Team Coordination on Graphs with Risky Edges (TCGRE) is a recently emerged problem, in which a robot team collectively reduces graph traversal cost through support from one robot to another when the latter traverses a risky edge. Resembling the traditional Multi-Agent Path Finding (MAPF) problem, both classical and learning-based methods have been proposed to solve TCGRE, however, they lacked either computation efficiency or optimality assurance. In this paper, we reformulate TCGRE as a constrained optimization and perform rigorous mathematical analysis. Our theoretical analysis shows the NP-hardness of TCGRE by reduction from the Maximum 3D Matching problem and that efficient decomposition is a key to tackle this combinatorial optimization problem. Further more, we design three classes of algorithms to solve TCGRE, i.e., Joint State Graph (JSG) based, coordination based, and receding-horizon sub-team based solutions. Each of these proposed algorithms enjoy different provable optimality and efficiency characteristics that are demonstrated in our extensive experiments.

We consider the problem of time-limited robotic exploration in previously unseen environments where exploration is limited by a predefined amount of time. We propose a novel exploration approach using learning-augmented model-based planning. We generate a set of subgoals associated with frontiers on the current map and derive a Bellman Equation for exploration with these subgoals. Visual sensing and advances in semantic mapping of indoor scenes are exploited for training a deep convolutional neural network to estimate properties associated with each frontier: the expected unobserved area beyond the frontier and the expected timesteps (discretized actions) required to explore it. The proposed model-based planner is guaranteed to explore the whole scene if time permits. We thoroughly evaluate our approach on a large-scale pseudo-realistic indoor dataset (Matterport3D) with the Habitat simulator. We compare our approach with classical and more recent RL-based exploration methods. Our approach surpasses the greedy strategies by 2.1% and the RL-based exploration methods by 8.4% in terms of coverage.