3D Motion Planning Algorithms for Steerable Needles Using Inverse Kinematics

Area of Science:

• Robotics and Medical Device Engineering
• Computational Geometry and Motion Planning

Background:

• Steerable needles offer precise navigation for medical interventions, particularly in reaching targets obscured by sensitive or impassable tissues.
• The motion of steerable needles exhibits nonholonomic kinematics, analogous to a Dubins car in 2D and an airplane model in 3D.

Purpose of the Study:

• To develop a constant-time motion planning algorithm for steerable needles.
• To leverage explicit geometric inverse kinematics for efficient path generation.
• To analyze the reachability and path efficiency of the proposed algorithm.

Main Methods:

• Developed a constant-time motion planning algorithm based on explicit geometric inverse kinematics.
• Analyzed 2D path competitivity using analytic comparisons with Dubins car shortest paths.
• Utilized numerical simulations for 3D path analysis and reachability.
• Implemented a local path adaptation algorithm using null-space methods from redundant manipulator theory.

Main Results:

• The proposed algorithm provides constant-time motion planning for steerable needles.
• Demonstrated efficient path generation and reachability in both 2D and 3D simulations.
• The inverse kinematics solution facilitates the generation of obstacle-avoiding needle paths.

Conclusions:

• The developed motion planning algorithm offers a robust solution for steerable needle-based medical applications.
• The geometric inverse kinematics approach enables precise and adaptable needle path control.
• This work provides a foundation for advanced steerable needle applications, including obstacle avoidance.