# Optimal Target Shape for LiDAR Pose Estimation

arXiv: https://arxiv.org/abs/2109.01181 · HTML: https://mlsanity.com/paper/2109.01181/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 43 references that are in the map.
- First posted on arXiv 2 Sep 2021.

## Builds on (most cited first, 14 of 14)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Lagrangian Duality in 3D SLAM: Verification Techniques and Optimal Solutions](https://mlsanity.com/paper/1506.00746/) (2015)
- [LiDAR-Camera Calibration using 3D-3D Point correspondences](https://mlsanity.com/paper/1705.09785/) (2017)
- [Automatic Extrinsic Calibration for Lidar-Stereo Vehicle Sensor Setups](https://mlsanity.com/paper/1705.04085/) (2017)
- [Automatic extrinsic calibration between a camera and a 3D Lidar using 3D point and plane correspondences](https://mlsanity.com/paper/1904.12433/) (2019)
- [ChromaTag: A Colored Marker and Fast Detection Algorithm](https://mlsanity.com/paper/1708.02982/) (2017)
- [Improvements to Target-Based 3D LiDAR to Camera Calibration](https://mlsanity.com/paper/1910.03126/) (2019)
- [A Novel Dual-Lidar Calibration Algorithm Using Planar Surfaces](https://mlsanity.com/paper/1904.12116/) (2019)
- [Extrinsic Calibration of a 3D-LIDAR and a Camera](https://mlsanity.com/paper/2003.01213/) (2020)
- [Efficient Anytime CLF Reactive Planning System for a Bipedal Robot on Undulating Terrain](https://mlsanity.com/paper/2108.06699/) (2021)
- [Automatic Calibration of Dual-LiDARs Using Two Poles Stickered with Retro-Reflective Tape](https://mlsanity.com/paper/1911.00635/) (2019)
- [LiDARTag: A Real-Time Fiducial Tag System for Point Clouds](https://mlsanity.com/paper/1908.10349/) (2019)
- [LFTag: A Scalable Visual Fiducial System with Low Spatial Frequency](https://mlsanity.com/paper/2006.00842/) (2020)
- [Global Unifying Intrinsic Calibration for Spinning and Solid-State LiDARs](https://mlsanity.com/paper/2012.03321/) (2020)

## Abstract (arXiv)

Targets are essential in problems such as object tracking in cluttered or textureless environments, camera (and multi-sensor) calibration tasks, and simultaneous localization and mapping (SLAM). Target shapes for these tasks typically are symmetric (square, rectangular, or circular) and work well for structured, dense sensor data such as pixel arrays (i.e., image). However, symmetric shapes lead to pose ambiguity when using sparse sensor data such as LiDAR point clouds and suffer from the quantization uncertainty of the LiDAR. This paper introduces the concept of optimizing target shape to remove pose ambiguity for LiDAR point clouds. A target is designed to induce large gradients at edge points under rotation and translation relative to the LiDAR to ameliorate the quantization uncertainty associated with point cloud sparseness. Moreover, given a target shape, we present a means that leverages the target's geometry to estimate the target's vertices while globally estimating the pose. Both the simulation and the experimental results (verified by a motion capture system) confirm that by using the optimal shape and the global solver, we achieve centimeter error in translation and a few degrees in rotation even when a partially illuminated target is placed 30 meters away. All the implementations and datasets are available at https://github.com/UMich-BipedLab/optimal_shape_global_pose_estimation.