Reduced Order vs. Discretized Lumped System Models with Absolute and Relative States for Continuum Manipulators

A reliable, accurate, and yet simple dynamic model is important to analyze, design and control continuum manipulators. Such models should be fast, as simple as possible and user-friendly to be widely accepted by the ever-growing robotics research community. In this study, we introduce two new modeling methods for continuum manipulators: a general reduced-order model (ROM) and a discretized model with absolute states and Euler-Bernoulli beam segments (EBA). Additionally, a new formulation is presented for a recently introduced discretized model based on Euler-Bernoulli beam segments and relative states (EBR). The models are validated in comparison to experimental results for dynamics of a STIFF-FLOP continuum appendage. Our comparison shows higher simulation accuracy (8-14% normalized error) and numerical robustness of the ROM model for a system with small number of states, and computational efficiency of the EBA model with near real-time performances that makes it suitable for large systems. The challenges with designing control and observation scenarios are briefly discussed in the end.