Virtual Spring Research Articles

Multi-robot consensus formation based on virtual spring obstacle avoidance

Abstract. A systematic improvement of the multi-robot formation control algorithm has been developed to address multi-robot formation instability. First, a static obstacle avoidance model based on spring force mapping is proposed, followed by an analysis of the influence of static and dynamic obstacles on the processing of multi-robot cooperative motion. Second, a leader is introduced to the formation to save computational costs. Third, the Velocity Obstacle (VO) algorithm is improved to resolve robot collisions during the dynamic mobility process caused by the increased number of multi-robot formations. Simultaneously, the dynamic speed limit function based on the position error for formation keeping is established. Finally, simulation experiments are carried out. Results show that when 5-robot and 20-robot formations were compared in the environment without dynamic conflict, the average value of the position error of 20-robot formations only increased by 39.47 %, and the average value of the path length did not differ significantly. In the dynamic conflict environment, the maximum position error of 20-robot formations increases by 73.03 % and the path length average value increases by 7.69 %. Our proposed method can control the motion of multiple robots in both conflict-free and conflict-filled environments, resulting in an effective motion planning scheme.

Robot motor learning shows emergence of frequency-modulated, robust swimming with an invariant Strouhal number.

Fish locomotion emerges from diverse interactions among deformable structures, surrounding fluids and neuromuscular activations, i.e. fluid-structure interactions (FSI) controlled by fish's motor systems. Previous studies suggested that such motor-controlled FSI may possess embodied traits. However, their implications in motor learning, neuromuscular control, gait generation, and swimming performance remain to be uncovered. Using robot models, we studied the embodied traits in fish-inspired swimming. We developed modular robots with various designs and used central pattern generators (CPGs) to control the torque acting on robot body. We used reinforcement learning to learn CPG parameters for maximizing the swimming speed. The results showed that motor frequency converged faster than other parameters, and the emergent swimming gaits were robust against disruptions applied to motor control. For all robots and frequencies tested, swimming speed was proportional to the mean undulation velocity of body and caudal-fin combined, yielding an invariant, undulation-based Strouhal number. The Strouhal number also revealed two fundamental classes of undulatory swimming in both biological and robotic fishes. The robot actuators were also demonstrated to function as motors, virtual springs and virtual masses. These results provide novel insights in understanding fish-inspired locomotion.

A Virtual Spring Strategy for Cooperative Control of Connected and Automated Vehicles at Signal-Free Intersections

A Virtual Spring Strategy for Cooperative Control of Connected and Automated Vehicles at Signal-Free Intersections

The Vibro-Acoustic Characteristics Analysis of the Coupled System between Composite Laminated Rotationally Stiffened Plate and Acoustic Cavities

In order to study vibro-acoustic characteristics between composite laminated rotationally stiffened plate and acoustic cavities in the coupled system, first-order shear deformation theory (FSDT) and modified Fourier series are used to construct a unified analysis model. The involved coupled systems primarily encompass three types: the coupled system between composite laminated rotationally stiffened plate and cylindrical-cylindrical cavities, spherical-cylindrical cavities, and conical-cylindrical cavities. First, the first-order shear deformation theory and the modified Fourier series are applied to construct the allowable displacement function of the composite laminated rotationally stiffened plate and the allowable sound pressure function of the acoustic cavities. Second, the energy functionals for the structural domain and the acoustic field domain are established, respectively. According to the continuity condition of the particle vibration velocity at the coupling boundary between the composite, laminated cylindrical shell and the enclosed cavity, the coupling potential energy between the stiffened plate and two acoustic cavities is introduced to obtain the energy functional of the coupled system. Third, the Rayleigh-Ritz method is utilized to solve the energy functional and, when combined with artificial virtual spring technology, the suggested theory may be used to study the vibro-acoustic characteristics of a coupled system with arbitrary elastic boundary conditions. Finally, based on validating the fast convergence and correctness of the model, this paper will analyze the impact of crucial parameters on vibro-acoustic characteristics. Furthermore, by incorporating internal point forces and point-sound source stimulation, a steady-state response analysis of the coupled system will be conducted. This research can give a theoretical foundation for the vibration and noise reduction of a vibro-acoustic coupling system.

