Infinite Degrees Of Freedom Research Articles

Modern Approaches in Domestic Psychology: Unity in Diversity

A brief result of the analysis of modern approaches undertaken within the framework of the collective monograph “Scientific approaches in modern domestic psychology” (M., 2023) is presented. 27 chapters (of different approaches) were divided into general psychological (developing within psychological science), general scientific approaches in psychology (interdisciplinary, resource, environmental, network, etc.), specific psychological in the field of psychology (personality psychology, social psychology, speech psychology, professional activities, etc.) and scientific approaches in applied psychology. Four options for comparisons are considered: the possibility of integration (V.A. Mazilov, V.A. Yanchuk) or comparison of scientific approaches (E.A. Sergienko, A.V. Yurevich). Based on the analysis, guidelines were proposed in an attempt to present the space of psychological science as differentiated by different approaches, and interconnected through the openness of borders and the flexibility of conceptual structures. The leading concepts, specifying concepts, methodological principles and leading methods of approaches are identified. all four groups demonstrate interconnections and complementarities in the understanding of nature, multidetermination of the psyche, and the ability to solve new and complex problems on their basis. Many approaches incorporate concepts and principles of other approaches in psychology. General scientific approaches have generated not only new concepts in psychology (interdisciplinarity, psychological resources), but also new methodological principles. I would like to emphasize that the analysis demonstrated a significant expansion of the methodological principles of psychological sciences, which are explicit not only in general psychological and general scientific, but also specific scientific approaches. The principles of interdisciplinarity, uncertainty, anticipation, subjectivity, evolution, multi-determination and self-development were justified, along with confirmation of the principles of systematicity, the unity of consciousness and activity, the unity of being and consciousness. But even the principles traditional for psychology are filled with new content, excluding determinism, which fetters a person by universal laws, and indeterminism, where a person is lost in infinite degrees of freedom. The author’s approach to the analysis of scientific approaches in psychology is an attempt to compare them and highlight trends in the development of methodology, which involves discussions and discussions, new solutions, new analysis possibilities, which is necessary for the development of our science and the implementation of the idea of the opponent circle.

Topology, dynamics, and control of a muscle-architected soft arm

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.

Model-less optimal visual control of tendon-driven continuum robots using recurrent neural network-based neurodynamic optimization

Tendon-driven continuum robots (TDCRs) have infinite degrees of freedom and high flexibility, posing challenges for accurate modeling and autonomous control, especially in confined environments. This paper presents a model-less optimal visual control (MLOVC) method using neurodynamic optimization to enable autonomous target tracking of TDCRs in confined environments. The TDCR’s kinematics are estimated online from sensory data, establishing a connection between the actuator input and visual features. An optimal visual servoing method based on quadratic programming (QP) is developed to ensure precise target tracking without violating the robot’s physical constraints. An inverse-free recurrent neural network (RNN)-based neurodynamic optimization method is designed to solve the complex QP problem. Comparative simulations and experiments demonstrate that the proposed method outperforms existing methods in target tracking accuracy and computational efficiency. The RNN-based controller successfully achieves target tracking within constraints in confined environments.

Vision‐Based Online Key Point Estimation of Deformable Robots

The precise control of soft and continuum robots requires knowledge of their shape, which has, in contrast to classical rigid robots, infinite degrees of freedom. To partially reconstruct the shape, proprioceptive techniques use built‐in sensors, resulting in inaccurate results and increased fabrication complexity. Exteroceptive methods so far rely on expensive tracking systems with reflective markers placed on all components, which are infeasible for deformable robots interacting with the environment due to marker occlusion and damage. Here, a regression approach is presented for three‐dimensional key point estimation using a convolutional neural network. The proposed approach uses data‐driven supervised learning and is capable of online markerless estimation during inference. Two images of a robotic system are captured simultaneously at 25 Hz from different perspectives and fed to the network, which returns for each pair the parameterized key point or piecewise constant curvature shape representations. The proposed approach outperforms markerless state‐of‐the‐art methods by a maximum of 4.5% in estimation accuracy while being more robust and requiring no prior knowledge of the shape. Online evaluations on two types of soft robotic arms and a soft robotic fish demonstrate the method's accuracy and versatility on highly deformable systems.

