Rigid Body Research Articles

Development of an Adaptive Force Control Strategy for Soft Robotic Gripping

Using soft materials in robotic mechanisms has become a common solution to overcome many challenges associated with the rigid bodies frequently used in robotics. Compliant mechanisms allow the robot to adapt to objects and perform a broader range of tasks, unlike rigid bodies that are generally designed for specific applications. However, soft robotics presents its own set of challenges in both design and implementation, particularly in sensing and control. These challenges are abundant when dealing with the force control problem of a compliant gripping mechanism. The ability to effectively regulate the applied force of a gripper is a critical task in many control operations, as it allows the precise manipulation of objects, which drives the need for enhanced force control strategies for soft or flexible grippers. Standard sensing techniques, such as motor current monitoring and strain-based sensors, add complexities and uncertainties when establishing mathematical models of soft grippers to the required gripping forces. In addition, the soft gripper creates a complex non-linear system, compounded by adding an adhesive-type sensor. This work develops a unique visual force sensor trained on synthetic data generated using finite element analysis (FEA) and implemented by integrating a non-linear model reference adaptive controller (MRAC) to control gripping force on a fixed 6-DOF robot. The robot can be placed on a mobile platform to perform various tasks. The virtual FEA sensor and controller, combined, are termed virtual reference adaptive control (VRAC). The VRAC was compared to other methods and achieved comparable control sensing and control performance while reducing the complexity of the sensor requirements and its integration. The VRAC strategy effectively controlled the gripping force by driving the dynamics to match the desired performance after a limited amount of training cycles. The controller proposed in this work was designed to be generally applicable to most objects that the gripper will interact with and easily adaptable to a wide variety of soft grippers.

Vibration mitigation of a model aircraft with high-aspect-ratio wings using two-dimensional nonlinear vibration absorbers

High-aspect-ratio (HAR) airplane wings have higher energy efficiency and present an economical alternative to standard airplane wings. HAR wings have a high span and a high lift-to-drag ratio, allowing the wing to require less thrust during flight. However, due to their length and construction, HAR wings exhibit low-frequency, high-amplitude vibrations in both vertical (yaw axis) and longitudinal (roll axis) directions. To combat these unwanted vibrations, a two-dimensional nonlinear vibration absorber (2D-NVA) is constructed and attached to a model HAR-wing airplane to verify its effectiveness at reducing vibrational motion. The 2D-NVA design, which was presented in a previous study, consists of two low-mass, rigid bodies namely the housing and the impactor. The housing consists of a ring-like rigid body in the shape of an ellipse, while the impactor is a solid cylindrical mass which resides inside the cavity of the housing. The 2D-NVA is designed such that the impactor can contact the inner surface of the housing under both impacts and constrained sliding motion. The present study focuses on the use of the 2D-NVA to mitigate multiple modes of vibration excited by impulsive loading of a model airplane with HAR wings in both vertical and longitudinal directions. The effectiveness of a single 2D-NVA is investigated computationally using a finite element model of the model airplane. These results are verified experimentally and the performance of two 2D-NVAs (one on each wing) is also investigated. The contributions of this work are that: 1) the 2D-NVA alters the global response of the model aircraft by mitigating all relevant modes in both directions simultaneously; 2) a single 2D-NVA is optimal for mitigating motion in the vertical direction, while two active 2D-NVAs are optimal for the longitudinal direction; and 3) the performance of the 2D-NVA is robust to changes in the frequency content of the parent structure.

Modeling the optimal deceleration for asymmetric rigid body motion under the influence of a gyrostatic moments and viscous friction

This study focuses on determining the required minimum-time (MT) for the spatial motion of a free rigid body (RB) experiencing gyrostatic moments (GMs) and viscous friction. The study assumes that the body’s center of mass coincides with the original point of two Cartesian systems of coordinates. An optimal control law for slow motion is established, and the corresponding time and phase pathways are analyzed. The innovative results are presented for two new cases through various graphs highlighting the positive effects of the GMs. A comparison is achieved between the obtained results and previous outcomes that did not consider gyrostatic moments, showing remarkable consistency with slight deviations that are discussed. The practical applications of this study, which limits itself to using gyroscopic theory to maintain the stability and balance of vehicles in which gyroscopes are used, as well as figuring out the trajectory of aircraft and marine vehicles, are what make it noteworthy.

