Kinematic Configuration Research Articles

From the EFT of spinning gravitating objects to Poincaré and gauge invariance at the 4.5PN precision frontier

We confirm the generalized actions of the complete NLO cubic-in-spin interactions for generic compact binaries which were first tackled via an extension of the EFT of spinning gravitating objects. We first reduce these generalized actions to standard actions with spins, where the interaction potentials are found to consist of 6 independent sectors, including a new unique sector that is proportional to the square of the quadrupolar deformation parameter, CES2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {C}_{{\ extrm{ES}}^2} $$\\end{document}. We derive the general Hamiltonians in an arbitrary reference frame, and for generic kinematic configurations. With these most general Hamiltonians we construct the full Poincaré algebra of all the sectors at the fourth and a half post-Newtonian (4.5PN) order, including the third subleading spin-orbit sector, recently accomplished uniquely via our framework, thus proving the Poincaré invariance of all relevant sectors. We then derive the binding energies with gauge-invariant relations useful for gravitational-wave applications. Finally, we also derive the extrapolated scattering angles in the aligned-spins configuration for the scattering problem. Yet, as made clear already as of quadratic-in-spin sectors, the aligned-spins simplification inherent to the scattering-angle observable, entails a great loss of physical information, that is only growing with higher-spin sectors. Our completion of the full Poincaré algebra at the present 4.5PN order provides strong confidence that this new precision frontier in PN theory has now been established.

An Ergodic Selection Method for Kinematic Configurations in Autonomous, Flexible Mobile Systems

An Ergodic Selection Method for Kinematic Configurations in Autonomous, Flexible Mobile Systems

On the anatomy and structural control of a dyke swarm that fed caldera-forming ignimbrite eruptions

The evolution of eruptive vents related to calderas is not fully understood. We focus on a structural, rock-magnetic and geochemical investigation of a 314 Ma rhyolite dyke swarm associated with the late-orogenic Altenberg–Teplice Caldera, Bohemian Massif, eastern Variscan belt. The whole-rock major element, trace element and Nd–Pb isotope geochemistry along with the published U–Pb zircon geochronology link the extra-caldera dyke swarm with intra-caldera ignimbrites. The magnetic fabrics determined using the anisotropy of magnetic susceptibility are interpreted to record a continuum from magma ascent to emplacement and eruption during sinistral shearing. The latter evidences an interplay with regional tectonics associated with the activity of crustal-scale shear zones. The sinistral kinematics and strike of the dyke swarm, the elongation of caldera intrusive units, and the kinematics of major caldera faults are consistent with the dextral Riedel shear system, where the dykes correspond to antithetic R’ or X shears. Such a kinematic configuration implies that the maximum and minimum principal stresses were oriented roughly north–south and east–west, respectively. The relation between the stress field and the caldera elongation and orientation is not typical. We suggest that a pre-existing mutually perpendicular set of cross-cutting structural lineaments largely controlled the magma chamber and caldera formation. Supplementary material : The whole-rock major, trace element and isotope geochemical tables, magnetic fabrics source data and details of methods are available at https://doi.org/10.6084/m9.figshare.c.6715893

Planar degeneracy of the three-gluon vertex

We present a detailed exploration of certain outstanding features of the transversely-projected three-gluon vertex, using the corresponding Schwinger–Dyson equation in conjunction with key results obtained from quenched lattice simulations. The main goal of this study is the scrutiny of the approximate property denominated “planar degeneracy”, unveiled when the Bose symmetry of the vertex is properly exploited. The planar degeneracy leads to a particularly simple parametrization of the vertex, reducing its kinematic dependence to essentially a single variable. Our analysis, carried out in the absence of dynamical quarks, reveals that the planar degeneracy is particularly accurate for the description of the form factor associated with the classical tensor, for a wide array of arbitrary kinematic configurations. Instead, the remaining three form factors display considerable violations of this property. In addition, and in close connection with the previous point, we demonstrate the numerical dominance of the classical form factor over all others, except in the vicinity of the soft-gluon kinematics. The final upshot of these considerations is the emergence of a very compact description for the three-gluon vertex in general kinematics, which may simplify significantly nonperturbative applications involving this vertex.

