# Extrinisic Calibration of a Camera-Arm System Through Rotation Identification

## TL;DR

This paper introduces a novel method for extrinsic calibration of camera-arm systems that uses structured arm motion and image observations to estimate calibration parameters without external artifacts, validated through simulation and real-world tests.

## Contribution

It presents a new approach combining known arm kinematics with conic observations to perform self-calibration without calibration targets.

## Key findings

- Method achieves accurate calibration comparable to ruler-based estimates.
- Validated in simulation and real-world experiments.
- Effective for outdoor and unstructured environments.

## Abstract

Determining extrinsic calibration parameters is a necessity in any robotic system composed of actuators and cameras. Once a system is outside the lab environment, parameters must be determined without relying on outside artifacts such as calibration targets. We propose a method that relies on structured motion of an observed arm to recover extrinsic calibration parameters. Our method combines known arm kinematics with observations of conics in the image plane to calculate maximum-likelihood estimates for calibration extrinsics. This method is validated in simulation and tested against a real-world model, yielding results consistent with ruler-based estimates. Our method shows promise for estimating the pose of a camera relative to an articulated arm's end effector without requiring tedious measurements or external artifacts. Index Terms: robotics, hand-eye problem, self-calibration, structure from motion