A novel method for measuring three-axis dynamic centrifugal acceleration field: the matrix transformation method

Abstract When a three-axis dynamic centrifuge is used to test the performance of inertial equipment (accelerometer, gyroscope, gyro-accelerometer, etc.), accurate estimating of the acceleration at the sensing position of the tested sensors is a key step. To solve the problem of the lack of relevant suitable methods, first, the principle of rigid body kinematics is used to prove that the acceleration of each point on a rigid body changes linearly with respect to the position. Subsequently, a matrix transformation method for accurately measuring the acceleration field on the three-axis dynamic centrifuge is presented. In this method, the distribution law (expressed by a 3×3 matrix) of the acceleration field is calculated based on the measured acceleration at multiple positions. After that the acceleration estimation value at any point on the centrifuge can be calculated. Finally, the uncertainty of the estimated acceleration value is analysed, and a verification experiment is carried out. The results show that the accuracy of this method is mainly limited by the accuracy of the acceleration measurements. The preliminary verification experiment system shows that the mean deviation of the estimated value error obtained by this method is less than 0.024 g, the standard uncertainty is less than 0.015 g, the left and right endpoints of the 95% probability inclusion interval are less than -0.026 g and 0.036 g, respectively, and the half width of the interval is less than 0.028 g. In all, this paper provides a powerful tool for examining the precision performance of inertial equipment on a three-axis dynamic centrifuge, and can also be used for calibration of this kind of centrifuge.

Mechanistic insights into a heterobifunctional degrader-induced PTPN2/N1 complex

PTPN2 (protein tyrosine phosphatase non-receptor type 2, or TC-PTP) and PTPN1 are attractive immuno-oncology targets, with the deletion of Ptpn1 and Ptpn2 improving response to immunotherapy in disease models. Targeted protein degradation has emerged as a promising approach to drug challenging targets including phosphatases. We developed potent PTPN2/N1 dual heterobifunctional degraders (Cmpd-1 and Cmpd-2) which facilitate efficient complex assembly with E3 ubiquitin ligase CRL4CRBN, and mediate potent PTPN2/N1 degradation in cells and mice. To provide mechanistic insights into the cooperative complex formation introduced by degraders, we employed a combination of structural approaches. Our crystal structure reveals how PTPN2 is recognized by the tri-substituted thiophene moiety of the degrader. We further determined a high-resolution structure of DDB1-CRBN/Cmpd-1/PTPN2 using single-particle cryo-electron microscopy (cryo-EM). This structure reveals that the degrader induces proximity between CRBN and PTPN2, albeit the large conformational heterogeneity of this ternary complex. The molecular dynamic (MD)-simulations constructed based on the cryo-EM structure exhibited a large rigid body movement of PTPN2 and illustrated the dynamic interactions between PTPN2 and CRBN. Together, our study demonstrates the development of PTPN2/N1 heterobifunctional degraders with potential applications in cancer immunotherapy. Furthermore, the developed structural workflow could help to understand the dynamic nature of degrader-induced cooperative ternary complexes.

Modeling analysis on the influence of the gyrostatic moment on the motion of a charged rigid body subjected to constant axial torque

Modeling analysis on the influence of the gyrostatic moment on the motion of a charged rigid body subjected to constant axial torque

Fixed-time prescribed performance consensus formation tracking control of multiple electrically driven nonholonomic mobile robots with complete unknown parameters

This paper delves into the fixed-time consensus formation problem for wheeled mobile robots (WMRs) with completely unknown parameters under prescribed constraints. By integrating the rigid body dynamics of the robot and the high-order dynamics of the drive circuit, and utilising voltage as the control input, we propose a fixed-time prescribed performance control (PPC) protocol. The controller aims to ensure that the formation error of WMRs evolves under prescribed constraints and converges to a small neighbourhood around zero within a fixed time. Furthermore, the designed adaptive laws ensure control accuracy even in scenarios where WMR parameters are unknown. Finally, the feasibility and effectiveness of the proposed controller are validated through simulations under various conditions.

Constrained motion of self-propelling eccentric disks linked by a spring.

