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.

Recent empirical and theoretical work has shown that the dynamics of the large eigenvalues of the training loss Hessian have some remarkably robust features across models and datasets in the full batch regime. There is often an early period of progressive sharpening where the large eigenvalues increase, followed by stabilization at a predictable value known as the edge of stability. Previous work showed that in the stochastic setting, the eigenvalues increase more slowly - a phenomenon we call conservative sharpening. We provide a theoretical analysis of a simple high-dimensional model which shows the origin of this slowdown. We also show that there is an alternative stochastic edge of stability which arises at small batch size that is sensitive to the trace of the Neural Tangent Kernel rather than the large Hessian eigenvalues. We conduct an experimental study which highlights the qualitative differences from the full batch phenomenology, and suggests that controlling the stochastic edge of stability can help optimization.

We introduce a multi-sensor navigation system for autonomous surface vessels (ASV) intended for water-quality monitoring in freshwater lakes. Our mission planner uses satellite imagery as a prior map, formulating offline a mission-level policy for global navigation of the ASV and enabling autonomous online execution via local perception and local planning modules. A significant challenge is posed by the inconsistencies in traversability estimation between satellite images and real lakes, due to environmental effects such as wind, aquatic vegetation, shallow waters, and fluctuating water levels. Hence, we specifically modelled these traversability uncertainties as stochastic edges in a graph and optimized for a mission-level policy that minimizes the expected total travel distance. To execute the policy, we propose a modern local planner architecture that processes sensor inputs and plans paths to execute the high-level policy under uncertain traversability conditions. Our system was tested on three km-scale missions on a Northern Ontario lake, demonstrating that our GPS-, vision-, and sonar-enabled ASV system can effectively execute the mission-level policy and disambiguate the traversability of stochastic edges. Finally, we provide insights gained from practical field experience and offer several future directions to enhance the overall reliability of ASV navigation systems.

Autonomous surface vessels (ASV) represent a promising technology to automate water-quality monitoring of lakes. In this work, we use satellite images as a coarse map and plan sampling routes for the robot. However, inconsistency between the satellite images and the actual lake, as well as environmental disturbances such as wind, aquatic vegetation, and changing water levels can make it difficult for robots to visit places suggested by the prior map. This paper presents a robust route-planning algorithm that minimizes the expected total travel distance given these environmental disturbances, which induce uncertainties in the map. We verify the efficacy of our algorithm in simulations of over a thousand Canadian lakes and demonstrate an application of our algorithm in a 3.7 km-long real-world robot experiment on a lake in Northern Ontario, Canada. Videos are available on our website https://pcctp.github.io/.

We address the problem of finding shortest paths in graphs where some edges have a prior probability of existence, and their existence can be verified during planning with time- consuming operations. Our work is motivated by real-world robot motion planning, where edge existence is often expensive to verify (typically involves time-consuming collision-checking between the robot and world models), but edge existence probabilities are readily available. The goal then, is to develop an anytime algorithm that can return good solutions quickly by somehow leveraging the existence probabilities, and continue to return better-quality solutions or provide tighter suboptimality bounds with more time. While our motivation is fast and high-quality motion planning for robots, this work presents two fundamental contributions applicable to generic graphs with probabilistic edges. They are: a) an algorithm for efficiently computing all relevant shortest paths in a graph with probabilistic edges, and as a by-product the expected shortest path cost, and b) an anytime algorithm for evaluating (verifying existence of) edges in a collection of paths, which is optimal in expectation under a chosen distribution of the algorithm interruption time. Finally, we provide a practical approach to integrate a) and b) in the context of robot motion planning and demonstrate significant improvements in success rate and planning time for a 11 degree-of-freedom mobile manipulation planning problem. We also conduct additional evaluations on a 2D grid navigation domain to study our algorithm’s behavior.