Energy-shaping control of a muscular octopus arm moving in three dimensions

Heng-Sheng Chang, Udit Halder, Chia-Hsien Shih, Noel Naughton, Mattia Gazzola, Prashant G. Mehta

Research output: Contribution to journalArticlepeer-review


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 SE(3). 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 environment Elastica. Results of numerical experiments mimicking observed octopus behaviours are reported.

Original languageEnglish (US)
Article number20220593
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2270
StatePublished - Feb 22 2023


  • Hamiltonian systems
  • Cosserat rod
  • soft robotics
  • energy-shaping control
  • octopus

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering
  • General Physics and Astronomy


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