A multi-arm robot system for efficient apple harvesting: Perception, task plan and control

Robot harvesting has emerged as an urgent need for apple industry due to a sharp decline in agricultural labor. In the field of harvesting robots, the use of multiple robotic arms to improve operational efficiency and promote industrial applications has gained significant attention. Despite the significant progress made in multi-arm harvesting robots in recent years, their widespread application in orchard production is hindered by insufficient efficiency of operation and the accuracy of fruit positioning. This paper focuses on the precise perception and multi-arm collaborative control issues of harvesting robots, and proposes a multi-arm apple harvesting robot system. Firstly, the paper introduces the hardware and software integration method and kinematic configuration of the robot, and presents its workspace division and asynchronous sequential operation mode. Secondly, the paper proposes a stereo vision fruit recognition and localization algorithm based on multi-task deep learning to enhance the accuracy of apple fruit positioning and a method of combining multiple perspectives to acquire a global fruit map is introduced. Finally, the paper presents a multi-arm task planning method based on the Markov game framework to optimize the target harvesting order of each arm and improve the collaboration efficiency. The effectiveness of the robot and its perception and control methods are verified through multiple field experiments in orchards. The field trials showed that the proposed vision system reduces the median locating error of the robot system by up to 44.43%; the proposed task planning algorithm can reduce the average cycle time by 33.3% compared to the heuristic-based algorithm, and time taken for optimizing task planning ranged from 1.14 s to 1.21 s; and the robot’s harvest success rate varied from 71.28% to 80.45%, and the average cycle time ranged from 5.8 s to 6.7 s.

Online active and dynamic object shape exploration with a multi-fingered robotic hand

The sense of touch can provide a robot with a wealth of information about the contact region when interacting with an unknown environment. Nevertheless, utilizing touch information to plan exploration paths and adjust robot posture to improve task efficiency remains challenging. This paper presents a novel approach for the online tactile surface exploration of unknown objects with a multi-degree of freedom robotic hand. We propose an exploration strategy that actively maximizes the entropy of the acquired data while dynamically balancing the exploration’s global knowledge and local complexity. We demonstrate that our method can efficiently control a multi-fingered robotic hand to explore objects of arbitrary shapes (e.g., with a handle, hole, or sharp edges). To facilitate efficient multi-contact exploration with a robotic hand, we offer an optimization-based planning algorithm that adapts the hand pose to the local surface geometry online and increases the kinematic configuration of each finger during exploration. Ultimately, we compared our approach to state of the art in a simulated environment. Experimental results indicate that our proposed methods can guide a multi-finger robotic hand to explore efficiently and smoothly, thereby reconstructing the unknown geometry of a variety of everyday objects, with significant improvements in data efficiency and finger compliance when compared to state-of-the-art approaches.

The nucleon-induced deuteron breakup process as a laboratory for chiral dynamics

The nucleon-induced deuteron breakup reaction is studied within the Faddeev approach at incoming nucleon laboratory energies of 135 and 200 MeV. The chiral semilocal momentum-space (SMS) potential developed up to N4LO+, supplemented by the N2LO three-nucleon interaction, is used. Our investigation is focused on the determination of theoretical uncertainties in a predicted cross section related to its dependence on the value of the cutoff parameter of the regulator. We also compare predictions based on the complete N2LO potential with those based on the two-nucleon force upgraded to the N4LO+ order and augmented with the N2LO three-nucleon force. In addition, we study the three-nucleon force effects predicted by this model of interaction. Our systematic study covers the entire kinematically allowed phase space; however, our main results are obtained when additional restrictions on energies and cross section values are imposed. In such a case, we observe that the dependence of the differential cross sections on the regulator cutoff is moderate at 135 MeV and much stronger at 200 MeV. For the latter energy, it can amount to up to 45% in specific kinematic configurations. Taking into account terms beyond, N2LO in a two-body interaction changes the cross section up to 20% (27%) at E = 135(200) MeV. The inclusion of the three-nucleon force leads to effects of approximately 27% at both energies. We illustrate these dependencies with a few examples of the exclusive cross section as a function of the arc length of the S-curve.

