Navegação de robôs móveis baseada na equação de laplace: uma nova abordagem utilizando elementos finitos - Luciano Cunha de Araujo Pimenta (2005)
This work addresses the mobile robot navigation problem. More specifically, we propose a novel approach, in the robotics context, for constructing navigation functions based on the Laplaces equation solution. This approach is based on Finite Elements Methods, which allows for complex shaped obstacles and robots. Also, we propose rules for attaching boundary conditions to the boundary domain, in order to solve the Laplaces Equation, thus guaranteeing completeness for the proposed methodology, i.e., if a path exists the robot always reach the goal in a finite time, independently of its initial position and orientation. A new boundary condition, called Periodic Condition, is proposed and used to take into account the robots orientation. Additionally, we propose an algorithm for constructing configurations spaces in R3, useful when three degrees of freedom, planar robots are considered. Our methodology is validated in actual, holonomic mobile robots