Energy Shaping Control of a CyberOctopus Soft Arm

Chang, Heng-Sheng; Halder, Udit; Shih, Chia-Hsien; Tekinalp, Arman; Parthasarathy, Tejaswin; Gribkova, Ekaterina; Chowdhary, Girish; Gillette, Rhanor; Gazzola, Mattia; Mehta, Prashant G.

doi:10.48550/arxiv.2004.05747

Cited by 3 publications

(8 citation statements)

References 28 publications

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“…The cross sectional area and the second moment of area are given by A = πφ 2 4 and I = A 2 4π . Parameters like moduli of elasticity are taken from [16]. Simulation parameters are tabulated in Table I.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…The dynamics of a soft arm are modeled using the Cosserat rod theory [14]- [16]. The internal muscle forces and couples, when considered as control inputs, give rise to a control system in an infinite-dimensional state space setting.…”

Section: B Contributionsmentioning

confidence: 99%

“…A quadratic stored energy function, which leads to a linear stress-strain relationship, is used in this work. The total energy function or the Hamiltonian H(q, p) := T (p) + V(q) yields the Hamilton's equations of the rod dynamics in the classical Cosserat theory [14], [16].…”

Section: A Dynamic Modeling Of An Arm As a Cosserat Rodmentioning

confidence: 99%

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Optimal Control of a Soft CyberOctopus Arm

Wang¹,

Halder²,

Chang³

et al. 2021

2021 American Control Conference (ACC)

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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 behaviors, 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 captured by 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.

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Section: Simulation Resultsmentioning

confidence: 99%

Section: B Contributionsmentioning

confidence: 99%

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Optimal Control of a Soft CyberOctopus Arm

Wang¹,

Halder²,

Chang³

et al. 2021

2021 American Control Conference (ACC)

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“…Indeed, given a boundary condition and deformations, ( 1) is integrated to obtain the static equilibrium. In our prior work [18], this motivated the following model of desired potential energy…”

Section: A Single Arm Modeled As a Cosserat Rodmentioning

confidence: 99%

“…. , N obs (4) The problem represents a modification of the intrinsic potential energy of the rod to include additional control task specific terms: the terminal cost function Φ tip penalizes the distance between the arm tip and a given target q * ∈ R 3 , Φ grasp is chosen to achieve a grasping task, parameters µ tip and µ grasp are designed according to the objective, the inequalities Ψ j < 0 represent obstacles in the environment (see [18] for more details including several bio-inspired examples).…”

Section: A Single Arm Modeled As a Cosserat Rodmentioning

confidence: 99%

Controlling a CyberOctopus Soft Arm with Muscle-like Actuation

Chang

Halder

Gribkova

et al. 2021

2021 60th IEEE Conference on Decision and Control (CDC)

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This paper entails the application of the energy shaping methodology to control a flexible, elastic Cosserat rod model of a single octopus arm. The principal focus and novel contribution of this work is two-fold: (i) reduced order controloriented modeling of the realistic internal muscular architecture in an octopus arm; and (ii) incorporation of such models into the energy shaping methodology, extending our prior work by formally accounting for muscle constraints. Extension of the control scheme to the under-actuated muscle control case involves two steps: (i) design of a desired potential energy function whose static minimizer solves a given control task; and (ii) implementing the resulting energy shaping control input into the dynamic model. Due to the muscle actuator constraints, the desired potential energy function may not be arbitrarily chosen. Indeed, the desired energy must now satisfy a partial differential equation, known as the matching condition, which is derived for the infinite dimensional Hamiltonian control system. A particular solution to those matching conditions is described, paving the way to the application of energy shaping methodology. The overall control design methodology including muscle models is implemented and demonstrated in a dynamic simulation environment. Results of several bio-inspired numerical experiments involving the control of octopus arms are reported.

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Elastica: A compliant mechanics environment for soft robotic control

Naughton¹,

Sun²,

Tekinalp³

et al. 2020

Preprint

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Soft robots are notoriously hard to control. This is partly due to the scarcity of models able to capture their complex continuum mechanics, resulting in a lack of control methodologies that take full advantage of body compliance. Currently available simulation methods are either too computational demanding or overly simplistic in their physical assumptions, leading to a paucity of available simulation resources for developing such control schemes. To address this, we introduce Elastica, a free, open-source simulation environment for soft, slender rods that can bend, twist, shear and stretch. We demonstrate how Elastica can be coupled with five state-of-the-art reinforcement learning algorithms to successfully control a soft, compliant robotic arm and complete increasingly challenging tasks.

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Energy Shaping Control of a CyberOctopus Soft Arm

Cited by 3 publications

References 28 publications

Optimal Control of a Soft CyberOctopus Arm

Optimal Control of a Soft CyberOctopus Arm

Controlling a CyberOctopus Soft Arm with Muscle-like Actuation

Elastica: A compliant mechanics environment for soft robotic control

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