Linear Degrees Of Freedom Research Articles

Modifications to ArduSub That Improve BlueROV SITL Accuracy and Design of Hybrid Autopilot

Improvements to ArduSub for the BlueROV2 (BROV2) Heavy, necessary for accurate simulation and autonomous controller design, were implemented and validated in this work. The simulation model was made more accurate with new data obtained from real-world testing and values from the literature. The manual control algorithm in the BROV2 firmware was replaced with one compatible with automatic control. In a Robot Operating System (ROS), a proportional–derivative (PD) controller to assist augmented reality (AR) pilots in controlling angular degrees of freedom (DOF) of the vehicle was implemented. Open-loop testing determined the yaw hydrodynamic model of the vehicle. A general mathematical method to determine PD gains as a function of the desired closed-loop performance was outlined. Testing was carried out in the updated simulation environment. Step response testing found that a modified derivative gain was necessary. Comparable real-world results were obtained using settings determined in the simulation environment. Frequency response testing of the modified yaw control law discovered that the bandwidth of the nonlinear system had a one-to-one correspondence with the desired closed-loop natural frequency of a simplified linear approximation. The control law was generalized for angular DOF and linear DOF were operated with open-loop control. A full six-DOF simulated dive demonstrated excellent tracking.

Design of a spherical parallel mechanism with controllable center of rotation using a spherical reconfiguration linkage

It is well known that Remote Center of the motion (RCM) mechanisms are highly suitable for many medical applications. While it is sometimes preferable that the mechanism can control their Center of Rotation (CoR), most RCM mechanisms do not have this possibility without being mounted on large and heavy translational platforms. By using a new concept of Spherical Reconfigurable Linkage (SRL), the present study offers an alternative solution. These new linkages are designed to control their radius and they are connected to form an RCM mechanism with controllable CoR. The newly mounted mechanism now has two linear Degrees of Freedom (DoF) for the displacement of its CoR in addition to its two angular DoF. The linear kinematic model is derived along with the angular kinematic one while taking into account the reconfiguration of the SRL. The velocity model is calculated and all singular configurations are identified. The mechanism performances in terms of workspace and kinematic performances are is also assessed. Finally, motion capture experiments on a prototype validated the models.

An improved inverse kinematics solution method for the hyper‐redundant manipulator with end‐link pose constraint

AbstractHyper‐redundant manipulators have strong flexibility that benefits from their redundant limb structure. However, a large number of redundant degrees of freedom will also lead the solution of inverse kinematics much more difficult, which restricts their motion performance to some extent. Inspired by the FABRIK (Forward and Backward Reaching Inverse Kinematics) method, an improved inverse kinematics solution method for the hyper‐redundant manipulator is proposed. Based on the space vector method, the kinematic model of the manipulator is established to dynamically acquire its endpoint position, and the workspace is further obtained by using the Monte Carlo method. The original search method is optimized, the include angle decoupling mechanism between adjacent links is established to obtain the rotation angles of each joint, and the joint angle limitation is introduced to meet the actual manipulator structural restriction. On this basis, the pose constraint mechanism is established to realize the control of the end‐link pose, and the linear degree of freedom is introduced to realize the solution after the directional expansion of the manipulator's workspace. A series of simulation experiments are carried out. In the experiments, the position error of the manipulator's endpoint is always less than 10−6 mm. Meanwhile, the comparative experimental results show that compared with the original method, the proposed method exhibits higher position accuracy under the condition that the computation time is almost the same. In addition, in the end‐link pose constraint experiment and path motion experiments, the pose error of the end‐link is always less than 10−7°, indicating that the end‐link pose can also meet the high accuracy requirements under the premise of ensuring high position accuracy. Finally, the prototype experiment further verifies its performance.

Super-twisting based sliding mode control of hydraulic actuator without velocity state

This paper provides a novel surface design and experimental evaluation of a super-twisting algorithm (STA) based control for hydraulic cylinder actuators. The proposed integral sliding surface allows to track a sufficiently smooth reference without using the velocity state which is hardly accessible in the noisy hydraulic systems. A design methodology based on LMI’s is given, and the STA gains are designed to be adjusted by only one free parameter. The feasibility and effectiveness of the proposed control method are shown on a standard hydraulic test bench with one linear degree of freedom and passive load, where a typical motion profile is tracked with a bounded average error below 1% from the total drive effective output.

