Exploiting Euclidean Distance Field Properties for Fast and Safe 3D planning with a modified Lazy Theta*

Abstract: Graph search planners have been widely used for 3D path planning in the literature, and Euclidean Distance Fields (EDFs) are increasingly being used as a representation of the environment. However, to the best of our knowledge, the integration of EDFs into heuristic planning has been carried out in a loosely coupled fashion, dismissing EDF properties that can be used to accelerate/improve the planning process and enhance the safety margins of the resultant trajectories. This paper presents a fast graph search planner based on a modified Lazy Theta* planning algorithm for aerial robots in challenging 3D environments that exploits the EDF properties. The proposed planner outperforms classic graph search planners in terms of path smoothness and safety. It integrates EDFs as environment representation and directly generates fast and smooth paths avoiding the use of post-processing methods; it also considers the analytical properties of EDFs to obtain an approximation of the EDF cost along the line-of-sight segments and to reduce the number of visibility neighbours, which directly impacts the computation time. Moreover, we demonstrate that the proposed EDF-based cost function satisfies the triangle inequality, which reduces calculations during exploration and, hence, computation time. Many experiments and comparatives are carried out in 3D challenging indoor and outdoor simulation environments to evaluate and validate the proposed planner. The results show an efficient and safe planner in these environments.