A Bayesian Modeling Framework for Estimation and Ground Segmentation of Cluttered Staircases

TL;DR

This work tackles robust perception of cluttered staircases under occlusions and sensor noise by introducing a Bayesian framework that jointly estimates staircase geometry and segments stair surfaces. It uses a split state-space model comprising an infinite-line staircase state $\boldsymbol{_LX}_k$ and a staircase endpoint state $\boldsymbol{_PX}_k$, fused through an Extended Kalman Filter with a measurement model $\boldsymbol{_LZ}_k,\boldsymbol{_PZ}_k$. Key contributions include (i) a parameterized six-parameter staircase model, (ii) a Mahalanobis-based data association for stair matching, (iii) a dynamic process model that grows the state as new steps appear, and (iv) a crop-box–based stair surface segmentation with a ground-parallel plane fit. The method achieves significant accuracy gains over baselines in real and simulated staircases, runs in real time (~<30 ms per frame at 20 Hz), and improves navigation safety for legged robots in cluttered environments. These results demonstrate the practical value of integrating prior staircase structure with probabilistic fusion for robust perception and segmentation in challenging indoor scenes.

Abstract

Autonomous robot navigation in complex environments requires robust perception as well as high-level scene understanding due to perceptual challenges, such as occlusions, and uncertainty introduced by robot movement. For example, a robot climbing a cluttered staircase can misinterpret clutter as a step, misrepresenting the state and compromising safety. This requires robust state estimation methods capable of inferring the underlying structure of the environment even from incomplete sensor data. In this paper, we introduce a novel method for robust state estimation of staircases. To address the challenge of perceiving occluded staircases extending beyond the robot's field-of-view, our approach combines an infinite-width staircase representation with a finite endpoint state to capture the overall staircase structure. This representation is integrated into a Bayesian inference framework to fuse noisy measurements enabling accurate estimation of staircase location even with partial observations and occlusions. Additionally, we present a segmentation algorithm that works in conjunction with the staircase estimation pipeline to accurately identify clutter-free regions on a staircase. Our method is extensively evaluated on real robot across diverse staircases, demonstrating significant improvements in estimation accuracy and segmentation performance compared to baseline approaches.

Figures (8)

• Figure 1: (a) Prior staircase estimate, $bel(\boldsymbol{_LX}_k)$ at time $k$ (solid blue). (b) Predicted staircase location, $p(\boldsymbol{_L\hat{X}}_{k+1|k})$ based on prior (dotted blue). (c) New noisy measurement, $p(\boldsymbol{_LZ}_{k + 1})$ at time $k\!+\!1$ (magenta). (d) Filtered staircase estimate $bel(\boldsymbol{_LX}_{k + 1})$ at time $k\!+\!1$ by combing prediction and measurement (green).
• Figure 2: Results of our proposed staircase modeling and estimation framework. (a) Robot navigating staircase environments (b) Estimated staircase highlighted by white marker. (c) Segmented clutter-free regions on each stair.
• Figure 3: Staircase annotated with the 'infinite-line' and 'staircase endpoint' state variables along with its model parameters.
• Figure 4: Block diagram depicting the overall estimation pipeline.
• Figure 5: Stair surface segmentation process for a cluttered staircase.