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Localization in Dynamic Planar Environments Using Few Distance Measurements

Michael M. Bilevich, Shahar Guini, Dan Halperin

TL;DR

The paper tackles localization of a sensor in a known planar workspace with unknown dynamic obstacles using a small set of distance measurements. It proposes a dynamic sparsity-based extension of a prior static-environment method, constructing voxel-cloud preimages of distance data and combining them across subsets to recover the ground-truth pose with guarantees. The method yields robustness to dynamic disturbances under mild obstacle density, supported by simulations across four scenes and open-source code. The work offers a practical approach to accurate, distance-based localization in environments with moving obstacles.

Abstract

We present a method for determining the unknown location of a sensor placed in a known 2D environment in the presence of unknown dynamic obstacles, using only few distance measurements. We present guarantees on the quality of the localization, which are robust under mild assumptions on the density of the unknown/dynamic obstacles in the known environment. We demonstrate the effectiveness of our method in simulated experiments for different environments and varying dynamic-obstacle density. Our open source software is available at https://github.com/TAU-CGL/vb-fdml2-public.

Localization in Dynamic Planar Environments Using Few Distance Measurements

TL;DR

The paper tackles localization of a sensor in a known planar workspace with unknown dynamic obstacles using a small set of distance measurements. It proposes a dynamic sparsity-based extension of a prior static-environment method, constructing voxel-cloud preimages of distance data and combining them across subsets to recover the ground-truth pose with guarantees. The method yields robustness to dynamic disturbances under mild obstacle density, supported by simulations across four scenes and open-source code. The work offers a practical approach to accurate, distance-based localization in environments with moving obstacles.

Abstract

We present a method for determining the unknown location of a sensor placed in a known 2D environment in the presence of unknown dynamic obstacles, using only few distance measurements. We present guarantees on the quality of the localization, which are robust under mild assumptions on the density of the unknown/dynamic obstacles in the known environment. We demonstrate the effectiveness of our method in simulated experiments for different environments and varying dynamic-obstacle density. Our open source software is available at https://github.com/TAU-CGL/vb-fdml2-public.
Paper Structure (5 sections, 1 theorem, 5 equations, 2 figures, 1 table)

This paper contains 5 sections, 1 theorem, 5 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. The method
  4. Experiments and Results
  5. Conclusion and Future Work

Key Result

Theorem III.1

The voxel cloud approximation $\hat{M}_{k'}$ is conservativeUp to some small set of voxels $\mathcal{A}_{n,\mathcal{W}}$, which we can treat specifically.. That is, if $q_* \in SE(2)$ is the ground truth, then $q_* \in \hat{M}_{k'}$. Furthermore, the distance between $q_*$ and the nearest predicted

Figures (2)

  • Figure 1: Example for why sampling a dynamic obstacle might lose the ground truth location. Our workspace $\mathcal{W}$ is in gray. We have one dynamic obstacle $\mathcal{D}_1$ with $\varphi_1 = 1 \in SE(2)$ (see remark in Section \ref{['problem-statement']}). We take three distance measurements $d_i$ with a rotation offset of $\pi/2$ radians clockwise. The robot is at $q_* \in SE(2)$. Left: The free region at time $t_1$, $\mathcal{W}_{t_1}$. Ignoring the existence of dynamic obstacle yields the red pose $q'$ which is false. Right: When we ignore the dynamic obstacles, and look for locations for which we would measure $d_i$, we get only $q'$ and lose $q_*$.
  • Figure 2: Example of the simulated experiment on the lab-lidar polygon, with $20$ dynamic obstacles. Ground truth location is in blue, and we cast $10$ rays for distance measurements, with $4$ of them sampling the dynamic obstacles (in red), and the rest sampling the static workspace $\mathcal{W}$ (in magenta).

Theorems & Definitions (2)

  • Definition III.1
  • Theorem III.1