Author: Suraj Raval
Date/Time: January 16th, 2025 at 2:00pm
Location: EGR-2164
Committee Members:
- Dr. Yancy Diaz-Mercado, Chair
- Dr. Jin-Oh Hahn
- Dr. Nikhil Chopra
- Dr. Hosam K. Fathy
- Dr. Axel Krieger
- Dr. Pratap Tokekar, Dean’s Representative
Title: RELIABLE AUTONOMY FOR MAGNETIC SURGICAL ROBOTS
Abstract:
Magnetic robots can leverage external magnetic fields to generate forces and torques for
untethered steering, enabling miniature tools for minimally invasive surgical procedures. Achieving safe, accurate motion requires reliable prediction of magnetic fields, gradients, and the resulting wrench on embedded permanent magnets. However, fields generated by electromagnetic coil arrays are strongly nonlinear, particularly near the coils, where commonly used dipole approximations can exhibit large errors. Because magnetic forces and torques decay approximately with the inverse cube of distance, modeling inaccuracies near the sources can render substantial regions of the workspace unsuitable for precision control. This dissertation develops modeling and control methods that improve accuracy and reliability of magnetic actuation in clinically relevant settings.
First, we experimentally quantify closed-loop control performance under different magnetic models by comparing a high-error dipole approximation against more accurate numerical and analytical models for estimating planar forces and torques as a function of robot pose. We show that improved field and gradient modeling translates directly into improved tracking performance and reduced control error.
Second, in developing model-based controllers for such systems, it is often assumed that
the magnetic needle orientation is aligned with the magnetic field direction. This assumption has enabled use of open-loop control techniques for orientation control of the magnetic agent. We present a time-scale separation analysis that characterizes when this alignment assumption is valid and when it can break down as a function of system parameters such as damping and magnetic torque dynamics. We support the analysis with simulations and validate the predicted behaviors experimentally on a real magnetic control platform, providing practical guidance for designing controllers and selecting parameters when accurate heading regulation is required for surgical task execution.
Third, we address configuration-dependent singularities and ill-conditioning in magnetic
manipulation Jacobians, which can destabilize standard inversion-based controllers. We use the nonlinear nature of the magnetic fields to analyze controllability of magnetic robots and understand the limits of singularity-free control without needing to increase number of magnetic actuators, which can lead to bulkier and costlier magnetic robotic systems. In particular, we leverage Chow’s Theorem to analyze the motion feasibility of a single magnetic robot moving
in a plane, powered by an array of stationary electromagnets. We determine the degree of nonholonomy for an underactuated case and show that we can achieve any desired motion in the state-space at the cost of more complex controls. Building on this insight, we develop an approximate steering controller that drives the robot between arbitrary planar poses while avoiding inversion singularities. Simulations demonstrate low tracking error using the proposed approach.
Finally, many surgical interventions require multiple tools to simultaneously operate within a confined workspace to perform task primitives such as triangulation, retraction, suturing, and handoffs. Coordinated multi-tool control is fundamentally challenging because all tools share the same coil inputs, inducing strong coupling and interaction effects, while imposing safety critical constraints (e.g., workspace boundaries and inter-tool collisions). Moreover, multi-tool controllers often rely on inverting stacked field-force actuation maps that can become ill-conditioned or singular for common tool configurations, resulting in unstable current commands. To address this, we propose a two-stage, optimization-based control framework for multi-robot magnetic manipulation that avoids dependence on singular full-map inversions while providing formal safety guarantees. A nominal coil-current command is first computed using a reduced order field-force inversion to achieve the primary motion objective for robot 1. A Control Barrier
Function-Quadratic Program (CBF-QP) then minimally modifies this nominal command to enforce forward invariance of a specified safe set for robot 2. We validate the approach experimentally on a planar two-robot system driven by an eight-coil electromagnetic array, demonstrating consistent tracking for the primary robot across repeated trials while maintaining safety for the secondary robot.