Navigation on point-cloud — A Riemannian metric approach

Mobile wheeled- or tracked-robots drive in 2.5-dimensional (2.5D) environments, where the traversable surface can be considered as a 2D-manifold embedded in a three-dimensional (3D) ambient space. In this work, we aim at solving the 2.5D navigation problem solely on point-cloud. The proposed method is independent of traditional surface parametrization or reconstruction methods, such as a meshing process, which generally has high computational complexity. Instead, we utilize the output of 3D tensor voting framework (TVF) using raw point-clouds. A novel local Riemannian metric is defined based on the saliency components of TVF, which helps the modeling of the latent traversable surface. Using this metric, we prove that the geodesic in the 3D tensor space leads to rational path-planning results. Compared to traditional methods, the results reveal the advantages of the proposed method in terms of facilitating the robot maneuver with minimum movement.