Deformable granular terrains introduce significant locomotion and immobilization risks in planetary exploration and are difficult to detect via remote sensing (e.g., vision). Legged robots can sense terrain properties through leg-terrain interactions during locomotion, offering a direct means to assess traversability in deformable environments. How to systematically exploit this interaction-derived information for navigation planning, however, remains underexplored. We address this gap by presenting PSANE, a Proprioceptive Safe Active Navigation and Exploration framework that leverages leg-terrain interaction measurements for safe navigation and exploration in unknown deformable environments. PSANE learns a traversability model via Gaussian Process regression to estimate and certify safe regions and identify exploration frontiers online, and integrates these estimates with a reactive controller for real-time navigation. Frontier selection is formulated as a multi-objective optimization that balances safe-set expansion probability and goal-directed cost, with subgoals selected via scalarization over the Pareto-optimal frontier set. PSANE safely explores unknown granular terrain and reaches specified goals using only proprioceptively estimated traversability, while achieving performance improvements over baseline methods.

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