Considering the biological or artificial control of a trajectory generation, we propose a biologically plausible model based on harmonic potentials. Such methods assume that obstacles to avoid (or constraints not to violate) correspond to maxima of the potential, while the goal corresponds to a unique 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, so that finding a trajectory reduces to «roll down» along this relief towards the minimal height location. The originality of the present work is to build an harmonic potential (thus without local minimum) as a finite linear combination of elementary harmonic functions. The set of these components samples the border of the admissible domain bounded by obstacles or constraints. This leads to an internal representation of the problem as a non-topographical map increment- ally builded during the system exploration and non-linearly linked to the real problem geometry. As such, it provides a biologically plausible quantitative model of some hippocampus mechanisms and of the related cognitive maps, in coherence with usual biological assumptions about such behavior.