Walking Straight into Circles

Honeybees as a model for the study of visually guided flight, navigation, and biologically inspired robotics

Research over the past century has revealed the impressive capacities of the honeybee, Apis mellifera, in relation to visual perception, flight guidance, navigation, and learning and memory. These observations, coupled with the relative ease with which these creatures can be trained, and the relative simplicity of their nervous systems, have made honeybees an attractive model in which to pursue general principles of sensorimotor function in a variety of contexts, many of which pertain not just to honeybees, but several other animal species, including humans. This review begins by describing the principles of visual guidance that underlie perception of the world in three dimensions, obstacle avoidance, control of flight speed, and orchestrating smooth landings. We then consider how navigation over long distances is accomplished, with particular reference to how bees use information from the celestial compass to determine their flight bearing, and information from the movement of the environment in their eyes to gauge how far they have flown. Finally, we illustrate how some of the principles gleaned from these studies are now being used to design novel, biologically inspired algorithms for the guidance of unmanned aerial vehicles.

Integration of vestibular and proprioceptive signals for spatial updating

Spatial updating during self-motion typically involves the appropriate integration of both visual and non-visual cues, including vestibular and proprioceptive information. Here, we investigated how human observers combine these two non-visual cues during full-stride curvilinear walking. To obtain a continuous, real-time estimate of perceived position, observers were asked to continuously point toward a previously viewed target in the absence of vision. They did so while moving on a large circular treadmill under various movement conditions. Two conditions were designed to evaluate spatial updating when information was largely limited to either proprioceptive information (walking in place) or vestibular information (passive movement). A third condition evaluated updating when both sources of information were available (walking through space) and were either congruent or in conflict. During both the passive movement condition and while walking through space, the pattern of pointing behavior demonstrated evidence of accurate egocentric updating. In contrast, when walking in place, perceived self-motion was underestimated and participants always adjusted the pointer at a constant rate, irrespective of changes in the rate at which the participant moved relative to the target. The results are discussed in relation to the maximum likelihood estimation model of sensory integration. They show that when the two cues were congruent, estimates were combined, such that the variance of the adjustments was generally reduced. Results also suggest that when conflicts were introduced between the vestibular and proprioceptive cues, spatial updating was based on a weighted average of the two inputs.

Finding the way with a noisy brain

Successful navigation is fundamental to the survival of nearly every animal on earth, and achieved by nervous systems of vastly different sizes and characteristics. Yet surprisingly little is known of the detailed neural circuitry from any species which can accurately represent space for navigation. Path integration is one of the oldest and most ubiquitous navigation strategies in the animal kingdom. Despite a plethora of computational models, from equational to neural network form, there is currently no consensus, even in principle, of how this important phenomenon occurs neurally. Recently, all path integration models were examined according to a novel, unifying classification system. Here we combine this theoretical framework with recent insights from directed walk theory, and develop an intuitive yet mathematically rigorous proof that only one class of neural representation of space can tolerate noise during path integration. This result suggests many existing models of path integration are not biologically plausible due to their intolerance to noise. This surprising result imposes significant computational limitations on the neurobiological spatial representation of all successfully navigating animals, irrespective of species. Indeed, noise-tolerance may be an important functional constraint on the evolution of neuroarchitectural plans in the animal kingdom.

The ability to navigate allows animals to vastly increase the action space for finding resources, mates, and to avoid predators. The benefits are many and it is commonly believed that modern brain functions have emerged from ancestral forms evolved for effective navigation. Since the time of Charles Darwin, it has been recognized that path integration is a navigation strategy innate to many species. Path integration involves adding the stepwise displacements during a circuitous journey to compute a net homeward direction. Over the past century, this phenomenon has been described for birds to mammals to arthropods, and a long list of mathematical, algorithmic, and neural network models have been proposed to explain the necessary computations. This work shows how the different types of models behave in the presence of noise. It turns out that only one class of models can function properly in the presence of noise. Since noise appears to be present at all levels of brain physiology, we arrive at the surprising conclusion that the general computational principles for path integration must be the same across all species. Two subtypes of path integration models share the same critical computational principles, and are compared to known neuroanatomy and physiology.