A comprehensive dynamic model and configuration control of a free-floating soft manipulator-spacecraft system

Space robots are inseparable components of many space missions. However, capabilities of space robots with rigid manipulators are restricted in confronting with unknown and confined environments and situations require high safety. To overcome these defects, the potential of bio-inspired soft robots for space applications has recently been addressed in the literature. Dynamic modeling and control of soft manipulators are challenging due to their infinite degrees of freedom. In this paper, a general comprehensive three-dimensional dynamic modeling framework is developed for a floating soft manipulator-spacecraft system employing the Euler-Lagrange method. This framework derives the coupled equations of motion adapting the generalized Jacobian approach. Consequently, the opportunity of exploiting model-based control methods will be provided. In addition, the proposed model avoids numerical singularities once the bending angles are near zero. Furthermore, the generalized Jacobian matrix is defined for any arbitrary point of the soft manipulator essential for the contact dynamics. Eventually, to verify the proposed dynamic modeling procedure, the dynamic response of a floating soft manipulator-spacecraft system released from an initial configuration is investigated. Then, a sliding mode controller is designed for the floating soft manipulator to track the desired shape and compared to the proportional-derivative control scheme. The obtained results follow the physical principles and fulfill the control objective.

Pressure-Based Soft Agents.

Biological agents have bodies that are composed mostly of soft tissue. Researchers have resorted to soft bodies to investigate Artificial Life (ALife)-related questions; similarly, a new era of soft-bodied robots has just begun. Nevertheless, because of their infinite degrees of freedom, soft bodies pose unique challenges in terms of simulation, control, and optimization. Herein I propose a novel soft-bodied agents formalism, namely, pressure-based soft agents (PSAs): spring-mass membranes containing a pressurized medium. Pressure endows the agents with structure, while springs and masses simulate softness and allow the agents to assume a large gamut of shapes. PSAs actuate both locally, by changing the resting lengths of springs, and globally, by modulating global pressure. I optimize the controller of PSAs for a locomotion task on hilly terrain, an escape task from a cage, and an object manipulation task. The results suggest that PSAs are indeed effective at the tasks, especially those requiring a shape change. I envision PSAs as playing a role in modeling soft-bodied agents, such as soft robots and biological cells.

Planar soft space robotic manipulators: Dynamic modeling and control

Space robots have proven their ability to accomplish many space missions impossible or dangerous for the human. However, the conventional space robots suffer from the low adaptability, heavy structures, and the low safety. In this regard, the bio-inspired soft robots, composed of the soft material, have been emerged to overcome these shortcomings and to expand the space missions’ diversity. The potential of soft robots for space applications has recently been investigated in the literature. Although the dynamic modeling and control of soft robotic arms are complicated due to their infinite degrees of freedom, soft manipulators are anticipated to provide the adaptive capture of targets, confined space operations, and the long-distance handling of space facilities. In this regard, a general novel dynamic modeling algorithm is presented here for soft space robotic manipulators (SSRM) in a specified orientation based on the generalized Jacobian method. The proposed algorithm could be employed for different numbers of soft manipulator constant-curvature elements and avoids numerical singularities using the Taylor expansion as well. In addition, the generalized Jacobian matrix is defined to compute the velocity of any arbitrary point on the soft manipulator for contact dynamics objectives. Accuracy of the proposed dynamic model has been verified via comparison to the simulation results of the existing fixed-base soft manipulators. Moreover, performance of the proposed model has been more investigated through two numerical simulation case studies. The first case verifies that the dynamic responses of the floating SSRM follows the physical principles. While the second one addresses the configuration tracking problem of the floating SSRM exposing a computed torque control scheme. The obtained results indicate the effectiveness of the presented dynamic modeling algorithm and the proposed control scheme.

Kinematics, dynamics and control of stiffness-tunable soft robots

Modeling and control methods for stiffness-tunable soft robots (STSRs) have received less attention compared to standard soft robots. A major challenge in controlling STSRs is their infinite degrees of freedom, similar to standard soft robots. In this paper, demonstrate a novel STSR by combing a soft-rigid hybrid spine-mimicking actuator with a stiffness-tunable module. Additionally, we introduce a new kinematic and dynamic modeling methodology for the proposed STSR. Based on the STSR characteristics, we model it as a series of PRP segments, each composed of two prismatic joints(P) and one revolute joint(R). This method is simpler, more generalizable, and more computationally efficient than existing approaches. We also design a multi-input multi-output (MIMO) controller that directly adjusts the pressure of the STSR’s three pneumatic chambers to precisely control its posture. Both the novel modeling methodology and MIMO control system are implemented and validated on the proposed STSR prototype.

