In the paper Painless Differentiable Rotation Dynamics, the IRE research group from Universidad Rey Juan Carlos demonstrates how colonoscopy simulation using a Cosserat rod model and a formulation of forward and differentiable rigid-body dynamics using Lie-algebra rotation derivatives, can create faster simulations, simplify the mathematics behind them, and improve stability in medical training simulators.
By replacing traditional rotation math with a Lie derivative–based approach, we avoid the mathematical complexity that often makes flexible instrument simulation slow and unstable. This new formulation runs more than four times faster than previous methods in our colonoscopy tests, while producing the same realistic bending, twisting, and contact behavior between the scope and the colon.
These improvements mean:
• More responsive simulators for doctors in training.
• More detailed and accurate anatomical models without performance loss.
• Better tools for planning challenging procedures or testing new endoscope designs.
Ultimately, this approach brings medical simulation a step closer to real-time, high-fidelity training environments that are safer for patients and more efficient for clinicians.
Authors: Magí Romanyà-Serrasolsas, Juan j. Casafranca, Miguel a. Otaduy. Thank you to: Christos Koutras.
Read the paper here