Stereotypical force patterns of the elephant trunk in planar reaching movements
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The elephant trunk is an excellent example of a muscular hydrostat, exhibiting extreme dexterity through continuous, distributed deformations driven by complex muscle coordination [1,2]. Despite significant advances in continuum and Cosserat-rod-based modeling of soft biological structures [3-5], a major open challenge remains the derivation of interpretable and generalizable relationships between trunk shape configurations and the internal forces generating them. In this work, we propose a 3D dynamic model of the elephant trunk based on rod theory and introduce a set of stereotypical linear laws that map macroscopic shape parameters—segment curvature and length—to internal muscle-analogue forces. The trunk is represented as a multi-segment structure composed of discrete point masses interconnected by longitudinal and radial rods, capturing the essential biomechanics of muscular hydrostats while preserving computational efficiency. Experimental motion-capture data from reaching movements are used to develop the model. Model performance is assessed on both pure bending and combined bending–elongation tasks. Simulated trajectories reproduce biological observations, with average tip-position errors below 8% across trials, while preserving the constant-volume constraint characteristic of muscular hydrostats. A sensitivity analysis further shows that introducing a proximodistal stiffness gradient improves trajectory accuracy. Through multilinear correlation and regression analyses, we identify force–shape relationships across trunk segments. In particular, curvature is primarily governed by differential longitudinal forces, while elongation is strongly associated with radial force activation and antagonistic longitudinal–radial coupling. These findings are condensed into low-dimensional linear mappings, named stereotypical laws, that predict internal force distributions required to generate desired trunk configurations. By reducing the high-dimensional dynamics of a continuum structure to simple, biologically grounded force–shape relationships, this framework enables to infer actuation strategies from shape parameters. Beyond advancing the biomechanical understanding of elephant trunk coordination, the proposed approach offers a promising approach for model-based control of continuum and soft robotic systems inspired by muscular hydrostats.
