Quasi-static Motion Research Articles

Status of off-bottom mariculture in wave-exposed environments. Part 2. Comparative loading and motion of longline designs currently used in exposed commercial farms

A global inventory of extractive species mariculture in wave-exposed temperate waters shows that the longline is the technology used in more than 99% of the sites (Part 1 of this review). In this second part, I compare the static (longline at rest), quasi-static (tidal sea surface elevation, steady currents and mainline lifting operation) and dynamic (wind seas and swells) loading and motion of surface, semi-submerged and fully submerged longlines used to grow bivalves and kelp. This review is based on a hundred papers published on the subject mostly after 2010 and on simple analytical models used to illustrate the many compromises that must be made to ensure the survivability of the structure and the survival (retention), growth and quality of the cultured biomass. Surface longlines are unsuitable for fully exposed environments. To mitigate storm energy it is necessary to minimize the volume of surface buoys and submerge the mainline to the maximum depth possible. There is however a limit to minimizing the volume of surface buoys due to the uplifting of the mainline by currents. In the case of kelp, its optimal growing depth is within a few meters from the sea surface. This limitation can be partly circumvented by having the kelp float above the mainline. In the case of bivalves, mainline depth can be tens of meters below the sea surface. This comes with some disadvantages including difficulties in maintaining the delicate buoyancy balance, particularly for fully submerged longlines without legs, and reduced access to the mainline, particularly for fully submerged longlines with legs. Devices that allow autonomous or remote-controlled changes of mainline depth on a daily, occasional (husbandry and harvest operations) or seasonal basis have been tested but are not yet used commercially on longlines.

Using Pose Estimation and 3D Rendered Models to Study Leg-Mediated Self-righting by Lanternflies.

The ability to upright quickly and efficiently when overturned on the ground (terrestrial self-righting) is crucial for living organisms and robots. Previous studies have mapped the diverse behaviors used by various animals to self-right on different substrates, and proposed physical models to explain how body morphology can favor specific self-righting methods. However, to our knowledge, no studies have quantified and modeled all of an animal's limb motions during these complicated behaviors. Here, we studied terrestrial self-righting by immature invasive spotted lanternflies (Lycorma delicatula), an insect species that must frequently recover from being overturned after jumping and falling in its native habitat. These nymphs self-righted successfully in 92-100% of trials on three substrates with different friction and roughness, with no significant difference in the time or number of attempts required. They accomplished this using three stereotypic sequences of movements. To understand these motions, we combined 3D poses tracked on multi-view high-speed video with articulated 3D models created using photogrammetry and Blender rendering software. The results were used to calculate the mechanical properties (e.g., potential and kinetic energy, angular speed, stability margin, torque, force, etc.) of these insects during righting trials. We used an inverted physical pendulum model (a "template") to estimate the kinetic energy available in comparison to the increase in potential energy required to flip over. While these insects began righting using primarily quasistatic motions, they also used dynamic leg motions to achieve final tip-over. However, this template did not describe important features of the insect's center of mass trajectory and rotational dynamics, necessitating the use of an "anchor" model comprising the 3D rendered body model and six articulated two-segment legs to model the body's internal degrees of freedom and capture the role of the legs' contribution to inertial reorientation. This anchor elucidated the sequence of highly coordinated leg movements these insects used for propulsion, adhesion, and inertial reorientation during righting, and how they frequently pivot about a body contact point on the ground to flip upright. In the most frequently used method, diagonal rotation, these motions allowed nymphs to spin their bodies to upright with lower force with a greater stability margin compared to the other less frequently used methods. We provide a concise overview of necessary background on 3D orientation and rotational dynamics, and the resources required to apply these low-cost modeling methods to other problems in biomechanics.

Modeling multi-contact point physical interaction between the anthropomorphic finger and soft robotic exo-digit for wearable rehabilitation robotics applications.

