Towards a PGD-Based Computational Vademecum for Robot Path Planning

The present paper describes the use of the technique known as PGD-Vademecum in potential-based path planning for mobile robots. The basic idea of the method is to obtain a Vademecum with all the possible robot paths from any start to any goal derived from a harmonic potential field in a predefined map, including any possible dynamic obstacle positions. The PGD is a numerical technique that offers three important advantages over other methods. First, the ability to calculate all the possible Poisson equation solutions for all start, goal and dynamic obstacle combinations in a map, ensuring that the resulting potential field does not have local minima. Second, the PGD-Vademecum can be expressed as a sum of uncoupled multiplied terms: the geometric map and the start and goal configurations. Consequently, the harmonic potential field for any start and goal robot positions can be reconstructed very fast, in an almost negligible computational time, allowing real-time path planning. Third, just a few uncoupled parameters are required to reconstruct the potential field with a minimum discretization error. The abilities of this technique are demonstrated by means of simulation results.