In robotic planetary surface exploration, strategic mobility planning is an important task that involves finding candidate long-distance routes on orbital maps and identifying segments with uncertain traversability. Then, expert human operators establish safe, adaptive traverse plans based on the actual navigation difficulties encountered in these uncertain areas. In this paper, we formalize this challenge as a new, risk-averse variant of the Canadian Traveller Problem (CTP) tailored to global planetary mobility. The objective is to find a traverse policy minimizing a conditional value-at-risk (CVaR) criterion, which is a risk measure with an intuitive interpretation. We propose a novel search algorithm that finds exact CVaR-optimal policies. Our approach leverages well-established optimal AND-OR search techniques intended for (risk-agnostic) expectation minimization and extends these methods to the risk-averse domain. We validate our approach through simulated long-distance planetary surface traverses; we employ real orbital maps of the Martian surface to construct problem instances and use terrain maps to express traversal probabilities in uncertain regions. Our results illustrate different adaptive decision-making schemes depending on the level of risk aversion. Additionally, our problem setup allows accounting for traversability correlations between similar areas of the environment. In such a case, we empirically demonstrate how information-seeking detours can mitigate risk.

Search is an ability foundational in many important tasks, and recent studies have shown that large language models (LLMs) struggle to perform search robustly. It is unknown whether this inability is due to a lack of data, insufficient model parameters, or fundamental limitations of the transformer architecture. In this work, we use the foundational graph connectivity problem as a testbed to generate effectively limitless high-coverage data to train small transformers and test whether they can learn to perform search. We find that, when given the right training distribution, the transformer is able to learn to search. We analyze the algorithm that the transformer has learned through a novel mechanistic interpretability technique that enables us to extract the computation graph from the trained model. We find that for each vertex in the input graph, transformers compute the set of vertices reachable from that vertex. Each layer then progressively expands these sets, allowing the model to search over a number of vertices exponential in the number of layers. However, we find that as the input graph size increases, the transformer has greater difficulty in learning the task. This difficulty is not resolved even as the number of parameters is increased, suggesting that increasing model scale will not lead to robust search abilities. We also find that performing search in-context (i.e., chain-of-thought) does not resolve this inability to learn to search on larger graphs.

In this paper, we solve the classical Multi-agent Pathfinding (MAPF) problem. Existing approaches struggle to solve dense MAPF instances. In this paper, we propose a Corridor Generating Algorithm for MAPF, namely CGA-MAPF. In CGA-MAPF, the agents build \emph{corridors}, a set of connected vertices, from current locations towards agents' goals and evacuate other agents out of the corridors to avoid collisions and deadlocks. The proposed algorithm has a reachability property, i.e. every agent is guaranteed to reach its goal location at some point. In the experimental section, we demonstrate that CGA-MAPF outperforms baseline algorithms in terms of success rate across diverse MAPF benchmark grids, achieving state-of-the-art performance.

When greedy search algorithms encounter a local minima or plateau, the search typically devolves into a breadth-first search (BrFS), or a local search technique is used in an attempt to find a way out. In this work, we formally analyze the performance of BrFS and constant-depth restarting random walks (RRW) -- two methods often used for finding exits to a plateau/local minima -- to better understand when each is best suited. In particular, we formally derive the expected runtime for BrFS in the case of a uniformly distributed set of goals at a given goal depth. We then prove RRW will be faster than BrFS on trees if there are enough goals at that goal depth. We refer to this threshold as the crossover point. Our bound shows that the crossover point grows linearly with the branching factor of the tree, the goal depth, and the error in the random walk depth, while the size of the tree grows exponentially in branching factor and goal depth. Finally, we discuss the practical implications and applicability of this bound.

With the expansion of the scale of robotics applications, the multi-goal multi-agent pathfinding (MG-MAPF) problem began to gain widespread attention. This problem requires each agent to visit pre-assigned multiple goal points at least once without conflict. Some previous methods have been proposed to solve the MG-MAPF problem based on Decoupling the goal Vertex visiting order search and the Single-agent pathfinding (DVS). However, this paper demonstrates that the methods based on DVS cannot always obtain the optimal solution. To obtain the optimal result, we propose the Multi-Goal Conflict-Based Search (MGCBS), which is based on Decoupling the goal Safe interval visiting order search and the Single-agent pathfinding (DSS). Additionally, we present the Time-Interval-Space Forest (TIS Forest) to enhance the efficiency of MGCBS by maintaining the shortest paths from any start point at any start time step to each safe interval at the goal points. The experiment demonstrates that our method can consistently obtain optimal results and execute up to 7 times faster than the state-of-the-art method in our evaluation.

