STATE-NAV: Stability-Aware Traversability Estimation for Bipedal Navigation on Rough Terrain

TL;DR

This work tackles the stability risk inherent in bipedal navigation on rough terrain by learning a stability predictor (TravFormer) that outputs a BSFA-based instability with uncertainty. Traversability is reframed as the maximum stability-safe command velocity, enabling risk-aware planning within a hierarchical TravRRT* global planner and MPC local controller. The approach unifies learning-based instability estimation with stability-constrained planning, demonstrating improved robustness and time efficiency in MuJoCo simulations and real-world Digit experiments across diverse terrains. The results show superior traversal safety and performance without extensive hyperparameter tuning, highlighting the practical potential for stable humanoid navigation in unstructured environments.

Abstract

Bipedal robots have advantages in maneuvering human-centered environments, but face greater failure risk compared to other stable mobile platforms such as wheeled or quadrupedal robots. While learning-based traversability has been widely studied for these platforms, bipedal traversability has instead relied on manually designed rules with limited consideration of locomotion stability on rough terrain. In this work, we present the first learning-based traversability estimation and risk-sensitive navigation framework for bipedal robots operating in diverse, uneven environments. TravFormer, a transformer-based neural network, is trained to predict bipedal instability with uncertainty, enabling risk-aware and adaptive planning. Based on the network, we define traversability as stability-aware command velocity-the fastest command velocity that keeps instability below a user-defined limit. This velocity-based traversability is integrated into a hierarchical planner that combines traversability-informed Rapid Random Tree Star (TravRRT*) for time-efficient planning and Model Predictive Control (MPC) for safe execution. We validate our method in MuJoCo simulation and the real world, demonstrating improved navigation performance, with enhanced robustness and time efficiency across varying terrains compared to existing methods.

Figures (7)

• Figure 1: Overall diagram of the proposed traversability estimation and the navigation framework. A transformer-based bipedal instability estimator, TravFormer, is trained using body-to-stance-foot angle (BSFA) instability as a self-supervised signal to generate stability-aware command velocity map from the geometric representation of the environment. This map is further used by a hierarchically integrated TravRRT* global planner and MPC local planner to safely navigate over diverse rough terrain.
• Figure 2: TravFormer architecture combines convolutional feature extraction with attention mechanisms to predict BSFA instability. The model processes an elevation map patch $m_{\rm ego}$ representing local terrain and a command vector $a = [v,\omega]^T$. During training, the model uses robot-centric map patches centered on the robot. At planning time, the global terrain map is divided into multiple local patches, which are processed in batch.
• Figure 3: Stability-aware command-velocity selection via iterative search. Starting from the maximum candidate velocity $a_{\max}$, the Iterative Search block feeds $a_{\max}$ into the TravFormer model and then successively replaces it with the next lower candidate sweeping downward until the risk-sensitive stability criterion is met.
• Figure 4: Comparison of estimated traversability maps and paths planned by the proposed method and baselines. The starting and goal points are marked by a gray diamond and a yellow star, respectively. (a) Diagonal bird-eye view of rough terrain environment and the snapshots of the robot traversing along the path by the proposed method. (b) Initialized elevation map of the MuJoCo environment (a). (c), (d), (e) Traversability maps based on (b) and path plans by the QuadFoothold wellhausen2021rough, ManualBiped mccrory2023bipedal, and LearnedInS baselines, respectively. Red and yellow paths are the results of different trade-off weight values $w=3$ and $0.5$. (f) Traversability map based on (b) and the path plan of the proposed method, STATE, with $\delta_{\rm limit} = 3$.
• Figure 5: Comparison of estimated traversability maps and paths planned by the proposed method and baselines. The starting and goal points are marked by a gray diamond and a yellow star, respectively. (a) Diagonal bird-eye view of ramp environment and the snapshots of the robot traversing along the path by the proposed method. (b) Initialized elevation map of the MuJoCo environment (a). (c) Traversability map based on (b) and path plans by the LearnedInS baseline. Red and yellow paths are the results of different trade-off weight values $w=3$ and $0.5$. (d) Traversability map based on (b) and the path plan of the proposed method, STATE, with $\delta_{\rm limit} = 3$.

Theorems & Definitions (2)

• Remark 1: Use of risk-sensitive traversability
• Remark 2: Environment-agnostic hyperparameter tuning of STATE