ProTrav: Probabilistic Traversability with Elevation Uncertainty Propagation for Risk-aware Off-road Navigation

Chuanlin Zuo; Miloš Prágr; Arun Kumar Singh; Mohammad Loni; Reza Ghabcheloo

cs.ROOct 22, 2026

ProTrav: Probabilistic Traversability with Elevation Uncertainty Propagation for Risk-aware Off-road Navigation

Authors: Chuanlin Zuo, Miloš Prágr, Arun Kumar Singh, Mohammad Loni, Reza Ghabcheloo

Organizations: Faculty of Engineering and Natural Sciences, Tampere University, Finland. · Institute of Technology, University of Tartu, Estonia. · AI and ML Department, Volvo Autonomous Solutions, Sweden.

Abstract

Reliable traversability estimation is essential for autonomous navigation on unstructured terrain. State-of-the-art approaches typically evaluate traversability from deterministic terrain elevation, thereby overlooking spatial correlations in the terrain and failing to account for how elevation uncertainty propagates through nonlinear traversability mappings. We propose ProTrav, a probabilistic terrain representation that uses function-space sampling to generate spatially correlated terrain realizations and propagate elevation uncertainty to traversability cost. First, a Sparse Variational Gaussian Process (SVGP) reconstructs a probabilistic elevation field from observations. Then, posterior function-space sampling generates spatially correlated terrain realizations, preserving spatial dependencies between neighboring locations while propagating elevation uncertainty through geometric features into traversability cost. Consequently, a distribution of traversability cost at arbitrary location is established, where the mean and standard deviation quantify the expected traversability cost and associated uncertainty, respectively. A risk term is defined by moment-based Upper Confidence Bound (UCB) and incorporated into a Model Predictive Path Integral (MPPI) controller for risk-aware navigation. Simulation experiments demonstrate navigation success rates exceeding 90% on different terrains, compared with below 40% for a baseline, while reducing attitude variations. Furthermore, the proposed approach is validated on a robot traversing real-world off-road terrain.

Figures & tables

Fig. 1: Comparison of the mean-first strategy (a) and proposed uncertainty-aware method (b), represented as terrain normals. Within a negative obstacle (c), the terrains observations are missing, and hence the terrain elevation prediction is uncertain. (a) The mean prediction of terrain elevation defines a single terrain property per query position. Since the mean elevation prediction remains flat despite higher uncertainty, the terrain descriptors are overly optimistic, indicating flat and thus safe terrain. (b) Multiple samples of terrains surface define multiple terrain properties per query position. Therefore, the elevation uncertainty propagates into the geometric description, highlighting possibly unsafe uncertain region.

Fig. 2: Overview of the proposed probabilistic terrain traversability representation and navigation framework. A point cloud is used to train an SVGP to construct a continuous probabilistic elevation field. Terrain realizations are generated through function-space sampling and terrain geometric features are extracted from each realization and fused into traversability costs. These realizations are aggregated to obtain moment-based Gaussian approximation, from which a risk term is constructed by UCB and injected into the MPPI rollout cost. The resulting velocity command is sent to the robot for execution.

Start (m)	Goal (m)	Method	$\|\phi\|_{\text{mean}}$ (deg)	$\|\phi\|_{\text{max}}$ (deg)	$\|\theta\|_{\text{mean}}$ (deg)	$\|\theta\|_{\text{max}}$ (deg)	Success Rate
(20, 13)	(7, -1)	Base-RRT*	–	–	–	–	0.00
		Base-MPPI	7.74 $\pm$ 4.10	21.66 $\pm$ 9.24	12.39 $\pm$ 1.45	36.66 $\pm$ 1.58	100.00%
		Prob-MPPI( $\kappa_{\delta}=0$ )	4.40 $\pm$ 0.11	11.87 $\pm$ 0.70	3.84 $\pm$ 0.03	10.88 $\pm$ 0.12	100.00%
		Prob-MPPI( $\kappa_{\delta}=0.842$ )	4.27 $\pm$ 0.08	11.16 $\pm$ 0.39	3.81 $\pm$ 0.06	10.89 $\pm$ 0.18	100.00%
		Prob-MPPI( $\kappa_{\delta}=1.645$ )	4.07 $\pm$ 0.09	10.60 $\pm$ 0.31	3.79 $\pm$ 0.03	10.87 $\pm$ 0.09	100.00%
(-7, -7)	(15, 18)	Base-RRT*	7.21 $\pm$ 3.03	21.87 $\pm$ 8.53	6.16 $\pm$ 2.42	23.52 $\pm$ 8.24	30.00%

