Terrain Sensing with Smartphone Structured Light: 2D Dynamic Time Warping for Grid Pattern Matching

Abstract

Low-cost mobile rovers often operate on uneven terrain where small bumps or tilts are difficult to perceive visually but can significantly affect locomotion stability. To address this problem, we explore a smartphone-based structured-light system that projects a grid pattern onto the ground and reconstructs local terrain unevenness from a single handheld device. The system is inspired by face-recognition projectors, but adapted for ground sensing. A key technical challenge is robustly matching the projected grid with its deformed observation under perspective distortion and partial occlusion. Conventional one-dimensional dynamic time warping (1D-DTW) is not directly applicable to such two-dimensional grid patterns. We therefore propose a topology-constrained two-dimensional dynamic time warping (2D-DTW) algorithm that performs column-wise alignment under a global grid consistency constraint. The proposed method is designed to be simple enough to run on resource limited platforms while preserving the grid structure required for accurate triangulation. We demonstrate that our 2D-DTW formulation can be used not only for terrain sensing but also as a general tool for matching structured grid patterns in image processing scenarios. This paper describes the overall system design as well as the 2D-DTW extension that emerged from this application.