Minimalistic model for navigation of mobile robots around obstacles based on complex-number calculus and inspired by human navigation behavior

It has recently been shown that the strategies and rules used by human agents to approach a goal position while avoiding collision with an obstacle can be used to construct a model for robot navigation. The robot navigation model thus obtained involves position variables for robot position and additional internal degrees of freedom. In the present work, we eliminate these internal degrees of freedom by means of a standard method of synergetics (theory of self-organization) while still making sure that the mobile robot will approach the goal position. In doing so, we arrive at a minimalistic navigation model that (i) is motivated by human navigation behavior, (ii) benefits from computational simplicity, (iii) can be re-formulated by means of complex number calculus, and (iv) allows to determine two-dimensional flow fields in analogy to hydrodynamic two-dimensional flows by means of computer simulations. We present the implementation of the navigation algorithm in terms of a complex-valued Euler forward scheme and exploit the simulation scheme to predict how the time to reach the goal position depends on some key parameters of the minimalistic robot navigation model.