E43 Navigation and motor control

Topic

Navigation requires two complementary processes: constructing and maintaining a cognitive map of the environment and continuously estimating one's own position within that map. In mammals, these functions rely on a neurobiological system that includes place cells in the hippocampus, grid cells in the entorhinal cortex, and head-direction cells in the subiculum. Together, these neuronal populations provide information regarding position, spatial structure, and orientation.

Path integration allows for position estimation by accumulating the successive displacements made by the organism, comparable to odometry based on integrating velocity over time. However, small errors associated with each displacement also accumulate. Consequently, the longer the time elapsed without external correction, the greater the uncertainty regarding position, and the organism may eventually lose track of its location. Environmental landmarks allow for the periodic correction of this drift.

According to the text, the desert ant is a remarkable example of path integration, as it can return to its nest from hundreds of meters away without requiring external landmarks during the journey. This behavior demonstrates the extent to which a navigation system can reconstruct its own movement based on accumulated information, although the general principle remains subject to error accumulation in the absence of an external reference.

Hippocampal place cells provide another component of the spatial system. Each cell fires preferentially when the organism occupies a specific region of the environment, with an approximately Gaussian firing field centered on that position. As the organism moves to a different region, the activity of some cells decreases while that of others increases. The entire population thus forms a distributed representation of space, conceptually comparable to a probabilistic occupancy map.

In contrast, grid cells in the entorhinal cortex exhibit multiple firing fields distributed periodically with hexagonal symmetry. This structure provides a sort of metric system for spatial coordinates. Together with place cells and head-direction cells, this system enables the representation not only of the organism's location but also of its orientation and the metric relationships within the environment.

An analogous problem arises in robotics when a system must simultaneously build a map and localize itself within it. Observations of landmarks involve uncertainty; consequently, a solution based on an extended Kalman filter maintains a joint distribution of the robot's position and the positions of the various landmarks. Each new observation sequentially updates this distribution. The more precise the observation, the greater the correction applied to the joint estimate.

According to the text, the hippocampus implements an analogous biological process, combining the representation provided by place cells with information regarding movement and external references. Navigation thus emerges from a continuous interaction between an internal estimate based on accumulated displacement and corrections derived from environmental observations.

The locomotion associated with this navigation also entails a metabolic cost. At low speeds, there is a roughly fixed expenditure associated with keeping the body in motion, whereas at high speeds—particularly during running—the cost increases approximately with the square of the speed. This creates a trade-off between moving quickly and expending energy.

The relevant criterion is not necessarily minimizing expenditure per unit of time, but rather the energy cost per unit of distance traveled. An optimal locomotion speed emerges from this balance, consistent with an optimal control framework that seeks to minimize the total cost of an action. According to the text, this speed corresponds to the preferred gait consistently observed across numerous species.

Overall, navigation combines spatial representation, position estimation, and locomotor efficiency. Path integration allows for continuous position updates but accumulates error; external references enable corrections; place, grid, and direction cells construct a distributed representation of space; and locomotion introduces an energy cost that favors specific speeds. Navigating effectively therefore entails knowing one's location, maintaining a map of the environment, and moving through it at an appropriate metabolic cost.

ID:2399