Exploring collision-free path planning by using homotopy continuation methods

Autonomous and semi-autonomous robots play significant roles in space and terrestrial exploration, even more in unfavorable and dangerous environments. Although recent advances allow robots to evolve in many such environments, one of the most important problems remains the establishment of collision-free trajectories in static or partially (temporal) static environments. This paper presents a different approach to address this problem, proposing a methodology based on homotopy continuation methods (HCM) capable of generating collision-free trajectories in two and three dimensions. The basic idea behind the proposal relies on the construction of a nonlinear equation representing the map of the environment, making it possible to apply HCM methods to obtain collision-free paths. A series of simulations are presented to show the effectiveness of the method avoiding circular, semi-rectangular, spherical shaped and semi-parallelepipeds obstacles.