[Paper Review] Hybrid Data-Driven and Analytical Model for Kinematic Control of a Surgical Robotic Tool

Francesco Cursi, Anh V. Nguyen+1 more|arXiv (Cornell University)|Jun 4, 2020

Gaussian Processes and Bayesian Inference18 references4 citations

TL;DR

This paper proposes a hybrid kinematic modeling approach for tendon-driven surgical robots by fusing an analytical model with Gaussian Process Regression (GPR)-based data-driven learning. The method adaptively weights the models based on GPR uncertainty, significantly improving accuracy over pure analytical or data-driven models, with a 40% reduction in RMSE for the x-direction on real robotic data compared to standalone GPR.

ABSTRACT

Accurate kinematic models are essential for effective control of surgical robots. For tendon driven robots, which is common for minimally invasive surgery, intrinsic nonlinearities are important to consider. Traditional analytical methods allow to build the kinematic model of the system by making certain assumptions and simplifications on the nonlinearities. Machine learning techniques, instead, allow to recover a more complex model based on the acquired data. However, analytical models are more generalisable, but can be over-simplified; data-driven models, on the other hand, can cater for more complex models, but are less generalisable and the result is highly affected by the training dataset. In this paper, we present a novel approach to combining analytical and data-driven approaches to model the kinematics of nonlinear tendon-driven surgical robots. Gaussian Process Regression (GPR) is used for learning the data-driven model and the proposed method is tested on both simulated data and real experimental data.

Motivation & Objective

• To address the challenge of modeling high nonlinearities in tendon-driven surgical robots, particularly hysteresis and slack.
• To overcome the limitations of purely analytical models (over-simplification) and purely data-driven models (poor generalization) in surgical robotics.
• To develop a hybrid modeling framework that leverages the strengths of both approaches for improved kinematic accuracy.
• To evaluate the performance of the hybrid model on both simulated and real experimental data from the Micro-IGES surgical tool.

Proposed method

• The analytical model is derived using geometric and kinematic assumptions based on the robot's physical structure and tendon routing.
• A data-driven model is built using Gaussian Process Regression (GPR) to learn the error between the analytical model and real measurements.
• The hybrid model combines the analytical and GPR models by weighting them based on the confidence (uncertainty) of the GPR predictions.
• The GPR model is trained using three variants: error learning (GPR on residuals), GP with prior (incorporating analytical model in kernel), and GP without prior.
• A weighting function dynamically adjusts the contribution of the analytical and data-driven models based on the GPR's predictive variance.
• The method is validated on simulated data and real-world experiments with the Micro-IGES robotic tool, using a lemniscate trajectory for evaluation.

Experimental results

Research questions

• RQ1 Can a hybrid model that combines analytical and data-driven approaches improve kinematic modeling accuracy for tendon-driven surgical robots compared to standalone methods?
• RQ2 How does the uncertainty estimation from GPR influence the fusion strategy between analytical and data-driven models?
• RQ3 Does incorporating prior knowledge (analytical model) into the GPR kernel improve generalization and reduce overfitting to training data?
• RQ4 How does the performance of the hybrid model compare to pure analytical and pure data-driven models on real robotic systems with complex nonlinearities?
• RQ5 What is the impact of the analytical model's accuracy on the final hybrid model's performance?

Key findings

• The hybrid model achieved an RMSE of 0.009 m in the x-direction on real robotic data, representing a 40% improvement over the standalone GPR model (RMSE 0.011 m).
• The hybrid model reduced maximum absolute error in the x-direction from 0.033 m (GPR) to 0.031 m, demonstrating improved robustness.
• Learning the error between the analytical model and real data (GPR on residuals) yielded the best performance among the three GPR variants tested.
• The hybrid model exhibited smoother predictions than the pure GPR model, particularly in regions of high uncertainty.
• The analytical model's accuracy significantly influenced the final hybrid result; a poor analytical model degraded the overall performance.
• The method successfully balanced model confidence and data-driven learning, with the hybrid model favoring the analytical model where GPR uncertainty was high.