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Continuous body 3-D reconstruction of limbless animals

Qiyuan Fu, Thomas W. Mitchel, Jin Seob Kim, Gregory S. Chirikjian, Chen Li

TL;DR

This work presents a backbone-optimization framework that reconstructs the continuous 3-D shape and orientation of limbless animals by modeling the body as a quasi-static elastic rod and enforcing end-constraints from tracked markers. By solving an Euler-Poincaré-based optimization and applying inverse kinematics, the method yields high-accuracy 3-D midlines across the entire body, outperforming traditional B-spline interpolation by about 50% in both position and orientation error while enabling analysis of body-terrain interactions. Ground-truth validation using multi-view midline extraction confirms the method’s precision (e.g., ~1.5 mm average error on a 3–7 cm segment) and highlights the trade-offs with marker setup and computation time. The approach generalizes to other long, slender biological systems and continuum robots, and the authors provide open-source MATLAB code and demonstrations to facilitate adoption.

Abstract

Limbless animals such as snakes, limbless lizards, worms, eels, and lampreys move their slender, long bodies in three dimensions to traverse diverse environments. Accurately quantifying their continuous body's 3-D shape and motion is important for understanding body-environment interactions in complex terrain, but this is difficult to achieve (especially for local orientation and rotation). Here, we describe an interpolation method to quantify continuous body 3-D position and orientation. We simplify the body as an elastic rod and apply a backbone optimization method to interpolate continuous body shape between end constraints imposed by tracked markers. Despite over-simplifying the biomechanics, our method achieves a higher interpolation accuracy (~50% error) in both 3-D position and orientation compared with the widely-used cubic B-spline interpolation method. Beyond snakes traversing large obstacles as demonstrated, our method applies to other long, slender, limbless animals and continuum robots. We provide codes and demo files for easy application of our method.

Continuous body 3-D reconstruction of limbless animals

TL;DR

This work presents a backbone-optimization framework that reconstructs the continuous 3-D shape and orientation of limbless animals by modeling the body as a quasi-static elastic rod and enforcing end-constraints from tracked markers. By solving an Euler-Poincaré-based optimization and applying inverse kinematics, the method yields high-accuracy 3-D midlines across the entire body, outperforming traditional B-spline interpolation by about 50% in both position and orientation error while enabling analysis of body-terrain interactions. Ground-truth validation using multi-view midline extraction confirms the method’s precision (e.g., ~1.5 mm average error on a 3–7 cm segment) and highlights the trade-offs with marker setup and computation time. The approach generalizes to other long, slender biological systems and continuum robots, and the authors provide open-source MATLAB code and demonstrations to facilitate adoption.

Abstract

Limbless animals such as snakes, limbless lizards, worms, eels, and lampreys move their slender, long bodies in three dimensions to traverse diverse environments. Accurately quantifying their continuous body's 3-D shape and motion is important for understanding body-environment interactions in complex terrain, but this is difficult to achieve (especially for local orientation and rotation). Here, we describe an interpolation method to quantify continuous body 3-D position and orientation. We simplify the body as an elastic rod and apply a backbone optimization method to interpolate continuous body shape between end constraints imposed by tracked markers. Despite over-simplifying the biomechanics, our method achieves a higher interpolation accuracy (~50% error) in both 3-D position and orientation compared with the widely-used cubic B-spline interpolation method. Beyond snakes traversing large obstacles as demonstrated, our method applies to other long, slender, limbless animals and continuum robots. We provide codes and demo files for easy application of our method.

Paper Structure

This paper contains 27 sections, 17 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Materials and Methods
  3. Overview
  4. Backbone curve
  5. Elastic energy of rod
  6. Backbone optimization
  7. Inverse kinematics
  8. Interpolation parameters
  9. Segment lengths, cross-sectional shape, and tapering
  10. Stiffness matrix
  11. Marker data pre- & post-processing and validation
  12. Marker orientation offset reduction
  13. Smoothing orientation
  14. Position translation
  15. Post-processing
  16. ...and 12 more sections

Figures (3)

  • Figure 1: Overview of interpolation method combining elastic rod modeling and backbone optimization. (A) Modeling of a snake body segment as an elastic rod segment, with its midline described by a backbone curve $g(s)$ (dashed). The rod segment is subject to two end constraints imposed by 3-D position and orientation of two body frames, $g(0)$ and $g(L)$, obtained from markers attached to it at both ends. $L$ is segment length. $g(s)$ is a body frame at length $s$. (B) Schematic of inverse kinematics to converge backbone curve towards marker end constraints. See Inverse Kinematics for description of the process. (C) Workflow to use method. (D) Definition of different types of elastic rod deformation: lateral and dorsoventral bending about $x$ and $y$ axes, twisting about $z$ axis, lateral and dorsoventral shearing along $x$ and $y$ axis, and extension or compression along $z$ axis. $x$-$y$-$z$ axes form a right-handed body frame attached to backbone curve, with +$x$ axis pointing upward along the axis of left-right symmetry of cross section, and +$z$ axis pointing backward tangent to segment backbone curve.
  • Figure 2: Midline extraction and comparison. (A) Experimental setup to obtain body midline ground truth. See Experimental protocol for description. (B, C) Representative top and side views of a snake traversing a step obstacle (yellow dashed lines) with interpolated backbone curve projected (magenta and yellow). (D, E) Representative binary top and side views with body midline projected (orange), which is extracted using computer vision techniques. (F, G) Average pointwise error of reconstructed backbone curve position from extracted midline in top and side views. Brackets and asterisks represent a significant increase of error with marker spacing ($P$ < 0.0001, linear regression). $N$ = 3 individuals, $n$ = 60 trials.
  • Figure 3: Comparison of interpolation accuracy between our method and B-spline method. (A) A representative snapshot of interpolation results. See Movie 3 for a representative trial. (B) Position error. (C) Orientation error. Data are shown using violin plots. Black and red lines show mean and median. Local width of graph is proportional to frequency of data along $y$ axis. Brackets and asterisks represent a significant difference ($P$ < 0.0001, ANOVA). $N$ = 3 individuals, $n$ = 122 trials.