Robotic Tree-fruit harvesting with arrays of Cartesian Arms: A study of fruit pick cycle times

In some cases, it has been shown that fruits on trees with SNAP (Simple, Narrow, Accessible, and Productive) architectures are reachable by robot arms using three linear degrees of freedom; hence, high fruit-picking efficiencies can be achieved with simpler arms. This paper uses digitized fruit position data to compute the fruit pick cycle times (PCT) of robotic fruit harvesters with multiple arms arranged in grid configurations, i.e., operating in disjoint rectangular work cells independently of each other. The effects of the robot joints’ maximum linear acceleration and maximum linear velocity on PCTs were studied. As Vmax increased, the PCT followed a negative exponent power law (diminishing return) for any given Amax. Similarly, for a constant Vmax, the improvement of PCT as Amax increased slowed down at higher acceleration values.Also, the PCTs were computed when each arm work cell was designed based on equal fruit load or equal size criteria, using four workspace partitioning schemes (height split, length split, height split matrix, and length split matrix). Equal fruit-load configurations resulted in load balancing and exhibited lower PCTs; the height-split configuration was the best among the four different partitioning schemes, possibly because it compensated better for the fruit distribution's non-uniformity along the trees' height.Finally, the PCTs were computed while harvesting one side of an orchard row or both sides concurrently. Harvesting sides separately resulted in lower PCTs (greater speed) due to non-uniform fruit distributions on the different sides of trees. The insights gained in this paper can inform the design of harvesting robots utilizing arrays of 3-dof linear arms.

Optimizing the utilization of structural resources of flight simulator motion systems

The object of the study is a six degrees-of-freedom motion system of the synergistic type of a flight simulator. The latter is the main technical means for training pilots and means of research and development of aircraft. The task of optimal utilization of its structural resources was solved, which provides an opportunity to improve the quality of motion cueing. The result is the developed method, which ensures optimal use of structural resources of motion systems of flight simulators. This is explained, first of all, by the use of the developed simplified operator for converting the movements of jacks into the movement of a motion system along individual degrees of freedom on the basis of quadratic approximation. Given this, it became possible to describe the coordinates of the centers of the axes of rotation of the motion system by cubic spline functions. Secondly, the solution of the task of estimating the structural resources of the motion system along linear degrees of freedom on the basis of the developed criterion was carried out by an effective modified method of the deformed polyhedron. This method combines the random search method in the first steps of the search and the gradient method in determining the global extremum. Thirdly, the problem of determining the dependence of the coordinates of the pitch and yaw axes along the pitch angle was stated and solved. Owing to the optimal utilization of the structural resources of motion systems, the coordinates of the axis of their rotation along pitch are as close as possible to the coordinate of the axis of the aircraft. Thus, the quality of motion cueing on the flight simulator is significantly increased and it is possible to use motion systems with shorter lengths of jacks, and therefore, to reduce the cost of their manufacture and operation

Problem of motion cueing along linear degrees of freedom on flight simulators

On the basis of Gibson's perception theory, a set of characteristic attributes of human motion perception is determined. On the basis of the system approach, the mathematical statement of the motion cueing problem along linear degrees of freedom on flight simulators of non-maneuvering aircraft is substantiated. This statement guarantees a motion cueing as close as possible to the real set of characteristic attributes of the motion cueing: nature, beginning time, direction, duration, and intensity of perception.

Low-Complexity High-Performance Cyclic Caching for Large MISO Systems

Multi-antenna coded caching is known to combine a global caching gain that is proportional to the cumulative cache size found across the network, with an additional spatial multiplexing gain that stems from using multiple transmitting antennas. However, a closer look reveals two severe bottlenecks; the well-known exponential subpacketization bottleneck that dramatically reduces performance when the communicated file sizes are finite, and the considerable optimization complexity of beamforming multicast messages when the SNR is finite. We here present an entirely novel caching scheme, termed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cyclic multi-antenna</i> coded caching, whose unique structure allows for the resolution of the above bottlenecks in the crucial regime of many transmit antennas. For this regime, where the multiplexing gain can exceed the coding gain, our new algorithm is the first to achieve the exact one-shot linear optimal DoF with a subpacketization complexity that scales only linearly with the number of users, and the first to benefit from a multicasting structure that allows for exploiting uplink-downlink duality in order to yield optimized beamformers ultra-fast. In the end, our novel solution provides excellent performance for networks with finite SNR, finite file sizes, and many users.

