This paper studies the multi-robot reliable navigation problem in uncertain topological networks, which aims at maximizing the robot team's on-time arrival probabilities in the face of road network uncertainties. The uncertainty in these networks stems from the unknown edge traversability, which is only revealed to the robot upon its arrival at the edge's starting node. Existing approaches often struggle to adapt to real-time network topology changes, making them unsuitable for varying topological environments. To address the challenge, we reformulate the problem into a Partially Observable Markov Decision Process (POMDP) framework and introduce the Dynamic Adaptive Graph Embedding method to capture the evolving nature of the navigation task. We further enhance each robot's policy learning process by integrating deep reinforcement learning with Graph Attention Networks (GATs), leveraging self-attention to focus on critical graph features. The proposed approach, namely Multi-Agent Routing in Variable Environments with Learning (MARVEL) employs the generalized policy gradient algorithm to optimize the robots' real-time decision-making process iteratively. We compare the performance of MARVEL with state-of-the-art reliable navigation algorithms as well as Canadian traveller problem solutions in a range of canonical transportation networks, demonstrating improved adaptability and performance in uncertain topological networks. Additionally, real-world experiments with two robots navigating within a self-constructed indoor environment with uncertain topological structures demonstrate MARVEL's practicality.

Inspired by human behavior when traveling over unknown terrain, this study proposes the use of probing strategies and integrates them into a traversability analysis framework to address safe navigation on unknown rough terrain. Our framework integrates collapsibility information into our existing traversability analysis, as vision and geometric information alone could be misled by unpredictable non-rigid terrains such as soft soil, bush area, or water puddles. With the new traversability analysis framework, our robot has a more comprehensive assessment of unpredictable terrain, which is critical for its safety in outdoor environments. The pipeline first identifies the terrain's geometric and semantic properties using an RGB-D camera and desired probing locations on questionable terrains. These regions are probed using a force sensor to determine the risk of terrain collapsing when the robot steps over it. This risk is formulated as a collapsibility metric, which estimates an unpredictable region's ground collapsibility. Thereafter, the collapsibility metric, together with geometric and semantic spatial data, is combined and analyzed to produce global and local traversability grid maps. These traversability grid maps tell the robot whether it is safe to step over different regions of the map. The grid maps are then utilized to generate optimal paths for the robot to safely navigate to its goal. Our approach has been successfully verified on a quadrupedal robot in both simulation and real-world experiments.