Introduction: Effective control of rehabilitation robots requires considering the distributed and multi-contact point physical human-robot interaction and users' biomechanical variation. This paper presents a quasi-static model for the motion of a soft robotic exo-digit while physically interacting with an anthropomorphic finger model for physical therapy. Methods: Quasi-static analytical models were developed for modeling the motion of the soft robot, the anthropomorphic finger, and their coupled physical interaction. An intertwining of kinematics and quasi-static motion was studied to model the distributed (multiple contact points) interaction between the robot and a human finger model. The anthropomorphic finger was modeled as an articulated multi-rigid body structure with multi-contact point interaction. The soft robot was modeled as an articulated hybrid soft-and-rigid model with a constant bending curvature and a constant length for each soft segment. A hyperelastic constitute model based on Yeoh's 3rdorder material model was used for modeling the soft elastomer. The developed models were experimentally evaluated for 1) free motion of individual soft actuators and 2) constrained motion of the soft robotic exo-digit and anthropomorphic finger model. Results and Discussion: Simulation and experimental results were compared for performance evaluations. The theoretical and experimental results were in agreement for free motion, and the deviation from the constrained motion was in the range of the experimental errors. The outcomes also provided an insight into the importance of considering lengthening for the soft actuators.

A closed-loop bin picking system for entangled wire harnesses using bimanual and dynamic manipulation

This paper addresses the challenge of industrial bin picking using entangled wire harnesses. Wire harnesses are essential in manufacturing but pose challenges in automation due to their complex geometries and propensity for entanglement. Our previous work tackled this issue by proposing a quasi-static pulling motion to separate the entangled wire harnesses. However, it still lacks sufficiency and generalization to various shapes and structures. In this paper, we deploy a dual-arm robot that can grasp, extract and disentangle wire harnesses from dense clutter using dynamic manipulation. The robot can swing to dynamically discard the entangled objects and regrasp to adjust the undesirable grasp pose. To improve the robustness and accuracy of the system, we leverage a closed-loop framework that uses haptic feedback to detect entanglement in real-time and flexibly adjust system parameters. Our bin picking system achieves an overall success rate of 91.2% in the real-world experiments using two different types of long wire harnesses. It demonstrates the effectiveness of our system in handling various wire harnesses for industrial bin picking. Supplementary videos and illustrations can be found at https://xinyiz0931.github.io/dynamic.

Adaptive sliding mode control applied to quadrotors - a practical comparative study

This paper presents a complete control architecture for the implementation of adaptive sliding controllers (ASMC) in quadrotors. Aiming into presenting a control solution for real-world scenarios, this paper presents a comparative study evaluating the advantages and disadvantages of the three most common methods to implement adaptive sliding mode controllers in quadrotors. Namely, two of the compared methods aim to reduce the SMC gains to ones that keep the tracking errors inside a user-defined bound, while the third method consists of obtaining the minimal SMC gain which permits the sliding mode to exist. To inspect the compared methods in realistic and harsh conditions, the three controllers are tested far from quasi-static motion and under severe disturbances. The quadrotor was subjected to disturbances such as stabilization under intermittent wind, landing precisely subject to wind-gusts, high-speed trajectory tracking while carrying an unmodeled suspended payload with a center-of-mass offset, and trajectory tracking with a damaged propeller. The performance of the analyzed adaptive sliding mode controllers was also compared to the industrial standard PID controller. Our experimental analysis demonstrates that, in face of such disturbances, one of the analyzed adaptive sliding mode controllers excels when compared to the others, and every ASMC excels when compared to the PID.

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.

On the Kelvin–Voigt model in anisotropic viscoelasticity

We propose an anisotropic and nonlinear generalization of the Kelvin–Voigt viscoelastic model obtained considering the additive splitting of the Cauchy stress tensor in an elastic and a dissipative part. The former one corresponds to a fiber-reinforced hyperelastic material while the dissipative effect is described by the most general linear transverse-isotropic tensorial function of symmetric part of the velocity gradient. In a such a way we characterize the dissipative contribution via three viscoelastic moduli. We then show, by a detailed analysis of the simple shear quasistatic motion and the corresponding creep phenomena, that this motion may be used to determine experimentally the viscoelastic parameters.