Finite Element Model Updating Method of Dynamic Systems

The finite element model updating method of dynamical systems based on results of modal tests is proposed. The purpose of updating is to change eigenspectrum. The method alters a stiffness matrix by adding an updating finite element model created on the nodes of the intial one with respect to the existing links between the linear degrees of freedom. The stiffnesses of the updating elements are utilized as the updating parameters to be defined. The objective function equals to the least square weighted sum of residuals between the target, which were determined experimentally, and current values of modal stiffnesses. The iterative solution process is carried out. At each iteration step the conjugate gradient method is applied to solve the unconstrained minimization problem. The modeshapes, which were calculated as the result of solving the generalized eigenvalue problem at the previous iteration step, are employed to calculate the current modal stiffnesses. The method does not have a limit to a size of matrices and keeps their sparsity and symmetry. It provides the model updating of selected regions of a structure and step-by-step model updating of predefined groups of eigenfrequencies. Moreover, geometrical features of a structure, such as the presence of the symmetry planes and structurally identical elements, may be taken into account. The method is implemented into a program and verified by the example of the free dynamically-scaled model of Tu-204. In order to perform the ground vibration testing, the model was suspended with a low-rigidity flexible support. The finite element model made of solid elements has been updated on the basis of the six experimentally determined sets of eigenfrequencies. The target frequencies from each set have been achieved with a high level of accuracy.

Condensation modeling of the linear structure with nonlinear boundary conditions

The problem of modeling for the linear structure with nonlinear boundary conditions in a more efficient manner is considered by proposing a novel condensation modeling method. The key idea of the proposed method is to reduce the overall number of degrees-of-freedom (DOFs) for the nonlinear jointed structure being analyzed, which can be implemented in the following two steps. Firstly, linear DOFs of the structure are truncated via finite element model reduction by using the free-interface mode synthesis method, as numerical integration of governing equations of structures with large numbers of DOFs is always time-consuming. Secondly, nonlinear DOFs at the boundary interface are reduced via coordinate condensation, so as to further minimize the model size of the structure being analyzed and make the subsequent analysis computationally efficient and memory economical. The performance of the proposed condensation modeling method is validated via case studies focused on an experimental structure with adjustable boundary conditions. Comparative results demonstrate that the computational efficiency can be extremely improved while the accuracy is simultaneously guaranteed by using the proposed method to model the linear structure with nonlinear boundary conditions.

Morphological Synthesis and workspace design for a parallel manipulator with linear actuators

This paper addresses the kinematic structure and workspace analysis of a parallel manipulator with linear actuators considering two studies.The first one was based on a morphological synthesis in which a kinematic connections approach was implemented. The set of combinations of joints and links for the desired system and their linkage are illustrated. Finally, the development regarding the conceivable morphologyis detailed, providing three linear degrees of freedom between the mobile and fixed platforms. The second study presented the dimensional synthesis of the manipulator, considering a workspace required and an input transmission index. The geometrical design was based on the maximum inscribed workspace volume; the cylindrical shape radius inscribed on a workspace intersection is also exemplified. The geometric determination of the workspace for the manipulator was demonstrated using computer-aided design. A design result of the Delta as checked with the stiffness and condition indices.

Centralized and Decentralized Cache-Aided Interference Management in Heterogeneous Parallel Channels

We consider the problem of cache-aided interference management in a network consisting of $K_{\mathrm {T}}$ single-antenna transmitters and $K_{\mathrm {R}}$ single-antenna receivers, where each node is equipped with a cache memory. Transmitters communicate with receivers over two heterogenous parallel subchannels: the P-subchannel for which transmitters have perfect instantaneous knowledge of the channel state, and the N-subchannel for which the transmitters have no knowledge of the instantaneous channel state. Under the assumptions of uncoded placement and separable one-shot linear delivery over the two subchannels, we characterize the optimal degrees-of-freedom (DoF) to within a constant multiplicative factor of 2. We extend the result to a decentralized setting in which no coordination is required for content placement at the receivers. In this case, we characterize the optimal one-shot linear DoF to within a factor of 3.