It has been supposed that the interplay of elasticity and activity plays a key role in triggering the non-equilibrium behaviors in biological systems. However, the experimental model system is missing to investigate the spatiotemporally dynamical phenomena. Here, a model system of an active chain, where active eccentric-disks are linked by a spring, is designed to study the interplay of activity, elasticity, and friction. Individual active chain exhibits longitudinal and transverse motions; however, it starts to self-rotate when pinning one end and self-beat when clamping one end. In addition, our eccentric-disk model can qualitatively reproduce such behaviors and explain the unusual self-rotation of the first disk around its geometric center. Furthermore, the structure and dynamics of long chains were studied via simulations without steric interactions. It was found that a hairpin conformation emerges in free motion, while in the constrained motions, the rotational and beating frequencies scale with the flexure number (the ratio of self-propelling force to bending rigidity), χ, as ∼(χ)4/3. Scaling analysis suggests that it results from the balance between activity and energy dissipation. Our findings show that topological constraints play a vital role in non-equilibrium synergy behaviors.

Pizza3: A general simulation framework to simulate food-mechanical and food-deconstruction problems

Current mesh-based simulation approaches face significant challenges in continuously modeling the mechanical behaviors of foods through processing, storage, deconstruction, and digestion. This is primarily due to the limitations of continuum mechanics in dealing with systems characterized by free boundaries, substantial deformations, mechanical failures, and non–homogenized mechanical properties. The dynamic nature of food microstructure and the transformation of the food bolus, in relation to its composition, present formidable obstacles in computer-aided food design. In response, the Pizza3 project adopts an innovative methodology, utilizing an explicit microstructural representation to construct and subsequently deconstruct food products in a modular, Lego-like fashion. Central to this simulation approach are “food atoms”, conceptualized from the principles of smoothed particle hydrodynamics. These units are significantly larger than actual atoms but are finely scaled to represent both solid and liquid states of food faithfully. In solid phases, food atoms interact via pairwise forces akin to bond-peridynamic methods, thus extending the capabilities of continuum mechanics to encompass large deformations and fracturing phenomena. For liquids, the model employs artificial conservative and dissipative forces, enabling the simulation of a variety of phenomena within the framework of partial compressibility. The interaction dynamics between rigid and soft objects and fluids are accurately captured through Hertzian contact mechanics, offering a versatile parameterization applicable to impermeable (but possibly penetrable) surfaces and enforcing no-slip conditions. The efficacy of this framework is showcased through the successful modeling of three time-dependent 3D scenarios, each rigorously validated against established analytical and experimental models. Advancing beyond these initial applications, the framework is further extended to more intricate cases inadequately addressed in current literature. This extension sheds light on the underlying mechanisms of in-mouth texture perception, offering new insights and tools for food engineering and design.

Nonlinear Analysis of Plane Frames Using a Co-Rotating Timoshenko Beam Element

The present work describes a co-rotating shear flexible beam element without shear locking and integrating Euler-Bernoulli's and Timoshenko's beam theories. The co-rotational kinematics is based on the separation of the motion in deformational and rigid body components. The deformation of the beam element is composed by three natural modes of deformation: the extension mode, the symmetric bending mode, and the anti-symmetric bending mode. The respective generalized stresses from these natural modes are self-balanced, allowing the achievement of a consistent tangent stiffness matrix. In this paper, it is detailed and deduced all the algebraic steps for the deduction of the elastic stiffness matrix, the geometric stiffness matrix, and the co-rotation stiffness matrix. Some examples are presented and the numerical results demonstrate that the beam element here presented is able to handle large rotations.

The Character of Couples and Couple Stresses in Continuum Mechanics

In this paper, the concepts of moments and couples in mechanics are examined from a fundamental perspective. Representing a couple by its moment vector is very useful in rigid body mechanics, where the states of internal stresses and deformation are not studied. This is because only the moment of couples appears in the governing equation of moment equilibrium. On the other hand, when considering the state of internal stresses and deformation in continuum mechanics, not only the moment of couples but also the line of action of their constituent parallel opposite forces must be specified. In defining a well-posed problem for a continuum, including the governing equations of moment equilibrium or motion, boundary conditions, and constitutive relations, only the moment of couples (e.g., body couples, couple tractions, couple stresses) appear without specifying the line of action of the constituent parallel forces. Nevertheless, the physical state of stress and deformation in the continuum must be unique and determinate. Therefore, this physical requirement imposes some restrictions on the form of body couples, couple tractions, and couple stresses. Here, the uniqueness of interactions in the continuum is used to establish that the continuum does not support a distribution of body couples or a distribution of surface twisting couple tractions with normal moments. Furthermore, the mechanism of action of the couple traction as a double layer of shear force tractions is established, along with the skew-symmetric character of the couple stress moment tensor.

