Robot Hand-Eye Calibration using Structure-from-Motion (2311.11808v2)

Abstract: In this paper we propose a new flexible method for hand-eye calibration. The vast majority of existing hand-eye calibration techniques requires a calibration rig which is used in conjunction with camera pose estimation methods. Instead, we combine structure-from-motion with known robot motions and we show that the solution can be obtained in linear form. The latter solves for both the hand-eye parameters and for the unknown scale factor inherent with structure-from-motion methods. The algebraic analysis that is made possible with such a linear formulation allows to investigate not only the well known case of general screw motions but also such singular motions as pure translations, pure rotations, and planar motions. In essence, the robot-mounted camera looks to an unknown rigid layout, tracks points over an image sequence and estimates the camera-to-robot relationship. Such a self calibration process is relevant for unmanned vehicles, robots working in remote places, and so forth. We conduct a large number of experiments which validate the quality of the method by comparing it with existing ones.

• The paper proposes a novel, rig-free hand-eye calibration method for robots that leverages structure-from-motion (SfM) techniques to overcome limitations of traditional methods in constrained environments.
• A key contribution is a linear formulation that efficiently handles small rotations and an extensive algebraic analysis detailing applicability across various robot motions.
• Extensive experiments validate the method's numerical accuracy compared to existing techniques, enabling critical in-situ recalibration for autonomous robots in dynamic or remote settings.

Overview of "Robot Hand-Eye Calibration using Structure-from-Motion"

The paper authored by Nicolas Andreff, Radu Horaud, and Bernard Espiau presents a novel approach to hand-eye calibration in robotics, leveraging the structure-from-motion (SfM) methodology. The research addresses the limitations faced by traditional calibration techniques, such as the need for calibration rigs and the impracticality of large or special robot motions, especially in constrained environments like unmanned vehicles or space-based robots.

Contributions and Methodology

This paper introduces a flexible and linear method for hand-eye calibration that does not require a predefined calibration rig, thereby broadening the applicability of calibration to on-site and remote scenarios. The central thesis of the approach involves combining structure-from-motion algorithms with known robot motions to resolve hand-eye relationships and the inherent unknown scale factor without the assistance of a calibration rig.

Key components of the proposed method include:

• Linear Formulation: The research articulates a linear solution to hand-eye calibration, which facilitates the handling of small rotations that are typically challenging due to their non-linear orthogonality constraints. This linear formulation is achieved by embedding the rotation problem into a larger space, allowing for an efficient linear extraction of the rotation matrices through orthogonal matrices that ensures the robustness against small-motion errors.
• Algebraic Analysis: The paper conducts a thorough algebraic analysis, providing insights into various motion scenarios such as pure translations, pure rotations, planar motions, and general screw motions. This analysis delineates conditions under which full or partial calibration can be executed successfully.
• Experiments and Validation: Extensive experiments validate the quality of the proposed method. Comparisons are made with existing techniques, demonstrating that using structure-from-motion does not detrimentally affect the numerical accuracy of the hand-eye calibration process.

Implications and Future Developments

The implications of this research are substantial for the field of robotics, particularly in enhancing the autonomy and flexibility of robots that operate in environments where conventional calibration methods are impractical. By relaxing the need for physical calibration rigs and enabling small amplitude motions, robots can be recalibrated in situ, which is critical for robotics applications in dynamic or hostile environments.

From a theoretical perspective, the paper suggests a paradigm shift in how calibration can be conceived and executed, highlighting the potential of SfM techniques to transcend traditional calibration limitations. Practically, this development could be vital for applications ranging from autonomous vehicles to robotic payloads in extraterrestrial settings.

Future research can explore the refinement of these techniques, possibly integrating advancements in computer vision and artificial intelligence to enhance the robustness and ease of automation in calibration tasks. Given the promising results, further interdisciplinary collaboration might also extend these methodologies to other areas like augmented reality, where camera calibration remains a core challenge.

In summary, the paper makes a significant contribution to robot hand-eye calibration, proposing a method that aligns with the requirements of increasingly autonomous and remote applications. The results suggest that this approach could be pivotal in enhancing robotic adaptability and precision in a variety of operational contexts.