Calibration-Free Floor Detection via Gravity-Aware SOAP Descriptors: Theory and Embedded Deployment for Reactive Humanoid Locomotion and Obstacle Avoidance

<title>Abstract</title> <p>The strongest baseline for calibration-free indoor floor detection—no labels, no per-environment height prior—is PCA surface normals combined with RANSAC plane fitting; on the S3DIS Area 5 benchmark this achieves 86.6% F1. Trained alternatives reach higher accuracy but require labeled point clouds and degrade under domain shift. We introduce a third geometry-based route: a gravity-aware variant of the Smooth Overlap of Atomic Positions(SOAP) descriptor, originally developed for computational chemistry. We retain the 𝒎-resolved SOAP coefficients(where ℓ is the spherical-harmonic degree and 𝒎 the azimuthal order) and compute them in a gravity-alignedframe, so the descriptor is invariant only to rotations about the vertical axis (𝑺𝑶 (2)); the ratio of the ℓ=2, 𝒎=0band power to the total ℓ=2 power yields a per-point score that discriminates horizontal surfaces from vertical andirregular surfaces. The only assumption is gravity alignment, available from any on-platform IMU; otherwise nolabeled data, no height threshold, no environment-specific parameters. On all 68 rooms of S3DIS Area 5, the SOAP 𝒎-band score combined with RANSAC plane refinement achieves 90.0% F1 (96.2% precision), out performing PCA-normal+RANSAC (86.6%). The descriptor exposes a 315-dimensional per-point feature space at the same compute cost as the binary floor decision, supporting multi-class surface classification and a continuous similarity field for potential-field steering. We deploy on a Unitree G1 EDU humanoid (Livox MID-360 LiDAR, NVIDIAJetson Orin NX). Real-time operation on the onboard GPU required a vectorized PyTorch implementation of the 𝒎-band-resolved SOAP power spectrum that runs in 0.08 s per scan, 20× faster than an optimized CPU implementation of the same computation. With this, the descriptor serves as the platform’s primary obstacle-avoidance system at 2 Hz; the same similarity field reduces simulated path length by 4.5× over a classical artificial potential field. To our knowledge this is the first deployment of SOAP descriptors as a real-time perception laye ron a humanoid.</p>