Unstructured environments such as mountains, caves, construction sites, or disaster areas are challenging for autonomous navigation because of terrain irregularities. In particular, it is crucial to plan a path to avoid risky terrain and reach the goal quickly and safely. In this paper, we propose a method for safe and distance-efficient path planning, leveraging Traversal Risk Graph (TRG), a novel graph representation that takes into account geometric traversability of the terrain. TRG nodes represent stability and reachability of the terrain, while edges represent relative traversal risk-weighted path candidates. Additionally, TRG is constructed in a wavefront propagation manner and managed hierarchically, enabling real-time planning even in large-scale environments. Lastly, we formulate a graph optimization problem on TRG that leads the robot to navigate by prioritizing both safe and short paths. Our approach demonstrated superior safety, distance efficiency, and fast processing time compared to the conventional methods. It was also validated in several real-world experiments using a quadrupedal robot. Notably, TRG-planner contributed as the global path planner of an autonomous navigation framework for the DreamSTEP team, which won the Quadruped Robot Challenge at ICRA 2023. The project page is available at https://trg-planner.github.io .

With the increasing presence of dynamic scenarios, such as Vehicle-to-Vehicle communications, radio propagation modeling tools must adapt to the rapidly changing nature of the radio channel. Recently, both Differentiable and Dynamic Ray Tracing frameworks have emerged to address these challenges. However, there is often confusion about how these approaches differ and which one should be used in specific contexts. In this paper, we provide an overview of these two techniques and a comparative analysis against two state-of-the-art tools: 3DSCAT from UniBo and Sionna from NVIDIA. To provide a more precise characterization of the scope of these methods, we introduce a novel simulation-based metric, the Multipath Lifetime Map, which enables the evaluation of spatial and temporal coherence in radio channels only based on the geometrical description of the environment. Finally, our metrics are evaluated on a classic urban street canyon scenario, yielding similar results to those obtained from measurement campaigns.

Radio propagation modeling is essential in telecommunication research, as radio channels result from complex interactions with environmental objects. Recently, Machine Learning has been attracting attention as a potential alternative to computationally demanding tools, like Ray Tracing, which can model these interactions in detail. However, existing Machine Learning approaches often attempt to learn directly specific channel characteristics, such as the coverage map, making them highly specific to the frequency and material properties and unable to fully capture the underlying propagation mechanisms. Hence, Ray Tracing, particularly the Point-to-Point variant, remains popular to accurately identify all possible paths between transmitter and receiver nodes. Still, path identification is computationally intensive because the number of paths to be tested grows exponentially while only a small fraction is valid. In this paper, we propose a Machine Learning-aided Ray Tracing approach to efficiently sample potential ray paths, significantly reducing the computational load while maintaining high accuracy. Our model dynamically learns to prioritize potentially valid paths among all possible paths and scales linearly with scene complexity. Unlike recent alternatives, our approach is invariant with translation, scaling, or rotation of the geometry, and avoids dependency on specific environment characteristics.