cs.ROOct 30, 2026

Physically Constrained Kinematic Calibration for High-Precision Robotic Needle Guidance

Authors: Prabhu Nithin Gollapudi, Andreas Maier, Franziska Mathis-Ullrich, Water Zhao, Jia Wang, Siming Bayer

Organizations: Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany · Precision Medtech Co., Ltd, Beijing, China

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Abstract

Percutaneous needle insertion is a common practice in minimally invasive procedures whose clinical success depends on accurate needle placement. However, achieving the necessary precision is a challenge for manual operators. Robotic assistance can improve targeting accuracy and reduce operator dependence, but residual millimeter-scale errors persist because nominal kinematic models do not fully represent the physical manipulator. This paper presents a robust bound-constrained kinematic calibration method designed to improve positional accuracy for a 6-Degree-of-Freedom (6-DoF) robotic needle-guidance manipulator. The approach uses physically plausible parameter ranges to regularize a compact 19-parameter geometric identification model. By treating these bounds as active optimization constraints rather than mere numerical safeguards, the framework effectively mitigates parameter coupling and overfitting, ensuring highly stable parameter identification. In simulation, the proposed method reduced end-effector Root Mean Square Error (RMSE) from 3.422 mm to 0.690 mm (a 79.8% improvement). In benchtop hardware experiments, the calibrated model achieved sub-millimeter validation accuracy, including 0.865 mm RMSE in experimental trajectory validation and 0.610 mm RMSE in a coordinate-lattice verification task. These results demonstrate that physically constrained kinematic calibration can enhance robotic needle-targeting accuracy, establishing a high-precision foundation for future clinical applications.

Figures & tables

Fig. 1: Calibration pipeline overview. The framework combines observability-optimized data acquisition, a compact 19-parameter error model, bound-constrained optimization, and 10-fold cross-validation for robust parameter identification. The simulation branch (dashed) is used for controlled validation before hardware experiments.
Link iiΔai\Delta a_{i} (mm)Δαi\Delta\alpha_{i} (rad)Δdi\Delta d_{i} (mm)Δθi\Delta\theta_{i} (rad)
1Δx1\Delta x_{1}0Δz1\Delta z_{1}Δθ1\Delta\theta_{1}
2Δa\Delta a00Δθ2\Delta\theta_{2}
3Δy3\Delta y_{3}00Δθ3\Delta\theta_{3}
400Δz4\Delta z_{4}Δθ4\Delta\theta_{4}
5000Δθ5\Delta\theta_{5}
6Δy6\Delta y_{6}0Δz6\Delta z_{6}Δθ6\Delta\theta_{6}
TABLE I: Mapping of the 13 Kinematic Error Parameters to the DH Table
Configuration StateRMSE (mm)Mean (mm)Max (mm)
Nominal (train)2.6452.4024.800
Nominal (test)3.4223.0107.662
Calibrated (train)0.5780.5161.411
Calibrated (test)0.6900.6091.258
TABLE II: Simulation results before and after calibration.
Fig. 2: Validation RMSE across the 10 folds for the nominal and calibrated models. The proposed framework consistently reduces error and exhibits high robustness.
Fig. 3: Estimated kinematic error parameters tracked across the ten independent validation folds. The low fold-to-fold variance demonstrates the high identifiability and robustness achieved by the bound-constrained optimization.
Dataset / StateRMSE (mm)Mean (mm)Max (mm)
A (nominal)1.0680.9722.214
A (calibrated)0.7140.6442.000
B (nominal)1.0490.9641.880
B (calibrated)0.6480.5851.801
C (nominal)3.2203.0505.008
C (calibrated)0.7260.6681.442
TABLE III: Offline physical calibration results.
Model StateRMSE (mm)Mean (mm)Max (mm)
Nominal model1.0490.9641.837
Calibrated model0.8650.8041.598
TABLE IV: Independent experimental validation on the physical robot.
Fig. 4: Three-dimensional coordinate lattice test after calibration, illustrating the spatial alignment between commanded target positions and actual measured positions.
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