Numerical techniques for robot path planning: artificial potential fields and proper generalized decomposition

Abstract

One of the most important tasks in the mobile robot navigation field is the planning of a collision-free path from a starting point to a target point. This project introduce the concept of Artificial Potential Field (APF) as a real time global path planner method and how it is modelled using the Poisson equation. To solve it, a recently developed numerical technique called Proper Generalized Decomposition (PGD) is considered, since it makes the resolution of the Poisson equation feasible for real-time calculations. To illustrate the properties of those methods, a simulation with a virtual robot on a virtual world has been produced. The Construct AI, a free online platform, has enabled us to develop the necessary code for this, based on the Robot Operating System (ROS) framework. This tools are used on the Robotics subject at Universitat de Barcelona, and that has proved to be very useful, because I had at my disposal some documentation and repositories that enabled me to avoid having to do all the settings from scratch. This work tries to be an accessible introduction to this topics, and it can serve as a basis for future multiple extensions, as we will comment at the end. The advantages and the projection of this approach inside the path planning area make it a candidate for become the future of robot navigation.