A neural network-based framework is developed and experimentally demonstrated for the problem of estimating the shape of a soft continuum arm (SCA) from noisy measurements of the pose at a finite number of locations along the length of the arm. The neural network takes as input these measurements and produces as output a finite-dimensional approximation of the strain, which is further used to reconstruct the infinite-dimensional smooth posture. This problem is important for various soft robotic applications. It is challenging due to the flexible aspects that lead to the infinite-dimensional reconstruction problem for the continuous posture and strains. Because of this, past solutions to this problem are computationally intensive. The proposed fast smooth reconstruction method is shown to be five orders of magnitude faster while having comparable accuracy. The framework is evaluated on two testbeds: a simulated octopus muscular arm and a physical BR2 pneumatic soft manipulator.

Continuum robotic grasping, inspired by biological appendages such as octopus arms and elephant trunks, provides a versatile and adaptive approach to object manipulation. Unlike conventional rigid-body grasping, continuum robots leverage distributed compliance and whole-body contact to achieve robust and dexterous grasping. This paper presents a control-theoretic framework for analyzing the statics of continuous contact with a planar object. The governing equations of static equilibrium of the object are formulated as a linear control system, where the distributed contact forces act as control inputs. To optimize the grasping performance, a constrained optimal control problem is posed to minimize contact forces required to achieve a static grasp, with solutions derived using the Pontryagin Maximum Principle. Furthermore, two optimization problems are introduced: (i) for assigning a measure to the quality of a particular grasp, which generalizes a (rigid-body) grasp quality metric in the continuum case, and (ii) for finding the best grasping configuration that maximizes the continuum grasp quality. Several numerical results are also provided to elucidate our methods.

In this article, a biophysically realistic model of a soft octopus arm with internal musculature is presented. The modeling is motivated by experimental observations of sensorimotor control where an arm localizes and reaches a target. Major contributions of this article are: (i) development of models to capture the mechanical properties of arm musculature, the electrical properties of the arm peripheral nervous system (PNS), and the coupling of PNS with muscular contractions; (ii) modeling the arm sensory system, including chemosensing and proprioception; and (iii) algorithms for sensorimotor control, which include a novel feedback neural motor control law for mimicking target-oriented arm reaching motions, and a novel consensus algorithm for solving sensing problems such as locating a food source from local chemical sensory information (exogenous) and arm deformation information (endogenous). Several analytical results, including rest-state characterization and stability properties of the proposed sensing and motor control algorithms, are provided. Numerical simulations demonstrate the efficacy of our approach. Qualitative comparisons against observed arm rest shapes and target-oriented reaching motions are also reported.

Muscular hydrostats, such as octopus arms or elephant trunks, lack bones entirely, endowing them with exceptional dexterity and reconfigurability. Key to their unmatched ability to control nearly infinite degrees of freedom is the architecture into which muscle fibers are weaved. Their arrangement is, effectively, the instantiation of a sophisticated mechanical program that mediates, and likely facilitates, the control and realization of complex, dynamic morphological reconfigurations. Here, by combining medical imaging, biomechanical data, live behavioral experiments, and numerical simulations, an octopus-inspired arm made of [Formula: see text]200 continuous muscle groups is synthesized, exposing "mechanically intelligent" design and control principles broadly pertinent to dynamics and robotics. Such principles are mathematically understood in terms of storage, transport, and conversion of topological quantities, effected into complex 3D motions via simple muscle activation templates. These are in turn composed into higher-level control strategies that, compounded by the arm's compliance, are demonstrated across challenging manipulation tasks, revealing surprising simplicity and robustness.

ABSTRACT In this report, passive elasticity properties of Octopus rubescens arm tissue are investigated using a multidisciplinary approach encompassing biomechanical experiments, computational modeling, and analyses. Tensile tests are conducted to obtain stress–strain relationships of the arm under axial stretch. Rheological tests are also performed to probe the dynamic shear response of the arm tissue. Based on these tests, comparisons against three different viscoelasticity models are reported.

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 groupSE(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 environmentElastica. Results of numerical experiments mimicking observed octopus behaviours are reported.

