navigation and path finding

Tobias Seidl∗ January 18, 2008

1 Abstract design.

Insects have a brain weighing about a tenth of a milligram. Nevertheless some in- 2 Introduction sect exhibit amazing performance in finding their daily paths when looking Evolutionarily challenged organisms opti- for food or shelter. Some species have even mize among others in terms of energy ex- found their ecological niche in being excel- penditure (e.g. avoiding detours), informa- lent navigators and hence can survive in ex- tion processing (e.g. energy, reliability), treme habitats. One remarkable and well safety (e.g. risk avoidance), failure avoid- studied model is the Saharan desert ance (e.g. simplicity, redundancy, failure Cataglyphis fortis that outruns its competi- tolerance). While the qualitative perfor- tors by performing egocentric navigation. mance is similar - the approach is differ- By using skylight cues as a compass and ent. It will be my mission to introduce you counting steps it is able to find its way to the study field of (behav- without using external visual cues. In com- ior associated with sensory information ), parison, the Australian desert ant Melopho- to outline the lessons learnt on insect navi- rus bagoti employs route learning strate- gation so far and finally present some rough gies, where it visually learns and in tests re- ideas for space related technical application. calls every point of their route. In studying the ’ strategies we can learn a great 2.1 Insect deal on how little information can be used to perform a navigational task. Also the orientation can be differentiated way of how information is processed within into two big fields: While migration is deal- such a tiny brain is intriguing. The conclu- ing with the relocation of an animal - some- sions drawn from this research are nowa- times over many generations - from one days not only used to understand human place to another, (ii) navigation denotes the behavior but find their way into technical systematic return to a previously left point ∗Advanced Concepts Team, ESA/ESTEC, Ke- of reference. Both types are found in differ- plerlaan 1, 2201 AN Noordwijk, The Netherlands, ent taxa, ranging from bacteria to whales. Email: [email protected] In the following I will focus on the cen-

1 tral place navigation techniques as found 2.2 Insects qualify in several in insects for a couple of reasons. The in- aspects as models sect model is a very variable one and many different ”technical solutions” are realized When reviewing the panel of this workshop by them. The system architecture of in- you will find two two other contributions sects is a rather simple one compared to on insects as model for technically vertebrate models and in consequence eas- oriented studies and application. In a way, ier to understand: First of all the hard- this stresses the fact of the amazing suc- ware (i.e. brain) is very small and hence cess of the insect Bauplan both for the vari- simple. Secondly, the behavioral patterns ability of the exoskeleton and the perfor- are reduced to the elementary motivations: mance neuronal system. While mechani- defense (fight), maintenance (food intake), cal aspects will be dealt by Stanislav Gorb, and reproduction. Since we deal with so- Nicolas Franceschini will introduce the in- cial insects, where the queen suppresses the sects’ visual autopilot. Using both mechan- workers’ reproductive behavior the discrim- ical and neuronal tools, the insects become ination of the two remaining motivations is able to perform high level tasks - also called much simpler than when studying a verte- insect intelligence or insect cognition - such brate model with its huge variety of moti- as navigation. In combining the results of vations and behaviors. In many cases, the these complementary approaches, we will food items found during a foraging trip can- not only learn more about the biological not be eaten by the insect itself. In conse- model, but also may be able to transfer this quence the mission goal becomes a rather knowledge to technical design. abstract one, where the agent-ant has to decide if the item found fulfills the profile set by the super-organism. On top of that, 3 Mastering egocentric it is technically easy to work with insects and so insect models have become very pop- navigation: the Saha- ular among behavioral scientists. Central ran ant Cataglyphis place foraging on the other hand is the type of behavior that involves highly elaborated One of the best studied models for in- signal processing, both in terms of preci- sect navigation is the Saharan desert ant sion and time, and hence appears to be the Cataglyphis. Several Cataglyphis species technically more interesting system. While have found their ecological niche in areas a migratory animal will interrupt its behav- that seem devoid of live: Desert areas con- ior once a suited living ground is found, a taining almost no vegetation and even less navigating forager is forced to locate the ex- animal live seem not to provide accept- act point of reference - usually the nest - in able living conditions. Nevertheless, once order to fulfill its mission. spending some time, the observer will dis- cover numerous rather large (approx 1 cm body length) with quite a distinct body shape and a rather fascinating behavior: In