Target-following Robotic Platform Based on UWB Localization and Depth Camera

A mobile robot capable of following a specified target using Ultra-Wideband (UWB) technology and an RGB-D camera is presented in this paper. One of our primary objectives is to promote the use of UWB as a precise and fast real-time localization system (RTLS) in mobile robotics, specifically the target following applications using the approach of non-fixed anchors. We use the depth camera as a complementary sensor to the omnidirectional UWB, to increase the robot’s awareness of its surroundings and possibly also as a way of providing human-machine interaction. This paper also describes creating a simplified mathematical model for computing the control action and the method we have used to measure the system’s rotational dynamics for system identification purposes. Thereafter, we combined a PD controller and proportional virtual spring regulation and selected parameters of the compound regulator to slowly pursue a non-linear movement of the followed person. Our robotic platform is originally meant to carry a toolbox and equipment. However, it might be just as well used in various applications such as material handling in industrial and manufacturing settings, as an assistive technology for load handling in warehouses, construction sites, even carrying airline baggage or military equipment. Most countries implement regulations regarding lifting and carrying loads that are even more strict in case of repetitive or long-term use. Therefore, using a robotic platform in such cases might be convenient.

Vibration Analysis of Internally Perforated Annular Plate with Discontinuous Boundary Conditions

Because of the introduction of modal coupling, discontinuous boundaries have a significant impact on the vibration characteristics of annular plates. Based on the spectral element method (SEM) and parametric equivalent method (PEM), the vibration calculation and analysis of internally perforated annular plate with discontinuous boundary are explained. Firstly, a uniform annular plate is regarded as a spectral element, and the vibration response of an annular plate with general elastic boundaries is obtained based on the motion equation of the annular plate and the virtual spring method (VSM). The displacement solution is described by the Bessel function, and a fitting method of discontinuous spring stiffness coefficient based on the weighted least square norm least square method is proposed. Based on the force equilibrium condition, the vibration response of an annular plate with a discontinuous boundary is derived, and the reasons for the change of vibration characteristics with a discontinuous boundary are explained from modal superposition. The dynamic stiffness matrix method is used to establish the vibration equation of an annular plate with a discontinuous boundary, and the influence of internal openings on the vibration characteristics of an annular plate is effectively calculated by the parametric equivalent method. Finally, a finite element simulation model is established to test the accuracy and stability of the proposed method. The influence of general discontinuous boundary conditions on structural dynamic behavior is analyzed by numerical examples, which provides useful guidance for structural vibration analysis with discontinuous boundary conditions.

Stochastic dynamics analysis of the rocket shell coupling system with circular plate fasteners based on spectro-geometric method

A numerical analysis model is established to predict the stochastic dynamic characteristics of the rocket shell coupling system. The virtual springs are employed to deal with the boundary conditions and assemble the sub structures. Firstly, the energy functional expressions of the sub structures are deduced with the medium-thick shell theory. Thereafter the equivalent dynamic model of the rocket shell coupling system is obtained. With the consideration of the random acceleration load excitation, the stochastic dynamic responses of the rocket shell coupling system are derived by solving the analytical model with the spectro-geometric method. By comparing with the results obtained with other numerical methods, the effectiveness of the proposed equivalent analysis model is successfully verified. Last but not the least, the parametric analysis is carried out to investigate the influence of some core factors on the stochastic dynamic response of the rocket shell coupling system.

Stiffness analysis and optimization of an asymmetric 3T1R parallel mechanism

In this paper, an asymmetric 3T1R parallel mechanism is proposed that has higher stiffness in specific directions. The stiffness model is established by using virtual spring theory, and the Cartesian stiffness matrix is obtained. The stiffness performance evaluation indices are deduced by the dimensionless parameterization method. Under the condition of satisfying the high-speed performance and dexterity, the optimal size parameters of the mechanism are got by using the DE (differential evolution) algorithm with stiffness performance as the index. By comparing the stiffness performance atlases before and after the optimization, it is showed that the stiffness performance has been improved and the reachable workspace has been increased. The results verify the feasibility of the proposed performance indices and optimization algorithm.