Dynamic reconstruction for digital tomosynthesis: a phantom proof of concept for breast care

Objective. Digital tomosynthesis (DTS) is a type of limited-angle Computed Tomography (CT) used in orthopedic and oncology care to provide a pseudo-3D reconstructed volume of a body part from multiple x-ray projections. Patient motion during acquisitions results in artifacts which affect screening and diagnostic performances. Hence, accurate reconstruction of moving body parts from a tomosynthesis projection series is addressed in this paper, with a particular focus on the breast. The aim of this paper is to assess the feasibility of a novel dynamic reconstruction technique for DTS and evaluate its accuracy compared to an available ground truth. Approach. The proposed method is a combination of a 4D dynamic tomography strategy leveraging the formalism of Projection-based Digital Volume Correlation (P-DVC) with a multiscale approach to estimate and correct patient motion. Iterations of two operations are performed: (i) a motion-corrected reconstruction based on the Simultaneous Iterative Reconstruction Technique (SIRT) algorithm and (ii) a motion estimation from projection residuals, to obtain motion-free volumes. Performance is evaluated on a synthetic Digital Breast Tomosynthesis (DBT) case. Three slabs of a CIRS breast phantom are imaged on a Senographe PristinaTM, under plate-wise rigid body motions with amplitudes ranging up to 10 mm so that an independent measurement of the motion can be accessed. Results. Results show a motion estimation average precision down to 0.183 mm (1.83 voxels), when compared to the independent measurement. Moreover, an 84.2% improvement on the mean residual error and a 59.9% improvement on the root mean square error (RMSE) with the original static reconstruction are obtained. Significance. Visual and quantitative assessments of the dynamically reconstructed volumes show that the proposed method fully restores conspicuity for important clinical features contained in the phantom.

Kyanite microstructural and microchemical characteristics reveal differences in growth, deformation and chemical modification: A case study from the Paleoproterozoic suture zone of South Harris, NW Scotland

Based on petrological association, cathodoluminescence (CL), trace element signatures and orientation relationships, two generations of kyanite are distinguished in a high temperature, high pressure garnet-biotite-aluminosilicate bearing migmatite of South Harris, NW Scotland. The migmatite shows a garnet and biotite rich domain (Grt-Bt domain) which is cut at a low angle by a dominantly coarse-grained plagioclase-quartz leucosome. In addition, a fine-grained plagioclase-quartz-kyanite domain (Plag-Qtz-Ky domain) is present intercalated with the Grt-Bt domain and subparallel to the plagioclase-quartz domain. Type 1 kyanite is coarse grained and associated with Bt clusters and garnet within the Grt-Bt domain. It grew relatively early, syn- to post-garnet growth, in a suprasolidus environment resulting in crystallographically determined oscillatory CL and trace element zoning. Grains record evidence of progressive deformation in the crystal plastic regime, where deformation is accommodated by dislocation glide, climb and deformation twinning. The dominant activated slip system is (100)<001> with minor component of <100>, while deformation twins show a ∼ 180° rotation around ∼<001> axis and a twin plane near (001). Grains appear to be impervious to deformation induced diffusion with all zoning remaining sharp despite crystal plastic deformation. Grains in direct contact with the Plag-Qtz-Ky domain show late modification of the CL and trace element signature suggesting melt-mediated interface-coupled dissolution-precipitation reaction. This modification resulted in crosscutting lobate high trace element regions and irregular rims with low Cr and V content. These rims show similar CL and trace element characteristics as Type 2 kyanite which are exclusively seen within the Plag-Qtz-Ky domain suggesting that Type 2 grains are cogenetic with Type 1 rims. Type 2 grains are finer grained than Type 1 grains and show near uniform CL and trace element distributions with rare oscillatory zoned and relatively higher Cr & V bright cores. Type 2 show either no or very localized internal deformation features. However, they exhibit a clear shape preferred orientation which coincides with a crystallographic preferred orientation where the longest shape axis is parallel to <001>. We propose that Type 2 kyanite grains underwent melt-present deformation by rigid body rotation in an externally derived melt with different trace element chemistry than the host rock. This melt thus interacted chemically by melt-mediated interface-coupled dissolution-precipitation reactions with the surrounding rocks forming the Type 1 rims.Our study shows detailed analysis of kyanite is an important tool for giving constraints on the deformation, P–T and melting history of high-grade metamorphic rocks and migmatites.