Cache-Aided Interference Management in Wireless Cellular Networks

We consider the problem of interference management in wireless cellular networks with caches at both base stations and receivers, and we characterize the degrees of freedom (DoFs) per cell to within an additive gap of (1/3) and a multiplicative gap of 2 for all system parameters, under one-shot linear schemes. Our result indicates that the one-shot linear DoF per cell scales linearly with the total amount of cache available in the cell, i.e., the sum of the caches at the central base station and all the receivers within the cell, resembling a similar phenomenon previously observed for the case of fully connected wireless networks. To establish the result, we propose a decentralized and randomized cache placement and a delivery scheme, which, on one hand, utilizes the overlap of contents at the base station caches to zero-force part of their outgoing interference and, on the other hand, uses the receiver cache contents to create coded multicasting opportunities, so that the receivers can eliminate the remaining interference due to undesired packets. We also provide a converse argument, which shows that our achievable one-shot linear DoF per cell is within a constant additive gap of (1/3) and a multiplicative gap of 2 of its optimum.

Numerical study of flow-induced vibrations of cylinders under the action of nonlinear energy sinks (NESs)

An isolated two-dimensional circular cylinder with two linear degrees of freedom, parallel and perpendicular to the free-stream direction, and owning a nonlinear energy sink (NES) is investigated by fluid–structure interaction (FSI) simulations to assess vortex-induced vibrations (VIV) at moderate Reynolds numbers. Subsequently, the wake-induced vibration (WIV) of a pair of identical cylinders under the action of two NES in a tandem arrangement and in a proximity–wake interference regime is explored using the same approach. The NES parameters (mass, nonlinear stiffness and damping) are investigated to determine their effects on the dynamic response of a single degree of freedom (in transverse flow direction) coupled system by a reduced-order model based on an experimentally validated van der Pol oscillator. The CFD model coupled with FSI method is also validated against VIV experimental data for an isolated cylinder in a uniform flow. The study is aimed to investigate the effect of the passive suppression NES device on VIV and WIV. The amplitude response, trajectories of cylinder motion and temporal evolutions of vortex shedding are obtained by conducting a series of numerical simulations. It is found that placing a tuned NES in the cylinders can provide good suppression effect; however, the effectiveness is function of the reduced velocity.

A novel stochastic linearization framework for seismic demand estimation of hysteretic MDOF systems subject to linear response spectra

This paper proposes a novel computationally economical stochastic dynamics framework to estimate the peak inelastic response of yielding structures modelled as nonlinear multi degree-of-freedom (DOF) systems subject to a given linear response spectrum defined for different damping ratios. This is accomplished without undertaking nonlinear response history analyses (RHA) or, to this effect, constructing an ensemble of spectrally matched seismic accelerograms. The proposed approach relies on statistical linearization and enforces pertinent statistical conditions to decompose the inelastic d-DOF system into d linear single DOF oscillators with effective linear properties (ELPs): natural frequency and damping ratio. Each such oscillator is subject to a different stationary random process compatible with the excitation response spectrum with damping ratio equal to the oscillator effective critical damping ratio. This equality is achieved through a small number of iterations to a pre-specified tolerance, while peak inelastic response estimates for all DOFs of interest are obtained by utilization of the excitation response spectrum in conjunction with the ELPs. The applicability of the proposed framework is numerically illustrated using a 3-storey Bouc-Wen hysteretic frame structure exposed to the Eurocode 8 elastic response spectrum. Nonlinear RHA involving a large ensemble of non-stationary Eurocode 8 spectrum compatible accelerograms is conducted to assess the accuracy of the proposed approach in a Monte Carlo-based context. The novel feature of iterative matching between the excitation response spectrum damping ratio and the ELP damping ratio enforces the required compatibility in the damping properties of the effective linear oscillators and the imposed elastic response spectra. It is found that this latter feature reduces drastically the error of the estimates (i.e., by an order of magnitude) obtained by a non-iterative application of the framework.

VIV trajectories of an elastically mounted sphere

In this paper, vortex-induced vibrations (VIV) of an elastically mounted sphere with two linear degrees of freedom have been experimentally studied. The dynamic response analysis shows that, for the range of reduced velocity from 2 to 14 here investigated, the sphere exhibits similar amplitudes and frequencies compared to the tethered sphere, and Modes I and II are detected. A new application of the phase average approach allowed extrapolating the periodic trajectory pattern from the experimental trajectories. In particular, more than one dominant harmonic component is observed in the streamwise oscillation, so the sphere trajectories are significantly different from the traditional figure-of-eight shape. The main difference is that these trajectories are not self-intersecting. Based on the experimental observations, an analytical model of the trajectory is built and discussed.