Inspired by the unique neurophysiology of the octopus, a hierarchical framework is proposed that simplifies the coordination of multiple soft arms by decomposing control into high‐level decision‐making, low‐level motor activation, and local reflexive behaviors via sensory feedback. When evaluated in the illustrative problem of a model octopus foraging for food, this hierarchical decomposition results in significant improvements relative to end‐to‐end methods. Performance is achieved through a mixed‐modes approach, whereby qualitatively different tasks are addressed via complementary control schemes. Herein, model‐free reinforcement learning is employed for high‐level decision‐making, while model‐based energy shaping takes care of arm‐level motor execution. To render the pairing computationally tenable, a novel neural network energy shaping (NN‐ES) controller is developed, achieving accurate motions with time‐to‐solutions 200 times faster than previous attempts. The hierarchical framework is then successfully deployed in increasingly challenging foraging scenarios, including an arena littered with obstacles in 3D space, demonstrating the viability of the approach.

Avian flocks display a wide variety of flight behaviors, including steady directed translation of center of mass, rapid change of overall morphology, re-shuffling of positions of individuals within a persistent form, etc. These behaviors may be viewed as flock-scale strategies, emerging from interactions between individuals, accomplishing some collective adaptive purpose such as finding a roost, or mitigating the danger from predator attacks. While we do not conceive the flock as a single cognitive agent, the moment-to-moment decisions of individuals, influenced by their neighbors, appear as if to realize collective strategies that are cognizant of purpose. In this paper, we identify the actions of the flock as allocation of energetic resources, and thereby associate a cognitive cost to behavior. Our notion of cognitive cost reflects the burden arising from rapid re-allocation of resource. Using a recently developed natural geometric approach to kinetic energy allocation, we map the flock behavior to a temporal signature on the standard (probability) simplex. Given the signature of a flocking event, we calculate the cognitive cost as a solution to an optimal control problem based on a game-theoretic model. Alternatively, one can associate to a signature an entropic cost. These two cost measures, when applied to data on starling flocks, show a consistent spread in value across events, and we suggest the possibility that higher cost may arise from predator attacks.

Muscular hydrostats, such as octopus arms or elephant trunks, lack bones entirely, endowing them with exceptional dexterity and reconfigurability. Key to their unmatched ability to control nearly infinite degrees of freedom is the architecture into which muscle fibers are weaved. Their arrangement is, effectively, the instantiation of a sophisticated mechanical program that mediates, and likely facilitates, the control and realization of complex, dynamic morphological reconfigurations. Here, by combining medical imaging, biomechanical data, live behavioral experiments and numerical simulations, we synthesize a model octopus arm entailing ~200 continuous muscles groups, and begin to unravel its complexity. We show how 3D arm motions can be understood in terms of storage, transport, and conversion of topological quantities, effected by simple muscle activation templates. These, in turn, can be composed into higher-level control strategies that, compounded by the arm's compliance, are demonstrated in a range of object manipulation tasks rendered additionally challenging by the need to appropriately align suckers, to sense and grasp. Overall, our work exposes broad design and algorithmic principles pertinent to muscular hydrostats, robotics, and dynamics, while significantly advancing our ability to model muscular structures from medical imaging, with potential implications for human health and care.

The octopus arm is a neuromechanical system that involves a complex interplay between peripheral nervous system (PNS) and arm musculature. This makes the arm capable of carrying out rich maneuvers. In this paper, we build a model for the PNS and integrate it with a muscular soft octopus arm. The proposed neuromuscular architecture is used to qualitatively reproduce several biophysical observations in real octopuses, including curled rest shapes and target-directed arm reaching motions. Two control laws are proposed for target-oriented arm motions, and their performance is compared against a benchmark. Several analytical results, including rest-state characterization and stability properties of the proposed control laws, are provided.

The main contribution of this paper is a novel sensory feedback control law for an octopus arm. The control law is inspired by, and helps integrate, several observations made by biologists. The proposed control law is distinct from prior work which has mainly focused on open-loop control strategies. Several analytical results are described including characterization of the equilibrium and its stability analysis. Numerical simulations demonstrate life-like motion of the soft octopus arm, qualitatively matching behavioral experiments. Quantitative comparison with bend propagation experiments helps provide the first explanation of such canonical motion using a sensory feedback control law. Several remarks are included that help draw parallels with natural pursuit strategies such as motion camouflage or classical pursuit.

This paper is concerned with the problem of estimating (interpolating and smoothing) the shape (pose and the six modes of deformation) of a slender flexible body from multiple camera measurements. This problem is important in both biology, where slender, soft, and elastic structures are ubiquitously encountered across species, and in engineering, particularly in the area of soft robotics. The proposed mathematical formulation for shape estimation is physics-informed, based on the use of the special Cosserat rod theory whose equations encode slender body mechanics in the presence of bending, shearing, twisting and stretching. The approach is used to derive numerical algorithms which are experimentally demonstrated for fiber reinforced and cable-driven soft robot arms. These experimental demonstrations show that the methodology is accurate (<5 mm error, three times less than the arm diameter) and robust to noise and uncertainties.

