The Path-of-Probability Algorithm for Steering and Feedback Control of Flexible Needles

Area of Science:

• Robotics
• Medical Device Engineering
• Computational Geometry

Background:

• Flexible needles are increasingly used in minimally invasive surgery.
• Accurate path planning is crucial for safe and effective needle insertion.
• Existing methods struggle with the complex dynamics of flexible needles, especially those with bevel tips.

Purpose of the Study:

• To develop a robust framework for path planning of flexible needles with bevel tips.
• To enable precise control and navigation for flexible needles in medical procedures.
• To address challenges in path planning, including obstacle avoidance and optimal port placement.

Main Methods:

• Developed a stochastic model for needle steering, approximating tip pose probability density as a Gaussian.
• Employed a second-order accurate error propagation algorithm for estimating Gaussian means and covariances.
• Adapted the path-of-probability (POP) algorithm for flexible needle path planning.
• Derived a closed-form solution for optimal port placement in obstacle-free environments.
• Proposed a novel method using reference splines with the POP algorithm for planning in complex, obstacle-laden scenarios.

Main Results:

• The proposed framework enables accurate path planning for flexible needles with bevel tips.
• The method facilitates feedback control for enhanced needle guidance.
• An efficient solution for port placement was derived for obstacle-free conditions.
• Successful path planning in general cases with obstacles was demonstrated using reference splines and POP.

Conclusions:

• The developed framework offers a significant advancement in flexible needle path planning.
• This approach enhances the precision and safety of robotic-assisted surgeries.
• The method provides versatile solutions for both simple and complex needle insertion tasks.