Discrete differential geometry modeling on the fully coupled vibration of the viscoelastic rod interacting with rigid cylinders

The coupled vibration of flexible rods in contact with rigid cylinders has been observed to generate disruptive noise and significantly decrease the service life. Although the coupling effect of cylindrical rotation with transverse vibration or axial motion of slender rods has been well studied, the full coupling of the three motions remains inadequately understood. To address this issue, we propose an improved discrete differential geometry model with a tri-linear friction method to deliver accurate reproduction of resonant frequencies and vibration responses. Our model features several advances: (i) Viscous forces associated with stretching and bending strain rates are incorporated into the motion equation of the viscoelastic rod, replacing the assumption of quasi-static axial motion; (ii) A tri-linear friction method is introduced to obtain the relative motion between the slender rod and cylinders on the contact zone, thus eliminating errors stemming from pre-prescribed contact regions; (iii) The model fully couples the axial and transverse motion over the entire rod as well as the rotation of cylinders, surpassing the limitation of the coupled rotational-transverse model which only establishes equations of transverse motion on the non-contact zone of the rod. The numerical results indicate that the axial and transverse vibrations of the upper and lower span of the slender rod and the cylindrical rotational vibration are mutually excited, with their resonant frequencies having overlapping sites, which validates the proposed coupling model. Moreover, we are able to capture the phenomenon of contact surface sliding during the coupled vibration, confirm that the sliding limits the vibration amplitude, and determine the nonlinear relationship between the excitation and vibration response. This work provides a theoretical basis for further optimization of composite transmission structures, particularly in terms of suppressing vibration and improving efficiency of power transmission.

Characteristic of hydrodynamic derivatives for a multi-hull navigation vessel in dynamic positioning mode

The Quadmaran vessel is a maritime multi-hull vessel developed for water quality observation in aquaculture farms. The vessel’s dynamic positioning (DP) performance is essential for the accuracy of the collected data. The maneuvering characteristics in DP mode have been investigated in our previous research using a quasi-static motion prediction model based on static planar motion mechanism (PMM) tests. However, since the Quadmaran vessel has a unique hull arrangement, the motion characteristics need to be determined with greater accuracy. Therefore, in this study, the maneuvering equations are newly established with higher accuracy hydrodynamic derivatives determined through dynamic PMM tests. The higher order hydrodynamic derivatives are obtained from pure sway, pure yaw and pure yaw with a constant angle tests. Model scale experiments are conducted to establish an advanced mathematical model and compared with the quasi-static assumption results. The result shows significant improvements in the motion prediction under DP mode, and a more accurate motion prediction model is successfully established. This study is a new attempt to utilize the dynamic PMM tests method on a vessel with unique shape and motion characteristics. The advanced mathematical model deepens our understanding of the maneuverability of a multi-hull vessel in DP mode.

Development of a miniature quadrupedal piezoelectric robot combining fast speed and nano-resolution

Miniature piezoelectric robots exhibit superior performances and have been favored by many researchers, however, there is an intractable contradiction between nano-resolution and fast speed. Inspired by motion of quadrupeds, we proposed a miniature quadruped piezoelectric robot (MQPR), which combined quasi-static motion and resonant motion to realize nano-resolution and high speed, respectively. Two theoretical models were established to determine the parameters of the proposed piezo-leg, and they were verified by experiments. A prototype with size of 35 × 44 × 12 mm3 and weight of 21.0 g was manufactured and tested. The measured results showed that the MQPR realized multi-DOF motions with resolution of less than 8.8 nm and range of about 2 μm in quasi-static motion, and achieved a linear speed of 393.5 mm/s (11.2 BL/s) and a rotational speed of 246.5 °/s in resonant motion. Moreover, a resolution of 0.31 μm was obtained by resonant motion in pulse mode, which could achieve effective cooperation of the above two motion mechanisms. In addition, the load capacity of the MQPR was 100 g, which was about 5 times its own weight. These characteristics help the MQPR have great potential to efficiently perform precision manipulations at multiple target locations over a large area, such as detection of circuit board in large integrated circuits or wafers.