Dynamic Modeling of a Fluidic Soft Actuator: First Results Within a Fractional Approach

Dynamic modeling of soft actuators is a challenging field of research mainly due to the nonlinear properties of the materials they are made of, as well as the infinite degrees of freedom that they exhibit. In this paper, the defection of an eccentric soft fluidic actuator is characterized in terms of the dynamic displacement using both integer and fractional order (FO) models. The actuator, which is cylindrical in shape, is made of a silicone polymer called polydimethylsiloxane (PDMS) from a water-soluble mold and a rod that, when placed eccentrically, allows to create the internal chamber of the actuator. Experimental results are presented to show that the best fitting is obtained with FO models. In fact, the dynamics of the actuator can be fully described with a two-parameter model, namely a fractional integrator of order of about 1.2 with a gain.

Anisotropy in magnetic materials for sensors and actuators in soft robotic systems.

The field of soft intelligent robots has rapidly developed, revealing extensive potential of these robots for real-world applications. By mimicking the dexterities of organisms, robots can handle delicate objects, access remote areas, and provide valuable feedback on their interactions with different environments. For autonomous manipulation of soft robots, which exhibit nonlinear behaviors and infinite degrees of freedom in transformation, innovative control systems integrating flexible and highly compliant sensors should be developed. Accordingly, sensor-actuator feedback systems are a key strategy for precisely controlling robotic motions. The introduction of material magnetism into soft robotics offers significant advantages in the remote manipulation of robotic operations, including touch or touchless detection of dynamically changing shapes and positions resulting from the actuations of robots. Notably, the anisotropies in the magnetic nanomaterials facilitate the perception and response with highly selective, directional, and efficient ways used for both sensors and actuators. Accordingly, this review provides a comprehensive understanding of the origins of magnetic anisotropy from both intrinsic and extrinsic factors and summarizes diverse magnetic materials with enhanced anisotropy. Recent developments in the design of flexible sensors and soft actuators based on the principle of magnetic anisotropy are outlined, specifically focusing on their applicabilities in soft robotic systems. Finally, this review addresses current challenges in the integration of sensors and actuators into soft robots and offers promising solutions that will enable the advancement of intelligent soft robots capable of efficiently executing complex tasks relevant to our daily lives.

Rotitome-G: Principles and design concept of experimental compliant continuum robotic microsurgical endoscopic sarcotome for pixel/voxel-level target access neurosurgery

The practice of minimal access surgery is widely accepted, and it has become prevalent with improved endoscope design. The traditional microscope in neurosurgery is gradually being challenged by the neuro-endoscope for its direct co-axial vision and direct illumination of the deep set subcortical pathology. The conceptualized design of Rotitome-G is based on compliant continuum robotic system. The system is a biomimicry of muscular hydrostat anatomy of the elephant trunk, a plant tendril, and many similar structures in the animal world with an infinite degree of freedom. The article describes the functional anatomy of these structures and the extensor expansion of the human finger as applied to the construction and implementation of the Rotitome-G. This flexible microsurgical endoscope integral to its design has unique cutting tool versions and multiple assistive tools passed through single ‘target access’ burr hole aperture. It is navigable within the surgical space co-relative to the image space to increase precision and improve the volume of tumour resection. The current study is theoretical and further work is in progress to assess its surgical capabilities to bring it to the clinical arena.

Robust Position Control of a Continuum Manipulator Based on Selective Approach and Koopman Operator

Continuum manipulators have infinite degrees of freedom and high flexibility, making it challenging for accurate modeling and control. Some common modeling methods include mechanical modeling strategy, neural network strategy, constant curvature assumption, etc. However, the inverse kinematics of the mechanical modeling strategy is difficult to obtain while a strategy using neural networks may not converge in some applications. For algorithm implementation, the constant curvature assumption is used as the basis to design the controller. When the driving wire is tight, the linear controller under constant curvature assumption works well in manipulator position control. However, this assumption of linearity between the deformation angle and the driving input value breaks upon repeated use of the driving wires which get inevitably lengthened. This degrades the accuracy of the controller. In this work, the Koopman theory is proposed to identify the nonlinear model of the continuum manipulator. Under the linearized model, the control input is obtained through model predictive control (MPC). As the lifted function can affect the effectiveness of the Koopman operator-based MPC (K-MPC), a novel design method of the lifted function through the Legendre polynomial is proposed. To attain higher control efficiency and computational accuracy, a selective control scheme according to the state of the driving wires is proposed. When the driving wire is tight, the linear controller is employed; otherwise, the K-MPC is adopted. Finally, a set of static and dynamic experiments has been conducted using an experimental prototype. The results demonstrate high effectiveness and good performance of the selective control scheme.