2 this featureless habitat, they run at rather ondly - evaporate the pheromones too fast high speeds (up to 1 m/s) in a seemingly in order to allow for a stable marking. And determined manner toward an invisible goal - thirdly - there are almost not abundant at the end of their trajectory. Indeed, the food sources available that would require ant will eventually disappear in a small in- or justify establishing a route. Food items conspicuous hole in the ground - the en- are sparsely distributed and hence can usu- trance to the colony’s nest, hosting up to a ally be carried away by a single ant. Pass- few thousand individuals. A deeper study ing on the knowledge of a feeding site to will reveal, that emerging from this nest, a nest mate would not contribute to the a cohort of ants will go foraging for food colony’s success. On the other hand, each throughout the day, performing one of the ant that can be found outside the nest fol- most fascinating behaviors in animal king- lows the very same programme of search- dom. Every little ant will leave the nest for ing for food and then safely and quickly a distance of up to twenty thousand times navigating home. Hence desert ants are their own body length, and search for a sin- an ideal study model for (biological) au- gle food item - a dead insect for example tonomous agents. that succumbed to the atrocious climatic conditions. Once successful, the ant will 3.1 The compass turn around and in a determined manner steer back home to the nest in a direct line Cataglyphis ants navigate egocentrically, without getting lost. Even in the absence i.e. without using external visual cues. This of any visual cue, i.e. landmarks, the ants implies that they constantly monitor their will successfully locate their nest and imme- own movements and update the knowledge diately initiate another foraging run. This of their position in respect to the nest, the behavior is somewhat different to the com- home vector. Path integration - as the ba- monly known routes that can be observed in sis of vector navigation - requires knowl- the majority on the European ant-species. edge of the direction, distance and incli- Wood ants for example establish a route to nation of the current segment of the path a feeding site, i.e. a dead mouse, by placing in order to calculate the home-vector. The olfactory marks along the way. Other ants by far best studied element of desert ant will follow this route and easily find the food navigation is the compass mechanism with source. Each of the ants will add its olfac- which the ants determine rotation around tory share to the route and in consequence, the vertical axis. The work on the sky- the route will be reinforced and even attract light compass of insects started with von more ants, until the source is getting ex- Frisch’s [3] Nobel-awarded discovery that ploited. Now this approach does not work use polarized light to determine flight with desert ants for several reasons. Firstly, directions. In short, many insects, includ- the light sand in the desert has little cohe- ing Cataglyphis have a part of their com- sion and hence the route marked onto it will pound eye specifically adapted for compass be carried away easily by wind. If not the tasks. The dorsal rim region, i.e. a small wind, the dry and hot climate will - sec- part on the very top of the head, has eyes