Wave propagation in tailored metastructures consisting of elastic beams and rigid bodies.

This paper presents a study of wave propagation through an infinite periodic structure that consists of elastic Timoshenko beams interconnected with rigid bodies. This is a generalized approach in which the beams are not coaxial and the centre of mass of each rigid body is placed away from the intersection of their neutral axes. An analytical approach is used by applying the transfer matrix method (TMM), along with the Floquet-Bloch theorem for elastic wave propagation. Subsequent parametric analysis is performed with visualization of resulting band diagrams of a representative structure. These results are verified through comparison with solutions obtained using the finite-element method (FEM). In this manner, a comprehensive dynamical analysis of tailored metastructures is provided.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Soft Crawling Microrobot Based on Flexible Optoelectronics Enabling Autonomous Phototaxis in Terrestrial and Aquatic Environments.

Many organisms move directly toward light for prey hunting or navigation, which is called phototaxis. Mimicking this behavior in robots is crucially important in the energy industry and environmental exploration. However, the phototaxis robots with rigid bodies and sensors still face challenges in adapting to unstructured environments, and the soft phototaxis robots often have high requirements for light sources with limited locomotion performance. Here, we report a 3.5 g soft microrobot that can perceive the azimuth angle of light sources and exhibit rapid phototaxis locomotion autonomously enabled by three-dimensional flexible optoelectronics and compliant shape memory alloy (SMA) actuators. The optoelectronics is assembled from a planar patterned flexible circuit with miniature photodetectors, introducing the self-occlusion to light, resulting in high sensing ability (error < 3.5°) compared with the planar counterpart. The actuator produces a straightening motion driven by an SMA wire and is then returned to a curled shape by a prestretched elastomer layer. The actuator exhibits rapid actuation within 0.1 s, a significant degree of deformation (curvature change of ∼87 m-1) and a blocking force of ∼0.4 N, which is 68 times its own weight. Finally, we demonstrated the robot is capable of autonomously crawling toward a moving light source in a hybrid aquatic-terrestrial environment without human intervention. We envision that our microrobot could be widely used in autonomous light tracking applications.

Trading particle shape with fluid symmetry: on the mobility matrix in 3-D chiral fluids

Chiral fluids – such as fluids under rotation or a magnetic field as well as synthetic and biological active fluids – flow in a different way than ordinary ones. Due to symmetries broken at the microscopic level, chiral fluids may have asymmetric stress and viscosity tensors, for example giving rise to a hydrostatic torque or non-dissipative (odd) and parity-violating viscosities. In this article, we investigate the motion of rigid bodies in such an anisotropic fluid in the incompressible Stokes regime through the mobility matrix, which encodes the response of a solid body to forces and torques. We demonstrate how the form of the mobility matrix, which is usually determined by particle geometry, can be analogously controlled by the symmetries of the fluid. By computing the mobility matrix for simple shapes in a three-dimensional (3-D) anisotropic chiral fluid, we predict counterintuitive phenomena such as motion at an angle to the direction of applied forces and spinning under the force of gravity.

