[Paper Review] Controlling a CyberOctopus Soft Arm with Muscle-like Actuation

Heng-Sheng Chang, Udit Halder+5 more|arXiv (Cornell University)|Oct 2, 2020

Soft Robotics and Applications31 references4 citations

TL;DR

This paper presents a novel energy-shaping control framework for a soft robotic octopus arm modeled as a Cosserat rod with muscle-like actuation. By modeling muscle forces through a stored energy function inspired by nonlinear elasticity, the method bypasses complex matching conditions in energy shaping control, enabling stable reaching and grasping via bilevel optimization. The approach successfully simulates biologically realistic arm motions in Elastica.

ABSTRACT

This paper presents an application of the energy shaping methodology to control a flexible, elastic Cosserat rod model of a single octopus arm. The novel contributions of this work are two-fold: (i) a control-oriented modeling of the anatomically realistic internal muscular architecture of an octopus arm; and (ii) the integration of these muscle models into the energy shaping control methodology. The control-oriented modeling takes inspiration in equal parts from theories of nonlinear elasticity and energy shaping control. By introducing a stored energy function for muscles, the difficulties associated with explicitly solving the matching conditions of the energy shaping methodology are avoided. The overall control design problem is posed as a bilevel optimization problem. Its solution is obtained through iterative algorithms. The methodology is numerically implemented and demonstrated in a full-scale dynamic simulation environment Elastica. Two bio-inspired numerical experiments involving the control of octopus arms are reported.

Motivation & Objective

• To develop a control-oriented model of the octopus arm’s longitudinal, transverse, and oblique muscles for use in robotic control.
• To integrate anatomically accurate muscle mechanics into the energy shaping control framework for soft robotic manipulation.
• To solve the challenge of matching conditions in energy shaping by modeling conservative muscle forces via a stored energy function.
• To enable stable, task-specific motion control (e.g., reaching, grasping) through bilevel optimization of muscle activation.
• To validate the control methodology in a full-scale dynamic simulation using the Elastica platform.

Proposed method

• Model the octopus arm as a planar Cosserat rod with variable cross-section and rest length $L_0 = 20$ cm, using $\nu_1^\circ = 1$, $\nu_2^\circ = 0$, $\kappa^\circ = 0$.
• Represent muscle forces using a stored energy function derived from Hill’s muscle model and nonlinear elasticity theory, avoiding explicit solution of matching conditions.
• Formulate the control problem as a bilevel optimization: the upper level optimizes muscle activation, the lower level enforces equilibrium via optimal control necessary conditions.
• Use the maximum principle to derive necessary conditions for optimality and design iterative algorithms for numerical solution.
• Simulate the full dynamics in Elastica with $N_d = 100$ discrete elements and $\Delta t = 10^{-5}$ s.
• Design task-specific cost functions: $\Phi_{\text{tip}} = \frac{1}{2}|r^* - r(L_0)|^2$ for reaching, and $\Phi_{\text{grasp}} = \text{dist}(\Omega, r(s))$ with $\mu_{\text{grasp}} = 10^5 \chi_{[0.4L_0, L_0]}(s)$ for grasping.

Experimental results

Research questions

• RQ1 Can a stored energy function for muscles effectively replace explicit matching conditions in energy shaping control for soft robots?
• RQ2 How can anatomically accurate longitudinal and transverse muscle architectures be modeled for control in a Cosserat rod framework?
• RQ3 Can bilevel optimization with necessary conditions from optimal control yield stable, task-specific motion in a soft robotic arm?
• RQ4 How does the integration of muscle mechanics affect the stability and performance of reaching and grasping tasks in simulation?
• RQ5 Can the control framework handle both point-target reaching and obstacle-avoiding grasping without penetration?

Key findings

• The stored energy function approach successfully bypassed the need to solve complex matching conditions in energy shaping control, enabling stable control design.
• The bilevel optimization framework with maximum principle-based necessary conditions yielded convergent iterative algorithms for muscle activation.
• In the reaching experiment, the arm achieved target positions with $\mu_{\text{tip}} = 10^5$, demonstrating effective tip positioning without angle constraints.
• In the grasping experiment, the distal 60% of the arm ($s \geq 0.4L_0$) wrapped around a spherical object without penetration, as enforced by $\mu_{\text{grasp}} = 10^5$ and inequality constraints.
• The simulation results in Elastica confirmed that constant muscle controls stabilize the rod equilibrium, validating the energy-shaping approach.
• The method successfully integrated muscle mechanics into a Hamiltonian framework, enabling complex manipulation tasks in a soft robotic system.