About biologically plausible trajectory generators

Considering the biological or artificial trajectory generation problem, we propose a biologically plausible model of the link between the (i) local "where-to-go-next" local mechanism in a locus map and the (ii) global trajectory generation problem. This explains how the well known hippocampal related areas containing place fields with local mechanisms are also very likely able to solve the global problem, providing the neural map activity is related to harmonic potentials. Such representation assume that obstacles to avoid (or constraints not to violate) correspond to maxima of a so-called potential, while the goal corresponds to its minimum. The corresponding algorithm thus behaves as if one throws a sheet onto this state space, this hyper-surface relief being elevated on obstacles, with a hole at the goal location. Finding a trajectory thus reduces to "roll down" along this relief, in the direction of the potential gradient. The originality of the present work is to build an harmonic potential (thus without local minimum) from a sparse adaptive combination of elementary place fields, as inspired by the biological modelization of the hippocampal structures. This leads to an internal representation of the problem as a non-topographical map, incrementally built during the system exploration. As such, it provides a key element for a biologically plausible model of the related hippocampus mechanisms in coherence with usual biological assumptions about such behavior.