# Simplified Kinematics of Continuum Robot Equilibrium Modulation via Moment Coupling Effects and Model Calibration

## TL;DR

This paper introduces a simplified kinematic model for continuum robots that captures micro and macro motion behaviors through moment coupling effects and calibration, validated by experiments with high accuracy.

## Contribution

It presents a novel, calibration-based modeling approach that explains micro-scale motion phenomena in continuum robots, including turning point behavior.

## Key findings

- Model accurately predicts micro and macro motions with RMS error of 5.82 micrometers.
- Calibration parameters effectively reproduce turning point behavior.
- Model fits experimental data well, especially when excluding motions past the turning point.

## Abstract

Recently, a new concept for continuum robots capable of producing macro-scale and micro-scale motion has been presented. These robots achieve their multi-scale motion capabilities by coupling direct-actuation of push-pull back-bones for macro motion with indirect actuation whereby the equilibrium pose is altered to achieve micro-scale motion. This paper presents a first attempt at explaining the micro-motion capabilities of these robots from a modeling perspective. This paper presents the macro and micro motion kinematics of a single segment continuum robot by using statics coupling effects among its sub-segments. Experimental observations of the micro-scale motion demonstrate a turning point behavior which could not be explained well using the current modeling methods. We present a simplistic modeling approach that introduces two calibration parameters to calibrate the moment coupling effects among the sub segments of the robot. It is shown that these two parameters can reproduce the turning point behavior at the micro-scale. The instantaneous macro and micro scale kinematics Jacobians and the calibration parameters identification Jacobian are derived. The modeling approach is verified against experimental data showing that our simplistic modeling approach can capture the experimental motion data with RMS position error of 5.82 micrometers if one wishes to fit the entire motion profile with the turning point. If one chooses to exclude motions past the turning point, our model can fit the experimental data with an accuracy of 4.76 micrometers.