An efficient variable-length viscoelastic beam model for dynamic analysis of hard-magnetic soft continuum robots

Abstract

The emerging hard-magnetic soft continuum robots (HMSCRs) enable groundbreaking applications in medical surgery, yet real-time dynamic simulations remain challenging due to the interplay of time-varying geometry, magnetoelastic large deformations, viscoelastic history dependence, and environmental interactions. Previous research was limited to modeling constant-length HMSCRs for the design, such that the previous models cannot be used for dynamic analysis and control during the variable-length motion. This work introduces a computationally efficient framework for variable-length HMSCRs, combining an arbitrary Lagrangian-Eulerian description with analytical modes discretization angle to capture large deformations using minimal degrees of freedom. The configurational force due to curvature discontinuity at the boundary is rigorously derived and the viscoelastic damping effect is introduced by the generalized Maxwell model. Various interaction forces induced by magnetic, hydrodynamic, and contact are considered to cope with various work scenarios. The dynamics of HMSCRs are studied to demonstrate the generality and applicability of the present modeling method. By enabling real-time simulation of complex telescopic dynamics in magnetic fields and fluid, this work establishes a foundation for adaptive control strategies and navigation in minimally invasive surgery.