For rearranging objects on tabletops with overhand grasps, temporarily relocating objects to some buffer space may be necessary. This raises the natural question of how many simultaneous storage spaces, or "running buffers", are required so that certain classes of tabletop rearrangement problems are feasible. In this work, we examine the problem for both labeled and unlabeled settings. On the structural side, we observe that finding the minimum number of running buffers (MRB) can be carried out on a dependency graph abstracted from a problem instance, and show that computing MRB is NP-hard. We then prove that under both labeled and unlabeled settings, even for uniform cylindrical objects, the number of required running buffers may grow unbounded as the number of objects to be rearranged increases. We further show that the bound for the unlabeled case is tight. On the algorithmic side, we develop effective exact algorithms for finding MRB for both labeled and unlabeled tabletop rearrangement problems, scalable to over a hundred objects under very high object density. More importantly, our algorithms also compute a sequence witnessing the computed MRB that can be used for solving object rearrangement tasks. Employing these algorithms, empirical evaluations reveal that random labeled and unlabeled instances, which more closely mimics real-world setups, generally have fairly small MRBs. Using real robot experiments, we demonstrate that the running buffer abstraction leads to state-of-the-art solutions for in-place rearrangement of many objects in tight, bounded workspace.

Multi-agent path finding (MAPF) is the problem of moving agents to the goal vertex without collision. In the online MAPF problem, new agents may be added to the environment at any time, and the current agents have no information about future agents. The inability of existing online methods to reuse previous planning contexts results in redundant computation and reduces algorithm efficiency. Hence, we propose a three-level approach to solve online MAPF utilizing sustainable information, which can decrease its redundant calculations. The high-level solver, the Sustainable Replan algorithm (SR), manages the planning context and simulates the environment. The middle-level solver, the Sustainable Conflict-Based Search algorithm (SCBS), builds a conflict tree and maintains the planning context. The low-level solver, the Sustainable Reverse Safe Interval Path Planning algorithm (SRSIPP), is an efficient single-agent solver that uses previous planning context to reduce duplicate calculations. Experiments show that our proposed method has significant improvement in terms of computational efficiency. In one of the test scenarios, our algorithm can be 1.48 times faster than SOTA on average under different agent number settings.

We study online Multi-Agent Path Finding (MAPF), where new agents are constantly revealed over time and all agents must find collision-free paths to their given goal locations. We generalize existing complexity results of (offline) MAPF to online MAPF. We classify online MAPF algorithms into different categories based on (1) controllability (the set of agents that they can plan paths for at each time) and (2) rationality (the quality of paths they plan) and study the relationships between them. We perform a competitive analysis for each category of online MAPF algorithms with respect to commonly-used objective functions. We show that a naive algorithm that routes newly-revealed agents one at a time in sequence achieves a competitive ratio that is asymptotically bounded from both below and above by the number of agents with respect to flowtime and makespan. We then show a counter-intuitive result that, if rerouting of previously-revealed agents is not allowed, any rational online MAPF algorithms, including ones that plan optimal paths for all newly-revealed agents, have the same asymptotic competitive ratio as the naive algorithm, even on 2D 4-neighbor grids. We also derive constant lower bounds on the competitive ratio of any rational online MAPF algorithms that allow rerouting. The results thus provide theoretical insights into the effectiveness of using MAPF algorithms in an online setting for the first time.

Both geometric and semantic information of the search space is imperative for a good plan. We encode those properties in a weighted colored graph (geometric information in terms of edge weight and semantic information in terms of edge and vertex color), and propose a generalized A* to find the shortest path among the set of paths with minimal inclusion of low-ranked color edges. We prove the completeness and optimality of this Class-Ordered A* (COA*) algorithm with respect to the hereto defined notion of optimality. The utility of COA* is numerically validated in a ternary graph with feasible, infeasible, and unknown vertices and edges for the cases of a 2D mobile robot, a 3D robotic arm, and a 5D robotic arm with limited sensing capabilities. We compare the results of COA* to that of the regular A* algorithm, the latter of which finds the shortest path regardless of uncertainty, and we show that the COA* dominates the A* solution in terms of finding less uncertain paths.

We introduce multi-goal multi agent path finding (MAPF$^{MG}$) which generalizes the standard discrete multi-agent path finding (MAPF) problem. While the task in MAPF is to navigate agents in an undirected graph from their starting vertices to one individual goal vertex per agent, MAPF$^{MG}$ assigns each agent multiple goal vertices and the task is to visit each of them at least once. Solving MAPF$^{MG}$ not only requires finding collision free paths for individual agents but also determining the order of visiting agent's goal vertices so that common objectives like the sum-of-costs are optimized. We suggest two novel algorithms using different paradigms to address MAPF$^{MG}$: a heuristic search-based search algorithm called Hamiltonian-CBS (HCBS) and a compilation-based algorithm built using the SMT paradigm, called SMT-Hamiltonian-CBS (SMT-HCBS). Experimental comparison suggests limitations of compilation-based approach.