SuReNav: Human-Like Navigation in Constrained Environments

• SuReNav is a navigation framework that models environments as superpixel graphs to clearly differentiate hard and soft constraints in over-constrained settings.
• It leverages a graph neural network to learn regional relaxation costs, integrating these into a differentiable A* planner for human-like, efficient path planning.
• Evaluations and real-world trials show SuReNav’s superior performance in safety, efficiency, and human-likeness compared to conventional navigation methods.

SuReNav is a navigation framework designed for over-constrained environments where regions present both hard (impassable) and soft (risky, but traversable) constraints. It addresses the challenge of guiding robots or agents through semi-static, real-world environments in a manner that closely matches human preferences: minimizing risk by avoiding hard constraints while traversing soft regions only when necessary, and doing so in an efficient, human-like manner. SuReNav combines superpixel-based map abstraction, regional-constraint relaxation via graph neural networks, differentiable path planning, and a closed-loop execution pipeline (Koh et al., 6 Feb 2026).

1. Superpixel Graph Map Construction

SuReNav represents the environment as a superpixel region adjacency graph, abstracted from either 2D semantic maps or rasterized 3D OpenStreetMap (OSM) data. Each input map is over-segmented using SLIC into compact superpixels $r_i$, which serve as graph nodes. This segmentation preserves semantic boundaries to ensure that each superpixel corresponds to a homogeneous environmental region.

Node features include:

• $f_{GR}(r_i) = c(r_i) \in \mathbb{R}^2$: Centroid for spatial reasoning.
• $f_{SR}(r_i) \in \{0,1\}^{M+2}$: One-hot vector encoding semantic class and goal/start region membership.

Edges $(r_i, r_j) \in E$ are created between adjacent superpixels if the shared boundary exceeds a threshold $\tau$:

• $$H(r_i, r_j) \equiv \text{length}(\partial r_i \cap \partial r_j)$$.
• $c(i,j) = d(c(r_i), c(r_j))$: Edge cost is the Euclidean centroid distance.

Regions are categorized as:

• $V_\text{free}$: Strictly traversable (e.g., sidewalk).
• $V_\text{soft}$: Soft constraints (road, grass).
• $V_\text{hard}$: Hard constraints (building, water).

Hard constraints enforce $\delta_\text{hard}(r_i) = 1$; such nodes are excluded from all paths. For $V_\text{soft}$, an initial or learned risk cost $R(r_i)$ quantifies the traversability penalty.

2. Regional-Constraint Relaxation via GNN

A graph neural network (GNN) models the function $\Psi_G : V \to \mathbb{R}_{\geq0}$, predicting the cost of traversing each soft-constraint superpixel and thereby parameterizing the trade-off between path length and risk. The architecture comprises stacked GraphGPS layers, combining GatedGCN message passing with sparse global attention transformers for effective spatial-semantic reasoning.

Inputs:

• $V^0 \in \mathbb{R}^{N \times (M+2)}$: Node semantic attributes.
• $E^0 \in \mathbb{R}^{|E|}$: Edge geometric costs.

The output is a non-negative vector $\Psi_G(r_i)$ for each node, controlling relaxation penalties.

Differentiable path-cost coupling is achieved by integrating $\Psi_G$ into a soft A* variant (GraphMP), where the cost for expanding node $r_i$ is

$g_i^{\rm ext} = g_i + \Psi_G(r_i)$

Soft selection and backpropagation allow end-to-end training from expert demonstrations.

The loss for matching expert relaxation choices is:

$$L_{\rm rlx}(v, v^*) = \frac{w_{\rm fp} \, v^\top (1-v^*) + w_{\rm fn} (1-v)^\top v^*}{1 + \|v^*\|_1},$$

where $v$ indicates predicted relaxed nodes, $v^*$ are ground truth, and $w_{\rm fn} > w_{\rm fp}$ strongly penalizes missed necessary relaxations.

Training proceeds via projection of demonstration paths onto $G$, generation of region sequences, differentiable planning, and batched loss accumulation:

$$L_\text{batch} = \frac{1}{|B|} \sum_{i \in B} w^i L_{\rm rlx}(v^{(i)}, v^{*(i)})$$

with stabilization via weighted examples.