3 that are sensitive to polarized UV-light of ing the energy spent, or the time spent to a preferred angle arranged in a fan shape cover a certain distance. Both were dis- configuration [15, 2, 12]. Theoretical con- carded for various reasons and hence only siderations propose the existence of three exploiting visual cues and proprioceptive integrator that are tuned to dif- ones (i.e. own movement) remained. While ferent directions and subsequently pass on flying insects such as bees use optic flow for the information of direction to so called optometry, this factor plays only a minor (and proposed) compass neurons. However, role in running animals (16%, [8, 9]). A there are some apparent constraints when series of studies finally demonstrated, that exploiting the polarization of the sky for distance estimation is performed by a pe- directional purposes. (i) Light, has to be dometer, i.e. a step integrator. In order present. This means only during day and to proof this hypothesis, [16] trained ants nights with full moon, the quality of the to forage to a feeder. Once arrived at the signal is good enough for the ants. (ii) Vis- feeder, the ants’ leg lengths were manipu- ibility to the sky has to be granted to a lated by microsurgery operations, leading degree of about 20% that is free of clouds. to longer (stilts) and shorter leg lengths (iii) During the day the sun turns at chang- (stumps). Once released in a test array, the ing speed. The compensation of the rota- ants on stilts overestimated the way home tion of the sky-pattern has to be performed and performed their search pattern behind accordingly. (iv) During the year, the so the position of the virtual nest, while the called ephemeris function changes its posi- stumps-ants under estimated the distance tion, and hence, the pre-programmed com- and looked for the nest entrance at an ear- pass has to be adaptive to that as well. (v) lier point of their search. However, as step Finally, the ephemeris on the south hemi- length changes with speed of locomotion, sphere is flipped. Even more so if the the ants do not only sum up the number of colony is located between the two tropics steps, but also incorporate the step length. and hence the December worker has to cope Studies on the kinematics of running ants with a flipped version of the curve, the July have not revealed the sensory mechanism worker is confronted with - both potentially responsible, but point towards force sensors being clones. The relationship between ge- in the animals’ leg, i.e. muscular tension re- netically inherited and deductively learnt ceptors or strain sensing campaniform sen- information on the current shape of the ever silla in the exoskeleton. changing ephemeris function is addressed in currently ongoing studies. 3.3 Integrating inclined paths

3.2 The odometer The initiator for Wittlinger’s studies was an experiment performed some years ear- In contrary to the compass mechanism, it lier and that revealed and interesting feat: has long been an open question on how When outbound ants, i.e. on the way from desert ants measure distances run. Several the nest to the feeder, were running on hypotheses had been posted, i.e. monitor- a corrugated path, i.e. crossing a series

4 of several artificial hills, they performed ear path to a series of loops with increasing much longer path than the actual -line diameter with the cross point centered on between nest and feeder measures. Once the position of the expected nest entrance. equipped with a food item and placed into With this systematic loops, the ant will a flat channel, the ants performed the typ- search for the nest entrance in the vicinity ical nest search after they had covered the with an intensity following a statistic distri- shorter of the two distances [17, 18]. Obvi- bution. ously, they integrated the inclination of the paths run and calculated the ground pro- 3.4.2 Linear and angular under- jection, which was the basis for the home shooting vector. This performance can be explained only by means of proprioceptive monitoring In linear test set-up, the estimated nest en- of the inclined surface during walking. All trance moves toward the feeder with in- other hypotheses such as visual integration creasing homing distance. In angular out- of inclination, or energy and time measures bound paths, the return angle is system- fall to fundamental flaws. However, the ex- atically pointing not toward the virtual act mechanisms of monitoring inclination nest but toward an estimated nest entrance for means of path integration has not been moved along the outbound path. An ant found so far. Again, force feedback during that has performed several foraging runs, walking currently seems the most favored will know the visual features of along the explanation. usually taken path better than those ”be- hind” the nest (ants show high sector fi- delity). Once a known structure is iden- 3.4 Coping with errors tified, the previously lost nest entrance is easier to be located. A typical foraging run of a desert ant can in- volve about 20 thousand single steps which are integrated to continuously update the 3.4.3 Resetting the vector information on the shortest way back to the During each foraging run, the ant will in- nest - home vector. It is evident, that even crementally accumulate errors on the posi- slightest errors may severely deviate the an- tion of the nest. The reference point with imal from its track and induce fatal conse- the highest significance to the animal is quences. In the following I want to outline the nest. Hence, only in the nest eventual some of the techniques used by the ants’ (or induced) errors on the vector will be navigational toolkit in order to maintain a deleted. Every ant leaving the nest for a satisfactory success rate. foraging run will be in an initial zero-vector state. 3.4.1 Systematic search 3.4.4 Exploiting external cues Once the ant has performed its run back home and the home vector reaches a state Even in the most homogeneous environ- close to zero, it will switch from the lin- ment once in a while, unique structures ap-