Acoustic frequency atomic spin oscillator in the quantum regime

Quantum noise reduction and entanglement-enhanced sensing in the acoustic frequency range is an outstanding challenge relevant for a number of applications including magnetometry and broadband noise reduction in gravitational wave detectors. Here we experimentally demonstrate quantum behavior of a macroscopic atomic spin oscillator in the acoustic frequency range. Quantum back-action of the spin measurement, ponderomotive squeezing of light, and virtual spring softening are observed at oscillation frequencies down to the sub-kHz range. Quantum noise sources characteristic of spin oscillators operating in the near-DC frequency range are identified and means for their mitigation are presented.

Effect of Low-Pass Filtering on Passivity and Rendering Performance of Series Elastic Actuation.

We study the effect of low-pass filtering on the passivity and performance of series elastic actuation (SEA) under velocity-sourced impedance control (VSIC) while rendering virtual linear springs and the null impedance. We analytically derive the necessary and sufficient conditions for the passivity of SEA under VSIC with filters in the loop. We demonstrate that low-pass filtered velocity feedback of the inner motion controller amplifies the noise at the outer force loop, necessitating the force controller also be equipped with low-pass filtering. We derive passive physical equivalents of the closed-loop systems to provide intuitive explanations of the passivity bounds and to rigorously compare the performance of controllers with and without low-pass filtering. We show that, while low-pass filtering improves the rendering performance by decreasing the parasitic damping effects and allowing for higher motion controller gains, it also introduces more strict bounds on the range of passively renderable stiffness. We experimentally verify the passive stiffness rendering bounds and performance improvements for SEA under VSIC with filtered velocity feedback.

Free Vibration and Dynamic Analysis on Free-Constrained Layer of Graphene Based on Composite Conical Shell via Jacobi–Ritz Method

Excessive vibration has always been a serious problem for conical shell structures, while the application of the graphene-based free-constrained layer (GFCL) based on carbon fiber-reinforced composite (CFRC) structure is a novel way to improve structural performance. An analytical model for vibration and dynamic characteristics of the GFCL-CFRC conical shell resting on the Winkler–Pasternak elastic foundation with arbitrary boundary conditions is constructed, and four types of GFCL porosity distribution and GFCL dispersion pattern are considered in this model. The multi-segment technique and virtual spring technique are utilized to simulate arbitrary boundary conditions. Then, the first-order shear deformation theory (FSDT) and Hamilton’s principle are employed to obtain the motion equation of the GFCL-CFRC conical shell, and the motion equation of the GFCL-CFRC conical shell is solved by the Ritz method. In conclusion, the dispersion mode of GFCL, thickness ratio of GFCL, and fiber angle have influence on the dynamic performance. With a reasonable design, the dynamic performance of the GFCL-CFRC conical shell can be further improved.

Vibration Analysis of a Plate Embedded or Attached with Acoustic Black Hole Using a Virtual Spring Energy Method

Acoustic black hole (ABH) with the power-law profile has the advantages of strong designability and vibration suppression. This study provides a novel virtual spring energy method (VEM) to solve the vibration characteristics of a plate embedded or attached with acoustic black hole. Firstly, the virtual springs in this study can deal with boundary conditions, continuity conditions, and periodic conditions. After solving the kinetic and potential energy of a plate cell embedded with acoustic black hole, the periodic structure’s kinetic and potential energy need not be calculated repeatedly. The method is verified by the finite element method. Secondly, to overcome the stiffness reduction owing to the varying thickness of ABH in the primary bearing structure, a composite ABH structure called “Plate–ABH” is proposed, in which a damping layer is designed with an ABH profile and attached to the primary plate structure. The two layers connect each other through the virtual springs. The vibration characteristics of the composite ABH plate are given by employing the VEM. The composite ABH structure shows strong damping ability and lighter weight compared with a plate attached with the uniform thickness damping layer. Plate–ABH can be effectively used in the engineering of vibration reduction.