Mechanisms of octopus arm search behavior without visual feedback

The octopus coordinates multiple, highly flexible arms with the support of a complex distributed nervous system. The octopus’s suckers, staggered along each arm, are employed in a wide range of behaviors. Many of these behaviors, such as foraging in visually occluded spaces, are executed under conditions of limited or absent visual feedback. In coordinating unseen limbs with seemingly infinite degrees of freedom across a variety of adaptive behaviors, the octopus appears to have solved a significant control problem facing the field of soft-bodied robotics. To study the strategies that the octopus uses to find and capture prey within unseen spaces, we designed and 3D printed visually occluded foraging tasks and tracked arm motion as the octopus attempted to find and retrieve a food reward. By varying the location of the food reward within these tasks, we can characterize how the arms and suckers adapt to their environment to find and capture prey. We compared these results to simulated experimental conditions performed by a model octopus arm to isolate the primary mechanisms driving our experimental observations. We found that the octopus relies on a contact-based search strategy that emerges from local sucker coordination to simplify the control of its soft, highly flexible limbs.

Control of soft robots with inertial dynamics.

Soft robots promise improved safety and capability over rigid robots when deployed near humans or in complex, delicate, and dynamic environments. However, infinite degrees of freedom and the potential for highly nonlinear dynamics severely complicate their modeling and control. Analytical and machine learning methodologies have been applied to model soft robots but with constraints: quasi-static motions, quasi-linear deflections, or both. Here, we advance the modeling and control of soft robots into the inertial, nonlinear regime. We controlled motions of a soft, continuum arm with velocities 10 times larger and accelerations 40 times larger than those of previous work and did so for high-deflection shapes with more than 110° of curvature. We leveraged a data-driven learning approach for modeling, based on Koopman operator theory, and we introduce the concept of the static Koopman operator as a pregain term in optimal control. Our approach is rapid, requiring less than 5 min of training; is computationally low cost, requiring as little as 0.5 s to build the model; and is design agnostic, learning and accurately controlling two morphologically different soft robots. This work advances rapid modeling and control for soft robots from the realm of quasi-static to inertial, laying the groundwork for the next generation of compliant and highly dynamic robots.

Investigating nonlinear forced vibration of functionally graded nanobeam based on the nonlocal strain gradient theory considering mechanical impact, electromagnetic actuator, thickness effect and nonlinear foundation

The present study proposes an investigation to nonlinear vibration response of a functionally graded (FG) nanobeam based on nonlocal strain gradient theory (NSGT) taking into consideration the longitudinal magnetic field and the thickness effect. The nonlinear terms from the governing equation are associated with the curvature of the nanobeam, the nonlinear foundation, the mean axial extension of the nanobeam and electromagnetic actuator for pinned-pinned nanobeam and the effect of discontinuities marked by the presence of the Dirac function (mechanical impact).The governing differential equation of motion and the boundary conditions are modeled within the framework of a simple supported Euler-Bernoulli nanobeam which accounts for the nonlinear von-Kármán strain and using so-called Hamilton's principle. To truncate the continuous system having an infinite degree of freedom, the Galerkin-Bubnov procedure is applied. The resulting nonlinear differential equation is studied by Optimal Auxiliary Functions Method. An explicit analytical solution is proposed for a complex problem near the primary resonance. Our proper procedure is a powerful tool to solve a nonlinear problem without presence of any small parameters. The main characteristic of our technique consists in the existence of some auxiliary functions derived from the expressions of the solution formed for initial linear equation and the form of nonlinear terms calculated for the solution of the linear equation. Also, the presence of some convergence-control parameters assures the rapid convergence of the solutions after only a single iteration. These parameters can be evaluated by means of some rigorous mathematical procedures. We have a large freedom to select the auxiliary functions and the number of convergence-control parameters. The proposed approach is proved to be very accurate, simple, and easy to implement for complicated nonlinear problems. The potential energy is analyzed in detail for different values of the parameters. The local stability of motion near the primary resonance is established using homotopy perturbation method.

Heat statistics in the relaxation process of the Edwards-Wilkinson elastic manifold.