5 pear and hence can be exploited by the the route without hesitation. The excep- ant for navigational purposes. May this tion to be made is, that an ant on outbound be visual landmarks such as tussocks or motivation will not recognize its inbound stones, tactile landmarks [11] such as the route and vice versa. Now the most intrigu- roughness of the ground or even olfactory ing question is, on how an ant with a brain landmarks not connected with food or nest of approximately 0.1 mg will be able to re- scent. These landmarks may temporarily member every section of a sequence of sev- override the path integrator, but not reset eral thousands of ”snapshots” and quickly it. retrieve the right match in the instant of being confronted with it. Obviously, it can- not be a simple hard-drive with a series of 4 Coping with the bitmaps that are constantly screened. Even more so in the sight of recent results that labyrinth: the showed that ants can learn and retrieve up -approach to three separate routes. Theoretical stud- ies on feature extraction and localization Cataglyphis is not the only genus of ants try to shed light onto this so far not un- that occupy the niche of hot and dry derstood mechanism. habitats. In the south of Africa we find Ocymyrmex velox and in the Australian outback Melophorus bagoti. The later one 5 Insect intelligence in exhibits a quite fascinating approach to cope with the peculiarities of its habitat: the space context Numerous and densely placed tussocks form rather a huge labyrinth than a free and uni- The the selection pressure acting upon the form are such as we can find it in the Sahara forgaging abilities of the species introduced [?]. In consequence, finding its way home in in the present account has led to an optimi- a time efficient manner is not only a mat- sation of the ants’ major survival feature: ter of getting direction and distance right, The navigational toolkit. Several different but also avoiding dead ends. In addition systems act in parallel in order to allow for to that, potential predators can hide much the ant to perform successfull navigation. easier and hence a safe route is worthwhile Although it is impossible to determine what to have. In consequence, Melophorus ants ”Evolution had in mind” we can indentify establish routes to an installed feeder and a number of basic demands that appear to maintain these routes rather conservatively. be set during the evolutionary development. On top of that, the outbound route and the An ant brain is rather small and computing inbound route do not have to be identical. power as well as data storage is highly re- On the other side a displaced ant will initi- stricted for several reasons. Both energy ate search loops and once it found its previ- constraints [5, 1] as well the general Bau- ously learnt route immediately recognize it - plan do not allow for indefinite expansion if it is the right one - and continue to follow of brain tissue. Hence incoming data has to

6 be highly reduced to the relevant and only already found its way into a technolog- the relevant bits. Extracting behaviorally ical demonstrator [4, 13] interesting features from the incoming data has to be performed in a real time manner • Only little exposition to the sunlight since predators are not known to wait. Ad- is necessary to determine the current ditionally, the calculations performed have shape of the ephemeris function. Un- to be done so in a reliable way, since er- derstanding the balance between pre- rors cannot be monitored or corrected dur- programmed and acquired knowledge ing a foraging run. Also rebcalibration is including the minimum input neces- only known for subsystems such as the com- sary to perform this task may lead to pass. The vector is only reset in the colony. a deeper understanding for adaptive On top of all that the ant has to deal with mechanisms in autonomous systems. insufficient sensory data. Its knowledge of • Not all available data is used by the the world is highly limited and it can be as- sensory system. Which features of sumed also noisy. The study of these highly a visual scenery is finally memorized evolved and carefully tuned system allows (snapshot) and subsequently compared us to draw some conclusions that can not to the actual scenery? The algorithms only entertain biologists, but also lead to a that are used by the technological com- systematic application in technological de- petetor to locate the nest with vi- velopment. sual cues could be usefull for ones own projects. • Each Cataglyphis-ant is able to per- form foraging runs with 20.000 trans- • On top of that, the Australian ant, lational steps including rotations and Melophorus bagoti: How does such inclines, integrating iteratively every a small and rather un-telligent be- single vector at a precision sufficient ing memorize and retrieve every sin- enough to relocate the nest while run- gle point of its route(s)? Again feature ning on a sometimes slippery ground extraction, data compression and com- in a rather shakey manner. Neuronal parison algorithms could be an inter- mechanisms of data fusion, error elim- esting starting point in machine vision ination, and the lot may provide new projects. tools for various applications. • One of the big questions in animal nav- • The architecture of the e-vector ana- igation in general is the dispute be- lyzers including the subsequent hard- tween map-like representation or pro- wired data processing leads to a fully cedural knowledge of the habitat. The functional skylight compass. It is ro- current state indicates that the use of bust enough to work under suboptimal maps seems to be rather unprobable conditions such as almost obscured sky since simpler models allow to explain or even during full moon nights. Still, all current data. Might autonomous it is a simple electronic system that has exploration vehicle be better off to use

