Calibration of a Three-Axis Robot Manipulator with a Single Lidar Camera for Indoor Hydroponic System

This paper presents the calibration and error evaluation of a three-axis (X-Y-Z) Cartesian robot in an eye-tohand configuration, integrated with an Intel RealSense LiDAR L515 camera for indoor hydroponic applications. The system leverages LiDAR depth data and point clouds to determine the (x, y, z) coordinates of source and target points within a 50 cm (X) × 35 cm (Y) × 30 cm (Z) workspace. The manipulator features a horizontally aligned <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{X}$</tex>-axis, a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{Y}$</tex>-axis mounted on the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{X}$</tex>-axis carriage, and a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{Z}$</tex>-axis end-effector on the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{Y}$</tex>-axis. We propose a calibration pipeline employing a Weighted Depth-Adaptive Kabsch (WDA-Kabsch) variant, compared with KabschProcrustes (K-P) and Levenberg-Marquardt (LM) optimization, to transform coordinates from the camera to the robot frame. Experimental validation with 10 reference markers demonstrates significant error reduction: WDA-Kabsch achieves an RMSE of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{10.59 ~ mm}$</tex>, a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{14.9 \%}$</tex> improvement over K-P and LM <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(12.44 ~\text{mm})$</tex>. The system's <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\sim 1 ~\text{cm}$</tex> accuracy and WDA-Kabsch's efficiency (0.507 ms) make it suitable for precise tasks, such as plant sucker pruning and fruit harvesting, in controlled hydroponic setups. These findings highlight the potential of single-camera LiDAR systems for cost-effective agricultural automation.