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Muscular hydrostats, such as octopus arms or elephant trunks, lack bones entirely, endowing them with exceptional dexterity and reconfigurability. Key to their unmatched ability to control nearly infinite degrees of freedom is the architecture into which muscle fibers are weaved. Their arrangement is, effectively, the instantiation of a sophisticated mechanical program that mediates, and likely facilitates, the control and realization of complex, dynamic morphological reconfigurations. Here, by combining medical imaging, biomechanical data, live behavioral experiments, and numerical simulations, an octopus-inspired arm made of $\sim$200 continuous muscle groups is synthesized, exposing “mechanically intelligent” design and control principles broadly pertinent to dynamics and robotics. Such principles are mathematically understood in terms of storage, transport, and conversion of topological quantities, effected into complex 3D motions via simple muscle activation templates. These are in turn composed into higher-level control strategies that, compounded by the arm’s compliance, are demonstrated across challenging manipulation tasks, revealing surprising simplicity and robustness. 

Flexible octopus arms exhibit an exceptional ability to coordinate large numbers of degrees of freedom and perform complex manipulation tasks. As a consequence, these systems continue to attract the attention of biologists and roboticists alike. In this article, we develop a three-dimensional model of a soft octopus arm, equipped with biomechanically realistic muscle actuation. Internal forces and couples exerted by all major muscle groups are considered. An energy-shaping control method is described to coordinate muscle activity so as to grasp and reach in three-dimensional space. Key contributions of this article are as follows: (i) modelling of major muscle groups to elicit three-dimensional movements; (ii) a mathematical formulation for muscle activations based on a stored energy function; and (iii) a computationally efficient procedure to design task-specific equilibrium configurations, obtained by solving an optimization problem in the Special Euclidean group $\text{SE}\left(3\right)$. Muscle controls are then iteratively computed based on the co-state variable arising from the solution of the optimization problem. The approach is numerically demonstrated in the physically accurate software environmentElastica. Results of numerical experiments mimicking observed octopus behaviours are reported.