Robust-Sub-Gaussian Model Predictive Control for Safe Ultrasound-Image-Guided Robotic Spinal Surgery

TL;DR

This paper introduces a novel sub-Gaussian noise model for uncertainty in high-dimensional sensory feedback, enabling a new Model Predictive Control framework that guarantees safety in ultrasound-guided robotic spinal surgery.

Contribution

It proposes a new noise characterization and uncertainty propagation technique, and develops a safety-guaranteed MPC framework for linear systems under this model, applied to robotic surgery.

Findings

Simulation demonstrates safety and effectiveness in complex surgical tasks.

The approach handles unknown, complex estimation errors in high-dimensional data.

Potential for real-world application in safe autonomous surgical procedures.

Abstract

Safety-critical control using high-dimensional sensory feedback from optical data (e.g., images, point clouds) poses significant challenges in domains like autonomous driving and robotic surgery. Control can rely on low-dimensional states estimated from high-dimensional data. However, the estimation errors often follow complex, unknown distributions that standard probabilistic models fail to capture, making formal safety guarantees challenging. In this work, we introduce a novel characterization of these general estimation errors using sub-Gaussian noise with bounded mean. We develop a new technique for uncertainty propagation of proposed noise characterization in linear systems, which combines robust set-based methods with the propagation of sub-Gaussian variance proxies. We further develop a Model Predictive Control (MPC) framework that provides closed-loop safety guarantees for linear systems under the proposed noise assumption. We apply this MPC approach in an ultrasound-image-guided robotic spinal surgery pipeline, which contains deep-learning-based semantic segmentation, image-based registration, high-level optimization-based planning, and low-level robotic control. To validate the pipeline, we developed a realistic simulation environment integrating real human anatomy, robot dynamics, efficient ultrasound simulation, as well as in-vivo data of breathing motion and drilling force. Evaluation results in simulation demonstrate the potential of our approach for solving complex image-guided robotic surgery task while ensuring safety.