Analysis of thermal-vibration coupling modeling of combined conical-cylindrical shell under complex boundary conditions

In this paper, a unified method is proposed to predict the free and forced vibration behavior of the combined conical-cylindrical shell (CCS) structure in the steady-state thermal environment. The first-order shear deformation theory (FSDT) and the thermal strain are utilized to establish the energy equation of the combined structure, and the artificial virtual spring technique is introduced to realize the coupling between the substructures and the arbitrary boundary conditions of the CCS. The displacement function of the structure is constructed by the spectral-geometry method, and the vibration equation is solved by using the Rayleigh–Ritz method. The accuracy of the present model is verified by comparing the numerical results with the finite element method. The factors that may affect the vibration behavior of the CCS under thermal environment are analyzed specifically, and the results demonstrate that point constraints on the shell surface can effectively suppress shell vibration. This paper provides a compelling reference for vibration control of CCS in practical applications.

Distributed Formation Control for Manipulator End Effectors

This paper addresses the problem of achieving and maintaining the 2D/3D formation shape of networked manipulator end-effectors. We firstly present a distributed formation controller for manipulators whose system parameters are perfectly known. The formation control objective is achieved by assigning virtual springs between end-effectors and by adding damping terms at joints, which provides a clear physical interpretation of the proposed solution. Subsequently, we extend it to the case where manipulator kinematic and system parameters are not exactly known. An extra integrator and an adaptive estimator are introduced for gravitational compensation and stabilization, respectively. Simulation results with planar manipulators and with seven degree-of-freedom humanoid manipulator arms are presented to illustrate the effectiveness of the proposed approach.

Theoretical and experimental investigations on free vibration characteristics of arbitrary spatially closed-coupled plates

A semi-analytical method and related experiments are present in this paper to investigate the free vibration characteristics of the closed-coupled plates with arbitrary spatial coupling angles and curved edges, which are the widely used structural form but researched for the first time. By combining the penalty function method with flexible setting virtual spring stiffness functions and the comprehensive relative motion relation matrices along the edges of the plates system, various types of boundary and spatial coupling connection conditions in practical engineering can be constructed. The semi-analytical solution formulas for the entire vibration model are established by using the first-order shear deformation theory (FSDT) and the two-dimensional Jacobian differential quadrature method (JDQM). To fulfill the requirements of integral operations for displacement approximation functions, the irregular domain mapping technique is employed to transform the irregular solving domain into the regular basic domain. The accuracy and applicability of the present method in predicting eigenfrequencies and mode shapes are proved by hammer modal tests concerning four pyramid/frustum-like built-up plates, comparisons with results from the open literature, as well as the finite element method (FEM) simulations of several specially designed cases. Moreover, many meaningful conclusions are drawn regarding the effects of spatial geometric parameters on the free vibration characteristics of spatially closed-coupled plates with curved edges.

Characteristics of band gaps of a metamaterial plate with membrane-type resonators based on the energy approach

Local resonance metamaterials have garnered substantial interest in recent years due to their potential to effectively control low-frequency noise and vibration. This study proposes a new metamaterial plate with double mass membrane-type resonators (DMMRs). Combining polynomial fitting and virtual spring method, the natural characteristics of the resonator and the dispersion surfaces of the metamaterial plate are obtained. Results show the proposed metamaterial plate exhibits multiple band gaps, resulting from the cancellation of shear forces in the plate by the reaction forces generated by the first two resonances of the resonators. Parametric analysis is performed to obtain the variation patterns of the band gaps, where approximate models of the resonator are adopted to explain the effects of the parameters. It is found that the occurrence and width of the two band gaps are closely related to the mass ratio between the masses on the resonator and the substrate plate. Furthermore, finite element analysis is conducted to verify the effectiveness of the theoretical derivation, as well as the suppression effect of the metamaterial plate. The findings demonstrate the advantages of the metamaterial plate in vibration control and band gap tuning. The study provides guidance for the design and analysis of elastic wave metamaterials.

