the default controller by randomly turning left or right at each call .', 'While the direction of rotation is chosen randomly , the magnitude is calculated as in the default controller .', 'Random B: The same controller as the Random A variant with the addition that the rotation speed of the bat is also chosen randomly from the interval 0 to 350 degrees per second .', 'Constrained: This controller is identical to the default controller , but it constrains the angle of the bat in the vertical plane .', 'The bat can maximally attain a climbing or descending angle of ±60 degrees .', 'The controller with fixed ears allows us to test the contribution of ear movement to obstacle avoidance .', 'The controller with the pinnae fixated in an off-axis position allows us to test whether the cues necessary for obstacle avoidance are still present if the ears are fixed but are not aligned with the horizontal plane .', 'Random A and Random B are included in the tests as baseline conditions against which to compare the other controllers .', 'Similarly , in behavioural obstacle avoidance experiments , the performance of the bat is typically compared to the number of collisions expected from following a random path through space , e . g . [3 , 25 , 26] .', 'Finally , the constrained controller adds more realistic constraints to the vertical rotation of the bats .'], ['We tested the controller and its four variants in environments populated with reflectors on hexagonal grids spaced 15 cm apart ( See Fig 4c and 4f for examples ) .', 'In these environments , collisions are counted as the number of time steps ( calls ) the controller was closer than 2 . 5 cm to any obstacle .', 'Hence , we modeled the synthetic bat as having a body width of 5 cm , in agreement with Mogdans et al . [3] .', 'In most results reported below , the various controller variants differed in the resulting average distance kept from reflectors and , therefore , in their average speed and distance travelled .', 'To compensate for this , we normalized the number of collisions for all controllers to the number of collisions per 100 m travelled .', 'The results show that the default controller successfully avoided both the vertical wires and the horizontal wires ( Fig 4 ) .', 'Indeed , in these 2D tasks the number of registered collisions was much lower than in both random A and B . The controller with the fixed ears performed equally well in avoiding the vertical wires .', 'However , avoidance of the horizontal wires was reduced to chance level by fixing the ears in the horizontal plane .', 'In contrast , fixating the pinnae off axis , restored the obstacle avoidance performance for the horizontal wires ( and did not reduce performance for the vertical wires ) .', 'The controller that was constrained in its vertical rotation performed much worse than the default controller in avoiding horizontal wires ( Fig 4d ) .', 'This indicates that while the moving ears supplied the necessary information to avoid obstacles , the imposed aerodynamic constraint is too restrictive to allow for successful obstacle avoidance in our grid of simulated wires .', 'Overall the performance results in the regularly spaced grids match the finding of Mogdans et al . [3] that obstructing the pinnae movements only interferes with the avoidance of horizontal wires , i . e . only obstacle avoidance in the vertical dimension is affected .', 'Fixating the ears did not have an effect on the avoidance of the vertical wires .', 'In addition , our simulations suggest that pinnae fixated in an off-axis position provide sufficient cues for obstacle avoidance in both azimuth and elevation .', 'Fig 5a and 5d show the number of collisions registered for the bat in 100 replications with reflectors scattered in either the horizontal or the vertical plane for the four variants of the controller .', 'In these runs , collisions are defined as the number of time steps ( per 100 m travelled ) the controller was closer than 15 cm to the nearest obstacle , i . e . approximately half the wingspan of R . rouxii .', 'The results indicate that the default controller is capable of avoiding obstacles in both the vertical and the horizontal plane .', 'Fixing the pinnae has no effect on obstacle avoidance in the horizontal dimension .', 'However , obstacle avoidance in the vertical dimension is reduced to chance level ( i . e . similar number of collisions than controller Random A ) .', 'In the horizontal plane , the constrained controller has the same degrees of freedom as the default controller and , therefore , has the same performance .', 'Constraining the elevation angle of the bat clearly limits its freedom .', 'Hence , the number of collisions does increase compared to the horizontal plane .', 'However , the number of collisions is still less than in both random baselines .', 'The reduction in performance for the constrained controller is less dramatic than for the regularly spaced obstacles discussed above as can be seen from comparing the performance of the constrained controller in Figs 4d and 5d .', 'We provide two movies illustrating the behaviour of the controllers in the 2D environments of Fig 5 as supplementary material .', 'The default controller , as well as the four derived controllers , were also tested for obstacle avoidance in 3D point clouds ( Fig 6 , also provided as MATLAB figure in the supplementary material ( S3 Fig ) .', 'The default algorithm performs best .', 'Fixing the ears does not result in an increase in the number of collisions .', 'However , it results in flying somewhat closer to obstacles .', 'The number of collisions does not increase by fixing the ears as the controller is still able to avoid obstacles in the horizontal plane .', 'This implies the controller with the fi
['Introduction', 'Methods', 'Results', 'Discussion']
['Bat echolocation is an ability consisting of many subtasks such as navigation , prey detection and object recognition .', 'Understanding the echolocation capabilities of bats comes down to isolating the minimal set of acoustic cues needed to complete each task .', 'For some tasks , the minimal cues have already been identified .', 'However , while a number of possible cues have been suggested , little is known about the minimal cues supporting obstacle avoidance in echolocating bats .', 'In this paper , we propose that the Interaural Intensity Difference ( IID ) and travel time of the first millisecond of the echo train are sufficient cues for obstacle avoidance .', 'We describe a simple control algorithm based on the use of these cues in combination with alternating ear positions modeled after the constant frequency bat Rhinolophus rouxii .', 'Using spatial simulations ( 2D and 3D ) , we show that simple phonotaxis can steer a bat clear from obstacles without performing a reconstruction of the 3D layout of the scene .', 'As such , this paper presents the first computationally explicit explanation for obstacle avoidance validated in complex simulated environments .', 'Based on additional simulations modelling the FM bat Phyllostomus discolor , we conjecture that the proposed cues can be exploited by constant frequency ( CF ) bats and frequency modulated ( FM ) bats alike .', 'We hypothesize that using a low level yet robust cue for obstacle avoidance allows bats to comply with the hard real-time constraints of this basic behaviour .']
['Echolocating bats can fly through complex environments in complete darkness .', 'Swift and apparently effortless obstacle avoidance is the most fundamental function supported by biosonar .', 'Despite this , we still do not know which acoustic cues , from among the many possible cues , bats actually exploit while avoiding obstacles .', 'In this paper , we show using spatial simulations ( 2D and 3D ) that the Interaural Intensity Difference ( IID ) and travel time of the first millisecond of the echo train in combination with alternating ear positions provide robust and reliable cues for obstacle avoidance .', 'Simulating the echoes received by a flying bat , we show that simple phonotaxis can steer a bat clear from obstacles without performing 3D reconstruction of the layout of the scene .', 'As such , this paper presents the first computationally explicit explanation for obstacle avoidance in realistic and complex 3D environments .', 'We hypothesize that using low level yet robust cues for obstacle avoidance allows bats to comply with the hard real-time constraints of this basic behaviour .']
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