MOGA 4WD: multi-objective genetic algorithm for four-wheel drive electrical vehicle torque distribution in challenging conditions

This article aims to present a strategy for multi-objective optimization based on torque distribution for electrical 4WD (four-wheel drive) vehicles. By considering applications on uneven terrain, common to the navigation of tractors, off-road vehicles, or even mobile robots, an algorithm is developed having as input the vehicle attitude and output the controlled torque on each actuated wheel. The main criterion adopted is to guarantee the execution of a stable trajectory. And, to avoid wheel slippage, which occurs when low torques are applied, as well as vehicle rollover, which can occur in the presence of high torques, it is necessary to use two objective functions. To find the Pareto optimal solutions, the simplified dynamic model of a vehicle is adopted, considering a quasi-static motion. For each vehicle, its electrical, mechanical, and geometric characteristics can be used as formulation constraints. From an optimization performed offline, and adopting a polynomial approximation-based approach for real-time application, simulations and experiments show an interesting behavior: solutions that go beyond allowing the ascent of simple ramps or the overcoming of smooth obstacles are found - it is possible, for example, to climb ramps with high slopes, taking the vehicle to the limit between stability and instability.

Ablation Study of a Dynamic Model for a 3D-Printed Pneumatic Soft Robotic Arm

Ongoing advancements in the design and fabrication of soft robots are creating new challenges in modeling and control. This paper presents a dynamic Cosserat rod model for a single-section 3D-printed pneumatic soft robotic arm capable of combined stretching and bending. The model captures the manufacturing variability of the actuators by tuning the pressure-strain relation for each actuator. Moreover, it includes a simple model of the pneumatic actuation system that incorporates the transient response of proportional pressure-controlled electronic valves. The model was validated experimentally for several quasi-static and dynamic motion patterns with actuation frequencies ranging from 0.2 Hz to 20 Hz. The model reproduced the quasi-static experiments with an average tip error of 4.83% of the arm length. In dynamic conditions, the average tip error was 4.33% for stretching and bending motions, 5.64% for five motor babbling experiments, and 22.53% for three challenging sinusoidal patterns. An ablation study of the model components found that the most influential factors for the average accuracy were gravity and strain gains, followed by damping and pressure transient. This work could assist researchers in focusing on the most significant aspects for closing the real-to-sim gap when modeling pneumatic soft robotic arms.

On Evolving Natural Curvature for an Inextensible, Unshearable, Viscoelastic Rod

We formulate and consider the problem of an inextensible, unshearable, viscoelastic rod, with evolving natural configuration, moving on a plane. We prove that the dynamic equations describing quasistatic motion of an Eulerian strut, an infinite dimensional dynamical system, are globally well-posed. For every value of the terminal thrust, these equations contain a smooth embedded curve of static solutions (equilibrium points). We characterize the spectrum of the linearized equations about an arbitrary equilibrium point, and using this information and a convergence result for dynamical systems due to Brunovský and Polácik, we prove that every solution to the quasistatic equations of motion converges to an equilibrium point as time goes to infinity.

Modified couple stress flexural–flexural quasi-static pull-in analysis of large deformable cantilever-based micro-gyroscopes

This paper aims to develop a size-dependent large deformable model to study the flexural–flexural quasi-static motion of cantilever-based micro-gyroscopes based on the modified couple stress theory. The micro-cantilever is assumed to undergo non-planar bending–bending–twisting motion. Based on this assumption, the displacement field associated with a point placed on the cross-section of the micro-beam is introduced. Employing the introduced displacement field, the components of the Green–Lagrange strain and curvature tensors are obtained. Neglecting the terms with the time derivatives, the nonlinear, coupled and higher-order equations governing on three-dimensional quasi-static motion of in-extensional cantilever-based micro-gyroscopes and their corresponding boundary conditions are then obtained. Normalizing the strain and kinetic energies as well as the works done by the external forces, the reduced equations governing the quasi-static motion of micro-gyroscopes are obtained through employing the Ritz method with linear mode-shapes of clamped-free beams as the approximating functions. Vanishing the Jacobian of the reduced equations, the governing stability equations of the system are then obtained. Afterward, employing the achieved reduced equations, both the stable and unstable branches of the micro-gyroscope equilibrium paths are extracted. To validate the accuracy of the present model, several verifications have been conducted. The performed verifications demonstrate that the current model can be considered as a promising tool in capturing the influence of small scales on micro-gyroscopes undergoing extremely large deformations.

