This work introduces an integrated Material Point Method (MPM) framework for optimizing tendon-driven hyperelastic robots under extreme 3D deformations. To overcome the mesh distortion limitations of the traditional FEM at large strains, we develop a coupled MPM–tendon hyperelastic model that integrates Yeoh constitutive laws with discrete tendon actuation forces. The model enables robust simulation of anisotropic stress propagation through Lagrangian particle tracking and Eulerian grid discretization, eliminating mesh entanglement artifacts. A strain-gradient-driven tendon path algorithm ensures mechanical efficiency using Fréchet distance-based similarity metrics and curvature smoothness screenin, enforcing spatial continuity in complex topologies. Validation demonstrates: (1) Sub 3 mm geometric errors and about 89% volumetric overlap in worm-inspired deformations; (2) optimal computational efficiency at 0.4–0.6 mm grid densities, balancing accuracy and resource overhead; and (3) projected alignment errors of 0.8 mm (XY), 1.3 mm (XZ), and 2.9 mm (YZ) in multi-view spatial analyses. The framework achieves about 89% ± 2% volumetric overlap in quadrupedal morphing via agonist–antagonist tendon optimization, demonstrating efficacy for extreme 3D deformation control.
Su et al. (Sat,) studied this question.