7 this form of ”mapping” their environ- [2] Fent K (1985) Himmelsorientierung ment? bei der Wuestenameise Cataglyphis bi- color: Bedeutung von Komplexaugen • One of the most amazing observations und Ocellen. PhD thesis, University of is that foraging ants usually fall to Zuerich. predators but only rarely get lost or miscalculate their energy budget. The [3] Frisch K von (1949) Die Polarisation ant-controlled part of a foraging excur- des Himmelslichts als orientierender sion appears to be rather robust and Faktor bei den Taenzen der Bienen. ”mission proof”. Examples are the Experientia 5:142148. self elimination of inevitable errors or the temporary dominance of the vi- [4] Lambrinos D, Moeller R, Labhart T, sual navigation system over the ego- Pfeifer R, Wehner R (2000) A mo- centric one during nest search. The bile robot employing insect strategies basis on which information is evalu- for navigation. Robot Autonom Syst ated and trusted can inspire the de- 30:39-64. velopment of autonomous, redundant systems in space applications [5] Martin RD (1981) Relative and metabolic rate in terrestrial verte- The lessons that can be learnt from sys- brates. Nature 293:5760. tematic analysis of biological systems is not only a time worthy activity but may also [6] Mueller M, Wehner R (2007): Wind lead to new insights for technical applica- and sky as compass cues in desert tions. Biological systems are subobtimal in ant navigation. Naturwissenschaften the respect that they have to follow the ge- (in press). netic history of the Bauplan and cannot de- sign freely in space and material. However, [7] Muser B, Sommer S, Wolf H, Wehner the solutions achived are sometimes unique R (2005): Foraging of the and justify a deeper look. On the other side, thermophilic Australian desert ant technological research has the big advan- Melophorus bagoti. Austr J Zool 53, tage that the competetor may be analyzed 301-311. at any time and subsequently imitated if the solution appears to be better. The com- [8] Ronacher B, Wehner R (1995): Desert petetors emanating from nature should not ants Cataglyphis fortis use self-induced be underestimated. optic flow to measure distances trav- elled. J. Comp. Physiol. A 177:21-27. References [9] Ronacher B, Gallizzi K, Wohlgemuth S, Wehner R (2000): Lateral optic flow [1] Allman JM (1999) Evolving brains. does not influence distance estimation Scientific American Library, New in the desert ant, Cataglyphis fortis.J York. Exp Biol 203:1113-1121.

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[11] Seidl T, Wehner R (2006). Visual and tactile learning of ground structures in desert ants. J Exp Biol 209, 3336-3344.

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[14] Wehner, R (2007). The desert ant’s navigational toolkit: procedural rather than positional knowledge, in press.

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[16] Wittlinger M, Wehner R, Wolf H (2006): The ant odometer: stepping on stilts and stumps. Science 312, 1965- 1967.

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[18] Wohlgemuth S, Ronacher B, Wehner R (2002). Distance estimation in the third dimension in desert ants. J Comp Physiol A 188:273281.

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