Resolving Collisions in Dense 3D Crowd Animations

We propose a novel contact-aware method to synthesize highly-dense 3D crowds of animated characters. Existing methods animate crowds by, first, computing the 2D global motion approximating subjects as 2D particles and, then, introducing individual character motions without considering their surroundings. This creates the illusion of a 3D crowd, but, with density, characters frequently intersect each other since character-to-character contact is not modeled. We tackle this issue and propose a general method that considers any crowd animation and resolves existing residual collisions. To this end, we take a physics-based approach to model contacts between articulated characters. This enables the real-time synthesis of 3D high-density crowds with dozens of individuals that do not intersect each other, producing an unprecedented level of physical correctness in animations. Under the hood, we model each individual using a parametric human body incorporating a set of 3D proxies to approximate their volume. We then build a large system of articulated rigid bodies, and use an efficient physics-based approach to solve for individual body poses that do not collide with each other while maintaining the overall motion of the crowd. We first validate our approach objectively and quantitatively. We then explore relations between physical correctness and perceived realism based on an extensive user study that evaluates the relevance of solving contacts in dense crowds. Results demonstrate that our approach outperforms existing methods for crowd animation in terms of geometric accuracy and overall realism.

An alternative to the Euler equation of rigid body rotational dynamics

The Euler equation provides a convenient framework for studying the rotational dynamics of rigid bodies in solid mechanics. While this equation is written from the point of view of an inertial observer, it is implemented in a non-inertial ancillary coordinate system attached to the rigid body and the equations of the rotation are consequently expressed in this ancillary system. We examine how the rotational dynamics of rigid bodies can be described by the inertial observer directly in the inertial coordinate system (instead of employing an ancillary non-inertial frame), and derive the differential equations of the rotation in this inertial system. This approach can have advantages in situations where the rigid body has both translational motion in addition to rotational motion.

Exploiting interfacial instability during peeling a flexible plate from elastic films

Adhesive interactions between soft materials are prevalent in both biological systems and various engineering applications, including soft robots, flexible electronics, and antifouling coatings. Many studies have demonstrated that cavitation and fingering instabilities emerge at the adhesive interface between rigid objects and soft films, owing to the geometric attributes of the contact region. However, in the context of peeling configurations, defining the geometric features is challenging, resulting in relatively scant exploration of interfacial instabilities. Hence, the modulation of instability patterns during the peeling process of a flexible plate from a thin elastic film, alongside the consequential effects on mechanical responses, remains poorly understood. To elucidate the mechanisms underlying interfacial instability during peeling process and its impacts on peel-off force, we use finite element methods to simulate the evolution of interface separation. Consistent with previous experimental observations, we find that the interfacial instability will occur when the bending stiffness of the flexible plate is bigger than a critical value. We show that the interfacial instability is mainly induced by the competition between the adhesion energy and the strain energy of the film, and the incompressibility of the thin film is critical for the appearance of the interfacial instability. Combining theory and finite element simulation, we propose the scaling laws for the critical peel-off force for stable and unstable peelings, respectively, and show that the critical peel-off force will decrease when the interfacial instability occurs. Finally, we demonstrate that weakening the tangential adhesion strength and loosening the constraints between the film and the rigid substrate effectively suppress fingering instability. Collectively, our findings elucidate the pivotal factors influencing interfacial instability, offering invaluable insights for the design of structures or systems involving soft materials.

Design and Control of a Novel 6-DOF Desktop Upper Limb Rehabilitation Robot

Abstract This paper presents the design, analysis, and development of a Novel six degrees of freedom (6-DOF) desktop upper limb rehabilitation robot. The upper limb rehabilitation robot is mainly composed of the Omnidirectional mobile platform, armrest, and 3-DOF wrist rehabilitation mechanism. The forward and inverse kinematics and Jacobian matrix of the upper limb rehabilitation robot are derived based on the kinematics of a rigid body, and its working space is analyzed based on arm kinematics as well. The forward and inverse kinematics of the arm are derived based on the D-H method. A new control strategy and control algorithm were developed based on the hardware structure of the robot system and arm model, and the control strategy and control algorithm are used to carry out the simulated rehabilitation experiment on a single joint of the arm and the simulated rehabilitation experiment on multiple joint linkages in the arm. The experimental results show that the maximum error in the simulated rehabilitation experiment on a single joint of the arm is 6.123 deg, and the maximum error in the simulated rehabilitation experiment of multiple joint linkages in the arm is 5.323 deg. Therefore, the control strategy and control algorithm can complete the corresponding rehabilitation training. This 6-DOF desktop upper limb rehabilitation robot can provide passive rehabilitation training for patients in the early stages of paralysis.