A PnP Algorithm for Two-Dimensional Pose Estimation

TL;DR

This work tackles pose estimation for a camera constrained to planar motion by exploiting the reduced degrees of freedom in the 2D plane. It introduces 2DPnP, which first obtains an approximate pose via a polynomial-system initialization that solves two cubics with resultants to produce candidate $(x,y)$, then determines the heading $\theta$ through a harmonic relation, and finally refines the solution with Levenberg–Marquardt to minimize the reprojection error $\text{Error}(\mathbf{R})$ while enforcing the planar constraint. The key contributions are the two-phase, all-correspondences initialization using $\text{Res}(A,B,y)$ and $\text{Res}(A,B,x)$, followed by efficient iterative optimization, and demonstrated improvements in speed and translational accuracy with robustness to noise compared to several 3D PnP baselines. The method is particularly applicable to wheeled robotics and other platforms where motion is naturally confined to a plane, with potential extensions to multi-camera setups and uncertainty-aware pose estimation for sensor fusion.

Abstract

We propose a PnP algorithm for a camera constrained to two-dimensional motion (applicable, for instance, to many wheeled robotics platforms). Leveraging this assumption allows accuracy and performance improvements over 3D PnP algorithms due to the reduction in search space dimensionality. It also reduces the incidence of ambiguous pose estimates (as, in most cases, the spurious solutions fall outside the plane of movement). Our algorithm finds an approximate solution by solving a polynomial system and refines its prediction iteratively to minimize the reprojection error. The algorithm compares favorably to existing 3D PnP algorithms in terms of accuracy, performance, and robustness to noise.

Figures (3)

• Figure 1: Ambiguity in a square's estimated pose Planar1
• Figure 2: Definitions of $\Delta\theta_{i}$ and $\Delta\phi_{i}$
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