Experimental Study of Accuracy of High-Rate GNSS in Context of Structural Health Monitoring

Global Navigation Satellite Systems (GNSS)-based technologies have become an indispensable part of current structural health monitoring (SHM) systems because of the unique capability of the GNSS technologies to provide accurate real-time displacement information. GNSS equipment with a data sampling rate of up to about 20 Hz has been widely used for this purpose. High-rate GNSS systems (typically up to about 100 Hz) offer additional advantages in structural health monitoring as some highly dynamic civil structures, such as some bridges, require high-rate monitoring data to capture the dynamic behaviors. However, the performance of high-rate GNSS positioning in the context of structural health monitoring is not entirely known, as studies on structural monitoring with high-rate GNSS positioning are very limited, especially considering that some of the satellite systems just reached their full constellations very recently. We carried out a series of experiments with the help of a shaking table to assess the SHM performance of a set of 100 Hz GNSS equipment and three commonly used GNSS positioning techniques, PPP (precise point positioning), PPP-AR (precise point positioning with ambiguity resolution), and RTK (real-time kinematic). We found that the standard deviations of the 100 Hz GNSS displacement solutions derived from PPP, PPP-AR, and RTK techniques were 5.5 mm, 3.6 mm, and 0.8 mm, respectively, when the antenna was in quasi-static motion, and about 9.2 mm, 6.2 mm, and 3.5 mm, respectively, when the antenna was in vibration (up to about 0.7 Hz), under typical urban observational conditions in Hong Kong. We also found that the higher a sampling rate is, the lower the accuracy of a measured displacement series is. On average, the 10 Hz and 100 Hz results are 5.5% and 10.3%, respectively, noisier than the 1 Hz results.

A Quasi-Static Motion Prediction Model of a Multi-Hull Navigation Vessel in Dynamic Positioning Mode

A Quadmaran vessel is a maritime navigation vessel with four hulls, and is expected to be utilized for high-density water quality observation in aquaculture farms. The performance of the vessel during dynamic positioning (DP) is integral to the accuracy of collected data. However, there are no models available to understand the motion characteristics of the multi-hull vessels in DP mode. Therefore, a computational model was developed to predict the DP motion of the Quadmaran vessel based on quasi-static assumptions. The fluid forces on the hulls, the thrust force of the propellers, and the external wind forces are modelled systematically, assuming the average speed while in DP does not exceed 0.25 m/s. A series of oblique towing tests and static turning tests were conducted on a 1/3 scale model to determine the hydrodynamic coefficients, while the Propeller Open Test was conducted to survey the propeller performance. The wind load was also incorporated into the computational model. Experimental validation tests were conducted in calm water and actual sea areas, and the correlation between experiment and simulation results was good. We concluded that the computational model can predict the DP motion of the Quadmaran vessel with an accuracy of roughly 2 m.

A singular limit of a family of variational evolutions for a brittle elastic bi-layer

We consider a system of one-dimensional elastic and brittle media coupled by an elastic term. Both the coupling and the fracture-energy coefficient depend on a small parameter ɛ. We describe the quasistatic motion of this system under varying boundary conditions at ɛ fixed, interpreting the fracture energy term as a dissipation as in the variational approach to fracture growth, by analysing a time-discrete approximation. The motion is characterized by the onset of successive fracture sites. We study the behaviour of these evolutions with vanishing dissipations as ɛ→0, characterizing the possible limit of the energies by a one-parameter family of time-parameterized functions. We show that, after an initial time interval, a function in this family corresponds to a minimum of the Γ-limit of the energies of the system only for a discrete set of the values of the quantity parameterizing boundary conditions.

