The challenge of traversability estimation is a crucial aspect of autonomous navigation in unstructured outdoor environments such as forests. It involves determining whether certain areas are passable or risky for robots, taking into account factors like terrain irregularities, slopes, and potential obstacles. The majority of current methods for traversability estimation operate on the assumption of an offline computation, overlooking the significant influence of the robot's heading direction on accurate traversability estimates. In this work, we introduce a deep neural network that uses detailed geometric environmental data together with the robot's recent movement characteristics. This fusion enables the generation of robot direction awareness and continuous traversability estimates, essential for enhancing robot autonomy in challenging terrains like dense forests. The efficacy and significance of our approach are underscored by experiments conducted on both simulated and real robotic platforms in various environments, yielding quantitatively superior performance results compared to existing methods. Moreover, we demonstrate that our method, trained exclusively in a high-fidelity simulated setting, can accurately predict traversability in real-world applications without any real data collection. Our experiments showcase the advantages of our method for optimizing path-planning and exploration tasks within difficult outdoor environments, underscoring its practicality for effective, real-world robotic navigation. In the spirit of collaborative advancement, we have made the code implementation available to the public.

This paper presents a novel feedback motion planning method for mobile robot navigation in 3D uneven terrains. We take advantage of the \textit{supervoxel} representation of point clouds, which enables a compact connectivity graph of traversable regions on the point cloud maps. Given this graph of traversable areas, our approach navigates the robot to any reachable goal pose using a control Lyapunov function (cLf) and a navigation function. The cLf ensures the kinodynamic feasibility and target convergence of the generated motion plans, while the navigation function optimizes the resulting feedback motion plans. We carried out navigation experiments in real and simulated 3D uneven terrains. In all circumstances, the experimental findings show that our approach performs superior to the baselines, proving the approach's efficiency and adaptability to navigate a robot in challenging uneven 3D terrains. The proposed method can also navigate a robot with a particular objective, e.g., shortest-distance or least-inclined plan. We compared our approach to well-established sampling-based motion planners in which our method outperformed all other planners in terms of execution time and resulting path length. Finally, we provide an open-source implementation of the proposed method to benefit the robotics community.