Mathematical and Computational Theory of Animal Navigation

Allen Cheung

Navigation is an umbrella term which encompasses a wide range of sensorimotor and information processing tasks, many of which are still poorly defined or understood. A primary goal of theme 2b is to develop a theoretical understanding of the underlying principles common to all navigating agents, animal or robot. To achieve this goal it has been necessary to dissect navigational tasks into their most basic components, to understand the information required to solve those tasks, to use those mechanistic building blocks to generate complex biomimetic behaviours, and to see whether sophisticated methods can pick the correct building blocks from observed behaviour.

 

 

A. Schematic representation of information flow during social insect foraging. In this scheme, navigation (medium range) directly controls locomotion. In turn, higher level commands and strategies direct the navigation system. B. Graphical example of an unknown mixture of simulated (unbiased) idiothetic and allothetic directed walks (IDWs and ADWs) with varying magnitudes of random angular displacement errors, and unknown axes of intended locomotion. In this example, the decision algorithm was correct 28 out of 30 times (ADWs = solid lines, IDWs = dotted lines), being unable to decide in the remaining two (dashed lines). C. Computer simulated PI (path integration) homing and searching trajectory expressed in egocentric coordinates, showing damped oscillatory behaviour and chaotic point attractors. D. A schematic illustration of the mapping of a straight trajectory in real space to a neural representational space. This is an example of an allocentric static vectorial PI system, the only noise-tolerant class of PI systems.

Ongoing Collaborative Research

1. Collaboration with D. Ball, M. Milford

Blind Bayes in a box – computer simulation and robotic implementation of Bayes-optimal navigation in confined spaces under a variety of conditions, particularly in the absence of visual cues. We investigate whether the observed instability in rodent head direction system in darkness is theoretically compatible with a stable representation of place. (Manuscript in preparation.)

2. Collaboration with D. Angus, J. Wiles

Conceptual navigation – concept mapping algorithms are used to generate graphs from view-similarity matrices, which are compared to ground-truth spatial layout. This is carried out in strictly controlled virtual environments, simulating those of real experiments, in order to understand the relationship between metric space and different visual environments. Metrics are developed to quantify that relationship so different experimental arenas may be compared in a quantitatively meaningful way, particularly with respect to spatial navigation tasks.

3. Collaboration with P. Stratton, F. Windels

Spike waveform analysis – in vivo extracellular action potential waveforms from awake and anaesthetized rats, with and without local pharmacological treatment, from various brain regions are analysed and compared. Waveform variability is quantified to determine the likely error rate when standard classification techniques are used.

4. Collaboration with T. Luu, D. Ball, M. Srinivasan

Honeybee flight behaviour in virtual reality – the evidence from simple tethered experiments seem to differ from free flight with respect to the functional class of EMDs (elementary motion detectors) used by flying insects. Using the existing setup, it is possible to visually simulate free flight, whilst tethered. Since the abdominal pitch has been shown to vary according to visually-perceived forward speed, the pitch may be used to gauge the perceived speed in the presence of visual patterns of different spatial and temporal frequencies.

5. Collaboration with G. Goodhill, M. Srinivasan

Distance travelled without a compass – animals do not always have access to stable directional cues (i.e., a compass) but it may be very difficult to ascertain experimentally, particularly since the animal’s intended travel direction may vary over short segments of the journey. However, the average radial distance travelled varies depending on whether internal or external directional cues are used. A simple formula to calculate the expected radial displacement has eluded researchers, but simple accurate approximations have been developed.

6. Collaboration with J. Reinhard

Key odorants – odours are important for guidance and localization in animal navigation. Yet it remains unclear how complex scent mixtures are processed and interpreted by the nervous system. Here, human subjects are asked to grade the odour similarity of constituent compounds to the mixture source. A novel theory of ‘key odorants’ has been developed to explain the data, which has implications for theories of olfactory learning, as well as applications in food and wine industries. (Manuscript in preparation.)