Numerical simulation of a fundamental mechanism of solar eruption with a range of magnetic flux distributions

Solar eruptions are an explosive release of coronal magnetic field energy manifested as solar flares and coronal mass ejections. Observations have shown that the core of eruption-productive regions are often a sheared magnetic arcade, namely, a single bipolar configuration, and, in particular, the corresponding magnetic polarities at the photosphere are elongated along a strong-gradient polarity inversion line (PIL). It remains unclear what mechanism triggers the eruption in a single bipolar field and why the one with a strong PIL is favorable for producing eruption. Recently, using highly accurate simulations, we established the fundamental mechanism behind solar eruption initiation by which a bipolar field driven by quasi-static shearing motion at the photosphere can form an internal current sheet, followed by fast magnetic reconnection that triggers and drives the eruption. Here, we investigate the behavior of the fundamental mechanism with different photospheric magnetic flux distributions, namely, magnetograms, by combining a theoretical analysis and a numerical simulation. Our study shows that the bipolar fields of different magnetograms, sheared continuously, all exhibit similar evolutions – from slow storage to the fast release of magnetic energy – that are in accordance with the fundamental mechanism and demonstrate the robustness of the proposed mechanism. Furthermore we found that the magnetograms with a stronger PIL produce larger eruptions and the key reason is that the sheared bipolar fields with a stronger PIL can achieve more non-potentiality and their internal current sheet can form at a lower height and with a higher current density, by which the reconnection can be more efficient. This also provides a viable trigger mechanism for the observed eruptions in active regions with a strong PIL.

Wind gust estimation for precise quasi-hovering control of quadrotor aircraft

This paper focuses on the control of quadrotor vehicles without wind sensors that are required to accurately track low-speed trajectories in the presence of moderate yet unknown wind gusts. By modeling the wind disturbance as exogenous inputs, and assuming that compensation of its effects can be achieved through quasi-static vehicle motions, this paper proposes an innovative estimation and control scheme comprising a linear dynamic filter for the estimation of such unknown inputs and requiring only position and attitude information. The filter is built upon results from Unknown Input Observer theory and allows estimation of wind and vehicle state without measurement of the wind itself. A simple feedback control law can be used to compensate for the offset position error induced by the disturbance. The proposed filter is independent of the recovery control scheme used to nullify the tracking error, as long as the corresponding applied rotor speeds are available. The solution is first checked in simulation environment by using the Robot Operating System middleware and the Gazebo simulator and then experimentally validated with a quadcopter system flying with real wind sources.

Towards a Live Feedback Training System: Interchangeability of Orbbec Persee and Microsoft Kinect for Exercise Monitoring

Many existing motion sensing applications in research, entertainment and exercise monitoring are based on the Microsoft Kinect and its skeleton tracking functionality. With the Kinect’s development and production halted, researchers and system designers are in need of a suitable replacement. We investigated the interchangeability of the discontinued Kinect v2 and the all-in-one, image-based motion tracking system Orbbec Persee for the use in an exercise monitoring system prototype called ILSE. Nine functional training exercises were performed by six healthy subjects in front of both systems simultaneously. Comparing the systems’ internal tracking states from ’not tracked’ to ‘tracked’ showed that the Persee system is more confident during motion sequences, while the Kinect is more confident for hip and trunk joint positions. Assessing the skeleton tracking robustness, the Persee’s tracking of body segment lengths was more consistent. Furthermore, we used both skeleton datasets as input for the ILSE exercise monitoring including posture recognition and repetition-counting. Persee data from exercises with lateral movement and in uncovered full-body frontal view provided the same results as Kinect data. The Persee further preferred tracking of quasi-static lower limb motions and tight-fitting clothes. With these limitations in mind, we find that the Orbbec Persee is a suitable replacement for the Microsoft Kinect for motion sensing within the ILSE exercise monitoring system.