Geometric Shape Optimization for Limbless Locomotion
2026-07-01 • Graphics
Graphics
AI summaryⓘ
The authors developed a new way to simulate how snake-like soft bodies move by representing their shape as a smooth 3D curve using special math tools called Fourier-Chebyshev polynomials. They find the best movement by solving math problems that consider how the body interacts with its surroundings, while making sure the shape doesn't bend or twist in impossible ways. This curve is then used to create a realistic-looking surface that moves naturally, similar to techniques used in animation. The authors tested their method in various situations and found it produces more believable motion than other current approaches.
locomotion simulationlimbless organismsdifferential geometryFourier-Chebyshev polynomialsparametric curveoptimizationbending energytorsional energysurface interpolationsoft robotics
Authors
Utpal Khanal, Avirup Mandal
Abstract
The simulation of locomotion in limbless, deformable organisms remains a challenging problem across computer graphics, soft robotics, and computational modeling. In this work, we present a novel differential-geometric framework for modeling the motion of slender soft bodies, such as snakes. The body is represented as a three-dimensional parametric curve using a Fourier-Chebyshev polynomial basis. Motion is computed by solving an optimization problem that determines the interaction between the curve and its environment by estimating polynomial coefficients. To ensure physically plausible and non-self-intersecting behavior, bending and torsional energy terms are incorporated into the formulation. The resulting curve is then used to drive a surface representation via interpolation, enabling realistic visualization analogous to skinning techniques. We evaluate the proposed approach across a range of complex scenarios and parameter settings to demonstrate its robustness and versatility. Comparative analysis with state-of-the-art methods indicates that our approach achieves improved simulation quality and generates more physically realistic motion.