A unified spectral-geometric model of FGM double conical/cylindrical/spherical shell coupled with annular plates

This paper presents the analysis of the free and force vibration characteristics of FGM double layered cylindrical/conical/spherical shell and annular plate coupled structures under various boundary conditions and coupled connection conditions. The spectral geometry method is utilized to represent the displacement variable for FGM shell and annular plate structures in the uniform form, which overcomes the discontinuity or jump phenomenon at the boundary. To simulate the boundary conditions and coupling connection relationship between the FGM plate and shell substructures, the artificial virtual spring technique is implemented by adjusting the stiffness values of linear or rotational springs. Based on the Rayleigh-Ritz procedure, the unified dynamic equations of the FGM double layered cylindrical/conical/spherical shell and annular plate coupled structures are derived. Numerical examples are provided to demonstrate the convergence of the proposed model, and the accuracy and correctness of the proposed analytical model are verified by comparing the results with the vibration results obtained by the finite element method. Furthermore, parametric analysis is conducted to investigate the effect of material parameters, geometric parameters, and position parameters on the inherent characteristics and steady-state response of the FGM double layered coupled structure under various boundary conditions. Overall, this paper contributes to the understanding of the dynamic behavior of FGM double layered coupled structures and provides a useful analytical tool for the design and optimization of such structures.

Neural Control of a Robotic Manipulator in Contact with a Flexible and Uncertain Environment

Abstract This article presents the synthesis of a neural motion control system of a robot caused by disturbances of constraints limiting the movement, which are the result of flexibility and disturbances of the contact surface. A synthesis of the control law is presented, in which the knowledge of the robot’s dynamics and the parameters of a susceptible environment is not required. Moreover, the stability of the system is guaranteed in the case of an inaccurately known surface of the environment. This was achieved by introducing an additional module to the control law in directions normal to the surface of the environment. This additional term can be interpreted as the virtual viscotic resistance and spring force acting on the robot. This approach ensured the self-regulation of the robot’s interaction force with the compliant environment, limiting the impact of the geometrical inaccuracy of the environment.

Shaping Human Movement via Bimanually-Dependent Haptic Force Feedback.

Haptic feedback can enhance training and performance of human operators; however, the design of haptic feedback for bimanual coordination in robot-assisted tasks (e.g., control of surgical robots) remains an open problem. In this study, we present four bimanually-dependent haptic force feedback conditions aimed at shaping bimanual movement according to geometric characteristics: the number of targets, direction, and symmetry. Haptic conditions include a virtual spring, damper, combination spring-damper, and dual springs placed between the hands. We evaluate the effects of these haptic conditions on trajectory shape, smoothness, and speed. We hypothesized that for subjects who perform worse with no haptic feedback (1) a spring will improve the shape of parallel trajectories, (2) a damper will improve the shape of point symmetric trajectories, (3) dual springs will improve the shape of trajectories with one target, and (4) a damper will improve smoothness for all trajectories. Hypotheses (1) and (2) were statistically supported at the p < 0.001 level, but hypotheses (3) and (4) were not supported. Moreover, bimanually-dependent haptic feedback tended to improve shape accuracy for movements that subjects performed worse on under no haptic condition. Thus, bimanual haptic feedback based on geometric trajectory characteristics shows promise to improve performance in robot-assisted motor tasks.

Haptic Exploration of Unknown Objects for Robust In-Hand Manipulation.

Human-like robot hands provide the flexibility to manipulate a variety of objects that are found in unstructured environments. Knowledge of object properties and motion trajectory is required, but often not available in real-world manipulation tasks. Although it is possible to grasp and manipulate unknown objects, an uninformed grasp leads to inferior stability, accuracy, and repeatability of the manipulation. Therefore, a central challenge of in-hand manipulation in unstructured environments is to acquire this information safely and efficiently. We propose an in-hand manipulation framework that does not assume any prior information about the object and the motion, but instead extracts the object properties through a novel haptic exploration procedure and learns the motion from demonstration using dynamical movement primitives. We evaluate our approach by unknown object manipulation experiments using a human-like robot hand. The results show that haptic exploration improves the manipulation robustness and accuracy significantly, compared to the virtual spring framework baseline method that is widely used for grasping unknown objects.