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CiiS Lab
Johns Hopkins University
112 Hackerman Hall
3400 N. Charles Street
Baltimore, MD 21218
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Lab Director
Russell Taylor
127 Hackerman Hall
rht@jhu.edu
Last updated: 01/05/2026
This project presents a simulation-based framework for modeling and propagating geometric uncertainty in complex surgical robotic systems. Multiple components—such as tracking sensors, robotic kinematics, and anatomical models—each introduce uncertainty through noise, calibration error, and modeling approximations, and these uncertainties interact through chains of geometric relationships. The framework represents the system as a network of uncertain frames and points connected by uncertain transformations, with uncertainty modeled using multivariate Gaussian distributions. Analytical, Jacobian-based methods are used to propagate uncertainty through composition, with Monte Carlo simulation available for validation. By allowing uncertainty to be computed between arbitrary nodes in the network, the framework provides a general and extensible tool for studying error propagation in surgical navigation and robot-assisted procedures, and serves as a foundation for future work on closed-loop updates and anatomy-aware uncertainty estimation.
Fig. 1: System components and basic scenario. The available components include an optical tracking system, a pointer with a user designed handle, and one or more user defined marker bodies.
Background:
Surgical robotic systems rely on multiple interacting geometric components, including robot
kinematic chains, tracking systems, surgical tools, sensors, and anatomical models. Each
component introduces uncertainty due to calibration error, measurement noise, modeling
assumptions, and manufacturing tolerances. These uncertainties interact through geometric
composition: transformations are chained, measurements are fused, and points of interest
must be expressed consistently across multiple coordinate frames.
Core problem: There is no unified, general framework to model and query uncertainty
propagation across an arbitrary geometric network.
Specific Aims:
Significance: This project develops a mathematically rigorous uncertainty propagation framework for interconnected rigid-body networks. By modeling 6-DOF pose uncertainty in SE(3) and supporting both open-chain and closed-loop structures, the framework enables quantitative estimation of how local uncertainty affects task-level quantities such as tool tip position, relative distances, and anatomical localization. Beyond theoretical analysis, this work will be developed into a design tool for robotic system evaluation. The software will allow users to define geometric networks, assign uncertainty models, and compute propagated covariance to compare system architectures before physical implementation. This enables sensitivity analysis, calibration evaluation, and early stage risk assessment. Additionally, the framework will serve as a teaching tool for future Computer-Integrated Surgery (CIS) courses. It will provide a structured computational environment where students can visualize uncertainty flow through geometric systems and connect multivariate Gaussian theory with real robotic applications. As such, the project contributes not only to research methodology but also to long-term educational infrastructure in surgical robotics.
The technical approach consists of three major layers:
Development will proceed in progressive phases:
Uncertainty Propagation
Uncertainty Modeling
Kalman Filter
Measurement Theory
