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Navigation requires two components: constructing and maintaining a map of the environment (cognitive map) and estimating one's position within that map (localization). Mammals have a neurobiological navigation system based on place cells (hippocampus), grid cells (entorhinal cortex) and head direction cells (subiculum).

Path integration calculates position by accumulating displacements: x(t) = x + v·cos()dt. The accumulated error grows as t^(3/2) for speed noise: without external correction (landmarks), the animal is lost. Insects (desert ants, Cataglyphis) use path integration with surprising precision to return to the nest from distances of hundreds of meters.

Hippocampal place cells are activated when the animal is in a specific region of the environment: their activation field is approximately Gaussian with _place 15150 cm in rat. The set of all place cells (place map) forms a distributed representation of space. Grid cells have hexagonally periodic activation fields: they act as the metric coordinate system of space.

SLAM (Simultaneous Localization and Mapping) is the problem of building a map and locating the robot simultaneously, using uncertain landmark observations. The EKF-SLAM solution maintains the Gaussian distribution of the joint state (robot position + landmark position) and updates it sequentially with each observation. Biologically, the hippocampus implements an analogous process.

The metabolic cost of locomotion grows with speed: at low speeds there is a fixed cost (supporting the body), and the total cost is approximately quadratic in v for running. This creates an evolutionary incentive for optimal speed of locomotion that minimizes cost per distance (not time). This optimal speed corresponds to the preferred gait observed in most animals.

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ID:('ky', 588)

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ID:(0, 588)