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.
Figures & tables
Fig. 1 : Overview of safe reactive navigation. (Red) Unsafe zones for the robot to avoid. (Brown) Measured terrain penetration resistance. (Blue Solid) Executed and planned paths. (Blue Dotted) Naive path to goal. (Yellow) Navigation Goal.
Fig. 2 : Overview of the proposed PSANE navigation framework.
Fig. 3 : Overview of terrain-aware traversal risk estimation and safety-aware planning. (A) The slip-ratio field and (B) its predictive uncertainty are inferred using a Gaussian Process. (C) The resulting confidence bounds are used to construct a conservative safety map, from which frontier boundaries are extracted via a border-following algorithm and filtered to obtain the Pareto-optimal frontier set. (D–F) For each Pareto frontier candidate, the expansion probability (D) and goal-directed heuristic (E) are evaluated and combined to produce an overall score (F) that balances safe-region expansion and goal progress.
Fig. 4 : Integration with the reactive controller. The certified safe region (green) is converted into obstacle polygons by subtracting it from the local workspace. The resulting boundaries are conservatively buffered by a safety margin (red) and geometrically simplified to obtain the final obstacle set (purple). The reactive controller then generates a velocity command consisting of forward speed and angular velocity.
Fig. 5 : Chrono simulation environments. Environment 1 (A) features smoother terrain variations, whereas Environment 2 (B) exhibits sharper spatial changes in terrain properties. Green denotes high penetration resistance (LHS-1), and yellow denotes low.
Fig. 6 : Comparison of navigation-to-goal behavior and performance across different algorithms. (A) and (B) show representative path visualizations in Environments 1 and 2, respectively. The green dot indicates the robot’s starting position, the red dot its final position, and the yellow star the navigation goal. A blue (low)–yellow–red (high) colormap represents the ground-truth slip-ratio distribution across the terrain. (C), (D), and (E) report the success rate (goal reached), completion time, and path length, respectively, averaged over three trials in each environment.
Fig. 7 : Comparison of exploration behavior and performance between PGH and PSANE. (A) Path and safe-region visualization. The black contour outlines the final certified safe region learned by the algorithm, with the green dot indicating the start position and the red dot the final position. (B) Coverage over time during the exploration phase. Coverage is computed as the ratio of the certified safe region area to the ground-truth safe region area.
Dynamic Legged Systems, Istituto Italiano di Tecnologia (IIT), Italy · Department of Industrial Engineering, University of Trento, Italy · Department of Computer Science, University of Manchester, UK +2