The stochastic thermodynamics of systems with a few degrees of freedom has been studied extensively so far. We would like to extend the study to systems with more degrees of freedom and even further-continuous fields with infinite degrees of freedom. The simplest case for a continuous stochastic field is the Edwards-Wilkinson elastic manifold. It is an exactly solvable model of which the heat statistics in the relaxation process can be calculated analytically. The cumulants require a cutoff spacing to avoid ultraviolet divergence. The scaling behavior of the heat cumulants with time and the system size as well as the large deviation rate function of the heat statistics in the large size limit is obtained.

Quantum Associative Memory with a Single Driven-Dissipative Nonlinear Oscillator.

Algorithms for associative memory typically rely on a network of many connected units. The prototypical example is the Hopfield model, whose generalizations to the quantum realm are mainly based on open quantum Ising models. We propose a realization of associative memory with a single driven-dissipative quantum oscillator exploiting its infinite degrees of freedom in phase space. The model can improve the storage capacity of discrete neuron-based systems in a large regime and we prove successful state discrimination between n coherent states, which represent the stored patterns of the system. These can be tuned continuously by modifying the driving strength, constituting a modified learning rule. We show that the associative-memory capability is inherently related to the existence of a spectral separation in the Liouvillian superoperator, which results in a long timescale separation in the dynamics corresponding to a metastable phase.

Electrical Impedance Tomographic Shape Sensing for Soft Robots

With infinite degrees of freedom, soft robots are expected to achieve dexterous and complex tasks, but this also puts forward higher requirements for their sensing capabilities. An important sensing task in soft robots is sensing their own deformation and current shape. Currently, most of the existing soft shaping sensors are limited by local perception abilities, stretchability, and fabrication difficulties. We propose a sensing method based on Electrical Impedance Tomography (EIT), which reconstructs conductivity patterns distributed on a surface, by considering the deformation-caused resistance changes. Comparison between the theoretical and experimental patterns reveals that even though the quality of the pattern is affected by a large amount of noise, the considered features are still able to reflect the change of shape. With the help of neural networks, the pattern is decoded to the physical data related to the deformation. Detection of the planar shape changes and proprioception of a sensor-integrated soft robot are presented to exhibit the capability of our method. Results show that the detected error ratios are mostly under 5% and 3% for 2D and 3D conditions respectively.

Harnessing Nonuniform Pressure Distributions in Soft Robotic Actuators

Herein, complex motion in soft, fluid‐driven actuators composed of elastomer bladders arranged around a neutral plane and connected by slender tubes is demonstrated. Rather than relying on complex feedback control or multiple inputs, the motion is generated with a single pressure input, leveraging viscous flows within the actuator to produce nonuniform pressure between bladders. Using an accurate predictive model coupling with a large deformation Cosserat rod model and low‐Reynolds‐number flow, all dominating dynamic interactions including extension and curvature are captured with two governing equations. Given insights from this model, five design elements are described and demonstrated in practice. By choosing the relative timescales between the solid, fluid, and input pressure cycles, the tip of the actuator can obtain almost any desired trajectory and can be placed anywhere temporarily within its 2D workspace. Finally, the benefits of viscous‐driven soft actuators are showcased in a six‐legged untethered robot able to walk 0.05 body lengths per second. The foundation is laid for a new class of morphologically intelligent, soft robotic actuators that enables complex deformations and multifunctionality without explicit drivers; whereby generating nonuniform pressure distributions, their infinite degrees of freedom can be exploited.

DefGraspSim: Physics-Based Simulation of Grasp Outcomes for 3D Deformable Objects

Robotic grasping of 3D deformable objects (e.g., fruits/vegetables, internal organs, bottles/boxes) is critical for real-world applications such as food processing, robotic surgery, and household automation. However, developing grasp strategies for such objects is uniquely challenging. Unlike rigid objects, deformable objects have infinite degrees of freedom and require field quantities (e.g., deformation, stress) to fully define their state. As these quantities are not easily accessible in the real world, we propose studying interaction with deformable objects through physics-based simulation. As such, we simulate grasps on a wide range of 3D deformable objects using a GPU-based implementation of the corotational finite element method (FEM). To facilitate future research, we open-source our simulated dataset (34 objects, 1e5 Pa elasticity range, 6800 grasp evaluations, 1.1M grasp measurements), as well as a code repository that allows researchers to run our full FEM-based grasp evaluation pipeline on arbitrary 3D object models of their choice. Finally, we demonstrate good correspondence between grasp outcomes on simulated objects and their real counterparts.