Optimal Control for CyberOctopus Arm
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Flexible octopus arms can achieve a rich repertoire of deformations – stretch, shear, bend, and twist. However, despite their virtually infinite degrees of freedom – and thus having many options to carry out a single task – octopuses are observed to engage in certain (task-specific) stereotypical movement strategies. In experimental studies, these strategies are broadly categorized into two groups: reaching with bend propagation and fetching with pseudo-joints. We systematically investigate the potential optimality bases of these stereotypical movement strategies.
Dynamic Model - Cosserat Rod
The dynamics of a soft arm are modeled using the Cosserat rod theory. The system is a Hamiltonian system with the Hamiltonian being the total energy, the kinetic energy and potential energy. Then the dynamics are described by the Hamilton’s equations, six PDEs in total. Internal muscle forces and couples, when considered as control inputs, give rise to a control system in an infinite-dimensional state space setting.
Optimal Control Methodology - Maximum Principle
The Pontryagin’s Maximum Principle (PMP) is used to derive the six adjoint PDEs for the costate variables. The resulting two-point boundary value problem is numerically solved in an iterative manner, referred to here as the forward-backward algorithm. A custom solver is implemented to simulate the backward path or the costate equations. The control is updated in the direction of the steepest gradient ascent so as maximize the pre-Hamiltonian.
Simulation Results
Reaching task:
iteration 2/20
iteration 6/20
iteration 12/20
iteration 20/20
Fetching task:
Shooting task:
Publication
T. Wang, U. Halder, H.S. Chang, M. Gazzola, and P.G., Mehta, "Optimal control of a soft cyberoctopus arm," in 2021 American Control Conference (ACC). IEEE, 2021, pp. 4757-4764. [DOI] (Presentation) (Poster)
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