Task-Induced Symmetry and Reduction with Application to Needle Steering.

Area of Science:

• Robotics
• Control Theory
• Mechanical Systems

Background:

• Lie group symmetry intrinsically simplifies mechanical system dynamics.
• Existing methods typically exploit symmetries inherent to the system's configuration or dynamics.

Purpose of the Study:

• To introduce and explore the application of extrinsic, task-induced symmetries for dimensional reduction in mechanical systems.
• To demonstrate the design of global feedback controllers using this reduction technique.
• To integrate task-induced symmetry with existing Lagrangian reduction methods.

Main Methods:

• Exploiting symmetries arising from extrinsic control tasks, rather than intrinsic system properties.
• Applying dimensional reduction to simplify complex dynamical equations.
• Designing global feedback controllers on the reduced-order systems.
• Integrating the technique with Lagrangian reduction.

Main Results:

• Task-induced symmetry enables significant dimensional reduction in mechanical systems.
• The reduction facilitates the design of essentially global feedback controllers.
• The methodology is successfully applied to a 6 DOF kinematic model of steerable bevel-tip needles.
• Controllers were developed to make the needle tip track a specific subspace.

Conclusions:

• Task-induced symmetry provides a powerful tool for simplifying mechanical system control.
• This approach offers a novel framework for planning and control in applications like robotic needle steering.
• The technique complements existing methods like Lagrangian reduction, enhancing control design possibilities.