3. Interleaved Relaxation, Planning, and Execution

SuReNav interleaves map updating, GNN-based relaxation, graph planning, and continuous path execution in an online feedback loop aimed at robust navigation under environment dynamics. At every time step, the system:

1. Updates semantic regions $(R_\text{free}, R_\text{soft}, R_\text{hard})$ based on new sensor observations, fusing camera and LiDAR data.
2. Regenerates the superpixel graph as necessary (e.g., upon significant environmental change).
3. Evaluates $\Psi_G$ to produce current node relaxation costs.
4. Uses differentiable A* planning over $G$ to determine which soft regions to relax, strictly avoiding $V_\text{hard}$.
5. Extracts the set $R_{\rm rlx}$ of soft superpixels included in the planned path.
6. Performs fine-grained A* planning at the continuous level over $R_\text{free} \cup R_\text{rlx}$.
7. Executes the next motion primitive.
8. Repeats until the goal is reached or a failure occurs.

The total planning cost for a sequence $P = [r_1, ..., r_K]$ is given by:

$$J(P) = \sum_{k=2}^{K} c(r_{k-1}, r_k) + \sum_{k=1}^{K} 1[r_k \in V_\text{soft}]\, \Psi_G(r_k)$$

subject to $\forall k: \delta_\text{hard}(r_k) = 0$.

4. Performance Evaluation and Results

SuReNav is evaluated against state-of-the-art baselines (D* Lite, COA*, RCR) on held-out test sets encompassing both 2D and OSM-derived map types. Human-likeness is quantified using normalized Fréchet distance between the planned and demonstration paths and intersection-over-union (IoU) over relaxed soft-regions.

Method	Fréchet↓	Relax. IoU↑
D* Lite	0.429	0.223
COA*	0.701	0.271
RCR	0.626	0.259
SuReNav	0.334	0.416

SuReNav yields the lowest Fréchet distance and substantially higher relaxation IoU compared to the best alternatives, closely aligning planned trajectories with human demonstrations.

Efficiency and safety are quantified using Success Rate (SR), Success weighted by Path Length (SPL), and estimated risk (summed pixel-wise LLM-inferred risk scores). Across 300 environments, SuReNav maintains SR=100%, SPL in the 0.80–0.85 range, and risk ≈0.09–0.15, achieving a favorable trade-off not matched by alternatives.

Qualitative analysis shows that SuReNav selectively relaxes soft constraints (e.g., taking short grass or crosswalk traversals only when safe) and otherwise adheres to low-risk, human-like paths, demonstrating both fidelity and efficiency (Koh et al., 6 Feb 2026).

5. Real-World Robotic Deployment

SuReNav's generalization and real-world applicability are established via deployment on a Boston Dynamics Spot quadruped equipped with RGB-D and LiDAR sensors. The online pipeline fuses semantic segmentation (PIDNet) with real-time occupancy data, re-segments via SLIC at regular intervals or upon significant map change, and uses the same GNN weights as in simulation.

Continuous A* planning is performed over a 10 cm grid, respecting Spot's locomotion constraints. In diverse campus navigation trials, SuReNav robustly selects minimal-risk soft traversals (e.g., crossing a single narrow parking lot only as needed), and otherwise opts for safe, longer detours, closely matching expert policy.

Direct transfer from simulation to hardware is achieved without recalibration or manual tuning of relaxation costs, underscoring the system's robustness and practicality for semi-static urban navigation scenarios.

6. Comparative Analysis and Significance

SuReNav establishes a new approach to navigation in over-constrained environments, distinguished by:

• A region-based abstraction leveraging superpixel adjacency graphs for scalable constraint representation.
• Learned regional relaxation costs via GNNs trained on human demonstrations, successfully generalizing costs to unseen environments.
• Differentiable planning that allows loss signal to shape relaxation and global efficiency.
• Superior trade-off between path efficiency (SPL), risk, and human-likeness metrics over both hand-designed (COA*, D* Lite) and learned relaxation baselines.

A plausible implication is that regional constraint relaxation, rather than uniform pixel- or cell-level cost assignments, enables more faithful imitation of human navigation in settings where certain risky regions are unavoidable. The architecture is amenable to new modalities and scalable to large urban maps (Koh et al., 6 Feb 2026).