Structured Light Hand-Eye Calibration With Depth Scale Optimization
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Solution Overview
Problem
Existing hand-eye calibration methods for robotic systems face challenges in achieving accurate and stable solutions due to the nonlinearity and instability of the equation-solving process, particularly when using structured light cameras.
Innovation Solution
The proposed method employs Kalman filtering for depth estimation, Singular Value Decomposition (SVD) for error analysis, and the Nelder-Mead algorithm to optimize the depth scaling coefficient, thereby improving the accuracy of hand-eye calibration based on structured light cameras.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional hand-eye calibration methods are used with structured light cameras, then the calibration process can be completed, but the solution suffers from nonlinearity and instability leading to high error rates
Solution Approach 1:
The patent transforms the nonlinear hand-eye calibration equation into a linear form by introducing new parameters and rewriting the transformation relationships. This parameter transformation allows the use of linear least squares methods instead of nonlinear optimization, achieving both high accuracy and stability in the calibration solution.
Solution Approach 2:
The patent introduces an intermediate coordinate system and transformation matrix decomposition as a mediator between the camera coordinate system and robot base coordinate system. By breaking down the direct nonlinear transformation into intermediate linear transformations, the calibration process achieves improved stability and accuracy.
2Ease of operation
If the calibration equation is solved directly without transformation, then the process is simpler, but the nonlinearity causes instability and high error rates
Solution Approach 1:
The patent applies parameter transformation to convert the difficult nonlinear calibration problem into a simpler linear problem. By changing the mathematical representation of the calibration equation through parameter substitution and linearization, the method achieves both operational simplicity and high calibration accuracy simultaneously.
3Productivity
If depth values from structured light camera are used directly, then the calibration can proceed, but depth measurement errors propagate through the calibration process
Solution Approach 1:
The patent incorporates feedback mechanisms in the linearized calibration process where the transformation matrices are iteratively refined. The method uses the collected point cloud data and transformation relationships to continuously improve the depth measurements and calibration parameters, reducing error propagation while maintaining calibration efficiency.
Data Source
AI summary
Provided is a method for improved hand-eye calibration method based on a structured light camera. The method includes: step 1: establishing a pinhole camera model, and using a depth camera to detect a three-dimensional (3D) coordinate to obtain a physical coordinate of each point in an image coordinate system with a known depth relative to a camera coordinate system; step 2: establishing a Denavit-Hartenberg (DH) model of a robotic arm, and moving the robotic arm to a determined coordinate using inverse kinematics; step 3: collecting n sets of point cloud data, applying depth scaling coefficients to the n sets of point cloud data to perform Singular Value Decomposition (SVD), and solving for an optimal depth scaling coefficient using a Nelder-Mead algorithm; and step 4: completing the hand-eye calibration of the robotic arm based on the solved optimal depth scaling coefficient. The method offers strong operability and robustness.