Bend propagation in an octopus arm refers to a stereotypical maneuver whereby an octopus pushes a bend (localized region of large curvature) from the base to the tip of the arm. Bend propagation arises from the complex interplay between mechanics of the flexible arm, forces generated by internal muscles, and environmental effects (buoyancy and drag) from the surrounding fluid. In part due to this complexity, much of prior modeling and analysis work has relied on the use of high dimensional computational models. The contribution of this paper is to present a control-oriented reduced order model based upon a novel parametrization of the curvature of the octopus arm. The parametrization is motivated by the experimental results. The reduced order model is related to and derived from a computational model which is also presented. The results from the two sets of models are compared using numerical simulations which is shown to lead to useful qualitative insights into bend propagation. A comparison between the reduced order model and experimental data is also reported.

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.

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 experimentally observed behaviors.

This paper entails the application of the energy shaping methodology to control a flexible, elastic Cosserat rod model. Recent interest in such continuum models stems from applications in soft robotics, and from the growing recognition of the role of mechanics and embodiment in biological control strategies: octopuses are often regarded as iconic examples of this interplay. The dynamics of the Cosserat rod, here modeling a single octopus arm, are treated as a Hamiltonian system and the internal muscle actuators are modeled as distributed forces and couples. The proposed energy shaping control design procedure involves two steps: (1) a potential energy is designed such that its minimizer is the desired equilibrium configuration; (2) an energy shaping control law is implemented to reach the desired equilibrium. By interpreting the controlled Hamiltonian as a Lyapunov function, asymptotic stability of the equilibrium configuration is deduced. The energy shaping control law is shown to require only the deformations of the equilibrium configuration. A forward-backward algorithm is proposed to compute these deformations in an online iterative manner. The overall control design methodology is implemented and demonstrated in a dynamic simulation environment. Results of several bio-inspired numerical experiments involving the control of octopus arms are reported.

This work considers the problem of minimizing the path-curvature of a unicycle moving between two configurations in SE(2) with free final time. The problem is posed as an optimal control problem and the necessary conditions are derived using the Pontryagin Maximum Principle and Lie-Poisson reduction. Solutions are categorized into three cases corresponding to the value of the Casimir. A numerical solver for obtaining the optimal control is described. Experimental results are reported on a ground robot.

In this paper we investigate a model of two agents (self-steering particles) engaged in a dyadic interaction, with one pursuing the other using a constant bearing strategy. The pursued agent is controlled independently. Analysis of this interaction shows that the dynamics on the joint state space of the two agents restricts to an invariant manifold in shape space, and shares certain features in common with the Kepler problem. This model is applied to the task of tracking a stationary beacon with the practical constraint of using a sensor with a limited field of view (FOV). An effective solution to this problem is derived using the preceding analysis, and demonstrated in a laboratory implementation on a robot equipped with a Kinect vision sensor. Essential to this solution is the augmentation of the pursuit strategy (and associated feedback law) by an odometry-driven estimator when the beacon falls outside of the FOV.

Drawing inspiration from flight behavior in biological settings (e.g. territorial battles in dragonflies, and flocking in starlings), this paper demonstrates two strategies for coverage and flocking. Using earlier theoretical studies on mutual motion camouflage, an appropriate steering control law for area coverage has been implemented in a laboratory test-bed equipped with wheeled mobile robots and a Vicon high speed motion capture system. The same test-bed is also used to demonstrate another strategy (based on local information), termed topological velocity alignment, which serves to make agents move in the same direction. The present work illustrates the applicability of biological inspiration in the design of multi-agent robotic collectives.

In this paper, we propose a frequency domain based model-free gait recognition approach from silhouette inputs using Fourier Transform. Gait sequences are first converted into frequency domain using Fourier transform. Information content of the frequency components are analysed next to determine the number of effective frequencies which can help in the recognition process. These principal frequencies are treated separately to obtain scores based on the correlation coefficient between the gallery and the probe images. The individual scores are fused in the last stage to obtain the final score. The proposed approach is compared with other state-of-the-art model-free gait recognition algorithms. Experimental results on the USF HumanID database clearly indicate the supremacy of our technique.