Risk-Averse Traversal of Graphs with Stochastic and Correlated Edge Costs for Safe Global Planetary Mobility

TL;DR

The paper addresses the problem of risk-averse global mobility planning on planetary graphs with stochastic and potentially correlated edge costs. It introduces CVaR-CTP, a risk-sensitive variant of the Canadian Traveller Problem, and develops CVaR-CTP-AO*, an exact forward AO*-based algorithm that augments the state with running cost and solves parallel AO trees for candidate cumulative costs $s$ to minimize $CVaR_\alpha(C^\pi)$. The work provides optimality guarantees with admissible heuristics, demonstrates efficiency enhancements, and validates the approach on simulated Martian traverses, showing how different levels of risk aversion drive distinct adaptive strategies and information-seeking detours when traversability is correlated. The results suggest that incorporating CVaR-based risk measures yields qualitatively safer strategies and highlights practical implications for autonomous planetary mobility, especially in scenarios with correlated terrain uncertainty. The methodology’s reliance on real orbital maps and terrain-driven edge probabilities supports its relevance for planning under uncertainty in space exploration missions.

Abstract

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.

Figures (15)

• Figure 1: Conceptual example of the problem addressed in this paper. A rover on the Jezero Crater floor, Mars, must reach a designated goal location by following the global route network shown. This graph has edges cutting through Séítah, a region with uncertain traversability. The rover may drive to the start of these edges to observe their traversability or follow a safe (but physically longer) route around Séítah. Here, prioritizing the shortest traverse through $e_0$ may be costly in the worst case; if this uncertain edge happens to be untraversable (or traversable at a very high cost), the rover would need to backtrack and follow a different route. A risk-averse strategy might forego $e_0$ and head towards $e_1$ or stick to the (known) blue edges only from the start. Accounting for traversability correlations between edges (e.g., based on underlyling terrain properties) would enable different risk aversion behaviours. For instance, if the terrain along $e_0$ and $e_2$ is very similar, a risk-averse strategy may prioritize a short information-seeking drive to the latter before deciding whether it is worth heading towards $e_0$.
• Figure 2: Sample CTP instance. An agent starts at vertex $v_0$ and must reach $v_g$. Solid edges are deterministic and have the indicated cost. Dashed edges are stochastic and their low-cost (L) and high-cost (H) statuses are specified. Status probabilities are independent and indicated in parentheses.
• Figure 3: Node selection, node expansion and backpropagation steps of the first two AO* iterations applied to the CTP instance depicted in \ref{['fig:example-graph']}. OR and AND nodes are labelled with the corresponding state in the CTP instance. In the node expansion step, the cost estimates of newly-expanded nodes ($f$) are the sum of a cost-to-come (orange) and a heuristic cost-to-go (pink). The latter is obtained through the assumption that unobserved stochastic edges have the lowest cost possible, i.e., a low-cost status (L).
• Figure 4: Optimal policy tree found with AO* applied to the CTP instance depicted in \ref{['fig:example-graph']}. The meaning of symbols and labels are the same as in \ref{['fig:example-aostar']}. The costs and probabilities at terminal AND nodes (doubly circled), which constitute the probability mass function of this policy, are included.
• Figure 5: Conceptual illustration of one CVaR-CTP-AO* iteration. Each step corresponds to a routine in the main loop of \ref{['alg:cvar-aostar-main']}. An interpretation of this algorithm is that it grows morphologically identical AO search trees in parallel, one for each possible cumulative cost $s \in \Omega_C$. (a) Consider a search tree with four leaf nodes, each assigned a unique heuristic cumulative cost $f$. Let the best partial policy be the one associated with $s^* = f_0$; its (non-terminal) leaf node is selected for expansion. (b) This leaf (AND) node is expanded into two successor (OR) nodes and their truncated costs are initialized using \ref{['eq:inner_exp']} for all $s \in \Omega_C$. One of those successors has a new unique heuristic cumulative cost, $f_4$. (c) A backpropagation step applies \ref{['eq:inner_exp']} on the ancestors of the newly-created nodes for all $s \in \Omega_C$. (d) Another backpropagation across the entire tree applies \ref{['eq:inner_exp']} only for ${s \in \Omega_\text{new} = \{f_4\}}$. (e) The CVaR of the policies computed in the backpropagation steps (one for each ${s \in \Omega_C \cup \Omega_\text{new}}$) are compared and the one with the lowest value is retained as the best partial policy for the next iteration.