Path planning of mobile robots using potential fields and swarms of Brownian particles

This paper proposes an algorithm for trajectory planning based on the motion of Brownian particles. One of the most popular approaches in path planning is to use the artificial potential fields method which, due to its easiness in implementation, might attract the robot towards a local minimum configuration, thus preventing it from reaching the desired final destination. Although there are different approaches to deal with this drawback, their modeling lacks the simplicity of the potential fields, adding thus an extra complexity to the problem. The solution proposed here combines the strengths of both approaches: it is easy to analyze and to implement, just like in the potentials method, while it preserves the robustness against local minima of more complex particle swarm models. An approximate analysis for the deterministic version of the selected model was performed and it was observed, via simulations, that the results obtained after this simplification were consistent with the behavior of the stochastic system.