TABLE I: Simulated Performance on Mountain Terrain,

\mu\pm\sigma

10

Trials and Success Rate.

Fig. 3: Simulation environments with start-goal pairs and expected path in Gazebo. Left: the mountainous terrain provided by the baseline. Right: the custom-built cliff terrain.

Fig. 4: Robot attitude evolution during navigation. The robot navigates from the start position

(17,-17)\,

m to the goal

(-7,-7)\,

m in mountainous terrain. Only successful trials are shown.

Start (m)	Goal (m)	Method	No. of Falls	Success Rate
(-14, -1)	(7, -1)	Base-RRT*	5	10.00%
		Base-MPPI	8	20.00%
		Prob-MPPI( $\kappa_{\delta}=0$ )	2	80.00%
		Prob-MPPI( $\kappa_{\delta}=0.842$ )	2	80.00%
		Prob-MPPI( $\kappa_{\delta}=1.645$ )	1	90.00%
(-14, -2)	(7, -2)	Base-RRT*	2	10.00%

TABLE II: Simulated Performance on Cliff Terrain, Measured by the Number of Falls and Success Rate over 10 Trials.

Panel of Figure 7 — Fig. 5: A typical behavior in the Mound scenario, where the robot is tasked to navigate to a goal behind a mound of loose soil. (top) A view of the environment, with the robot position shown in approx. $20\text{\,}\mathrm{s}$ steps. The robot trajectory in blue, and its goal in red. (remaining rows) Visualization of the system at the time steps corresponding to the robot positions in the environment view; (1) the initial state facing the mound, (2) avoiding mound, (3) driving along the mound edge, and (4) approaching the goal. The predicted cost grimap at the position (green-red), local MPPI planned path (black), and the trajectory so far. Aggregate point cloud of the environment built from scans available so far in the execution (blue-purple); used only for visualization, while the robot navigates using the current scan.

Panel of Figure 8 — Fig. 6: The Ramp scenario, where the robot is tasked to navigate downhill. (top) A view of the environment, with the robot position shown in approx. $30\text{\,}\mathrm{s}$ steps. The robot trajectory in blue, and its goal in red. (bottom) Visualization of the system at the time steps corresponding to the robot positions in the environment view; (1) the initial state uphill, (2) on the slope, and (3) approaching the downhill goal. The predicted cost grid map at the position (green-red), local MPPI planned path (black), and the trajectory so far. Aggregate point cloud built from scans available so far in the execution (blue-purple); used only for visualization, while the robot navigates using the current scan.

Fig. 7: The Sequence scenario. Overhead view of the test area, with the traversed path and waypoints of the Sequence scenario in blue and red, respectively, and the areas used in the Mound and Ramp scenario in purple and green, respectively.

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Advances in robotics and autonomous navigation systems hinge on the ability to predict terrain traversability accurately. Traditional methods for generating datasets to train these prediction models often involve putting robots into potentially hazardous environments, posing risks to equipment and safety. To solve this problem, we present ZeST, a novel approach that treats repeated VLM outputs as stochastic measurements and fuses them into an uncertainty-aware posterior. Our approach not only performs zero-shot traversability and mitigates the risks associated with real-world data collection but also accelerates the development of advanced navigation systems, offering a cost-effective and scalable solution. To support our findings, we present navigation results, in both controlled indoor and unstructured outdoor environments. As shown in the experiments, ZeST provides safer navigation with a 90-100% success rate while no baseline exceeds 60%, and keeps complete success under query latencies up to 3.6s.

Abstract

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