Optimal Control of a Soft CyberOctopus Arm

TL;DR

This paper develops an optimal control framework for a flexible robotic arm modeled after octopus limbs, using Cosserat rod theory and numerical methods to replicate biologically inspired movement patterns.

Contribution

It introduces a novel optimal control approach for continuum robotic arms based on Cosserat rod theory and Hamiltonian control systems, with numerical solutions for movement optimization.

Findings

Trajectories minimizing control effort are successfully generated.

The framework qualitatively replicates observed octopus arm behaviors.

Numerical methods enable simulation of complex continuum manipulator dynamics.

Abstract

In this paper, we use the optimal control methodology to control a flexible, elastic Cosserat rod. An inspiration comes from stereotypical movement patterns in octopus arms, which are observed in a variety of manipulation tasks, such as reaching or fetching. To help uncover the mechanisms underlying these observed morphologies, we outline an optimal control-based framework. A single octopus arm is modeled as a Hamiltonian control system, where the continuum mechanics of the arm is modeled after the Cosserat rod theory, and internal, distributed muscle forces and couples are considered as controls. First order necessary optimality conditions are derived for an optimal control problem formulated for this infinite dimensional system. Solutions to this problem are obtained numerically by an iterative forward-backward algorithm. The state and adjoint equations are solved in a dynamic simulation environment, setting the stage for studying a broader class of optimal control problems. Trajectories that minimize control effort are demonstrated and qualitatively compared with observed behaviors.