Linear Degrees of Freedom of Full-Duplex Cellular Networks With Reconfigurable Antennas

In this paper, we characterize the linear degrees of freedom (DoF) of a cellular network in which the base station (BS) operates in a full-duplex (FD) mode and the users operate in a half-duplex mode. We assume that the BS and the users are equipped with reconfigurable antennas which can be switched between their preset modes. We consider two practical scenarios for different assumptions on channel state information at the transmit sides (CSIT), referred to as no CSIT and partial CSIT models. To derive the inner-bounds for two scenarios, we propose a new achievable scheme which enables interference alignment between uplink and downlink interference signals at each user via preset mode switching of reconfigurable antennas. The key concept of our scheme is to align the interference signals of uplink transmission at the downlink users, through the identical preset mode pattern over the multiple of downlink transmission periods and silence periods of the BS. We also develop an outer-bound on the linear sum DoF of the cellular network for the no CSIT model, which matches up with the inner-bound. Moreover, we also provide a natural variant of the proposed scheme when considering residual self-interference at the FD BS, which can alleviate the shortcoming of the existing self-interference cancellation techniques.

Topological Interference Management With Reconfigurable Antennas

We study the symmetric degrees-of-freedom (DoF) of partially connected interference networks under linear coding strategies without channel state information at the transmitters beyond topology. We assume that the receivers are equipped with reconfigurable antennas that can switch among their preset modes. In such a network setting, we characterize the class of network topologies in which half linear symmetric DoF is achievable. Moreover, we derive two general upper bounds on the linear symmetric DoF for arbitrary network topologies. We also demonstrate the tightness of our bounds for the class of network topologies in which all the transmitters in the network have at most two co-interferers.

Linear Degrees of Freedom for $K$ -user MISO Interference Channels With Blind Interference Alignment

In this paper, we characterize the degrees of freedom (DoF) for $K$ -user $M \times 1$ multiple-input single-output interference channels with reconfigurable antennas, which have $N$ -preset modes at the receivers, assuming linear coding strategies in the absence of channel state information at the transmitters, i.e., blind interference alignment. Our linear DoF converse builds on the lemma that if a set of transmit symbols is aligned at their common unintended receivers, those symbols must have independent signal subspace at their corresponding receivers. This lemma arises from the inherent feature that channel state’s changing patterns of the links towards the same receiver are always identical, assuming that the coherence time of the channel is long enough. We derive an upper bound for the linear sum DoF, and propose an achievable scheme that exactly achieves the linear sum DoF upper bound when both of the ${n^{*}}/{M}=R_{1}$ and ${MK}/{n^{*}}=R_{2}$ are integers, where $n^{*}$ denotes the optimal number of preset modes out of $N$ preset modes. For the other cases, where either $R_{1}$ or $R_{2}$ is not an integer, we only give some guidelines how the interfering signals are aligned at the receivers to achieve the upper bound. As an extension, we also show the linear sum DoF upper bound for downlink/uplink cellular networks.

A Taylor Series Expansion Approach for Nonlinear Blade Forced Response Prediction Considering Variable Rotational Speed

In the field of turbomachinery, great efforts are made to enhance computational tools to obtain reliable predictions of the vibrational behavior of friction-damped bladed disks. As a trade-off between computational burden and level of simplification, numerous methods were developed to reduce the nonlinear systems dimension. Using component mode synthesis methods (CMS), one is capable to describe the systems motion by interface and modal coordinates. Subsequently or alternatively, the dynamic compliance matrix can be evaluated efficiently by means of modal superposition to avoid the inversion of the dynamic stiffness matrix. Only the equations corresponding to the degrees-of-freedom (DOF) subject to localized nonlinear contact forces need to be solved simultaneously, whereas the solution of the linear DOF is obtained by exploiting the algebraic character of the set of equations. In this paper, an approach is presented to account for rotational speed-dependent stiffness in the subset of nonlinear DOF without the need to re-evaluate the associated eigenvalue problem (EVP) when rotational speed is changed. This is done by means of a Taylor series expansion of the eigenvalues and eigenvectors used for the modal superposition to reconstruct the dynamic compliance matrix. In the context of forced response predictions of friction-damped blisks, the expansion is performed up to different order for a simplified blisk model with nonlinear contact interfaces. The results are compared to the solution obtained by direct evaluation of the EVP at selected rotational speeds and the solution when dynamic compliance matrix is built up by direct inversion of the dynamic stiffness matrix. Finally, the proposed methods computational performance is analyzed.