Bootstrapping multi-field inflation: non-Gaussianities from light scalars revisited

Primordial non-Gaussianities from multi-field inflation are a leading target for cosmological observations, because of the possible large correlations generated between long and short distances.These signatures are captured by the local shape of the scalar bispectrum. In this paper, we revisit the nonlinearities of the conversion process from additional light scalars into curvature perturbations during inflation.We provide analytic templates for correlation functions valid at any kinematical configuration, using the cosmological bootstrap as a main computational tool. Our results include the possibility of large breaking of boost symmetry, in the form of small speeds of sound for both the inflaton and the mediators.We consider correlators coming from the tree-level exchange of a massless scalar field.By introducing a late-time cutoff, we identify that the symmetry constraints on the correlators are modified. This leads to anomalous conformal Ward identities, and consequently the bootstrap differential equations acquire a source term that depends on this cutoff.The solutions to the differential equations are scalar seed functions that incorporate these late-time growth effects. Applying weight-shifting operators to auxiliary “seed” functions, we obtain a systematic classification of shapes of non-Gaussianity coming from massless exchange.For theories with de Sitter symmetry, we compare the resulting shapes with the ones obtained via the δN formalism, identifying missing contributions away from the squeezed limit. For boost-breaking scenarios, we derive a novel class of shape functions with phenomenologically distinct features in scale-invariant theories.Specifically, the new shape provides a simple extension of equilateral non-Gaussianity: the signal peaks at a geometric configuration controlled by the ratio of the sound speeds of the mediator and the inflaton.

A Bamboo-Inspired Exoskeleton (BiEXO) Based on Carbon Fiber for Shoulder and Elbow Joints

This paper presents a novel cable-driven exoskeleton (BiEXO) for the upper limb including shoulder and elbow joints. BiEXO is made of carbon fiber that is inspired by the Bamboo structure. The key components of BiEXO are carbon fiber tubes that mimic bamboo tubes. A combined driver is developed for BiEXO with two cable-driven mechanisms (CDMs) and a power transmission belt (PTB). The CDMs are used for shoulder and elbow flexion/extension movement utilizing cables to mimic the skeletal muscles function, while the PTB system drives a shoulder link to mimic the scapula joint for shoulder abduction/adduction movement. Simulation studies and evaluation experiments were performed to demonstrate the efficacy of the overall system. To determine the strength-to-weight of the bamboo-inspired links and guarantee high buckling strength in the face of loads imposed from the user side to the structure, finite element analysis (FEA) was performed. The results show that the carbon fiber link inspired by bamboo has more strength in comparison to the common long carbon fiber tube. The kinematic configuration was modeled by the modified Denavit-Hartenberg (D-H) notation. The mean absolute error (MAE) was 5.9 mm, and the root-mean-square error (RMSE) was 6 mm. In addition, verification experiments by tracking the trajectory in Cartesian space and the wear trials on a subject were carried out on the BiEXO prototype. The satisfactory results indicate BiEXO to be a promising system for rehabilitation or assistance in the future.

Multi-objective optimization approach for Inverse Kinematics of redundant manipulator for welding applications

This article presents an optimization-based approach for determining the Inverse Kinematics (IK) of redundant robot manipulators for industrial welding applications. Nine degrees of freedom (DOF) kinematic configuration of a robot manipulator with one prismatic and eight revolute joints has been modelled to improve maneuverability in a welding environment. To perform welding operations at desired task space locations (TSLs), the IK are to be determined. The IK problem is solved using a constrained multi-objective optimization technique with the objective of a reachability manipulator with minimal positional and orientational errors. An obstacle avoidance algorithm is also implemented to avoid collisions during welding operations. IK Simulations of the redundant manipulator in different welding applications were performed in a MATLAB environment. The obtained results shows that the welding manipulator reached desired locations successfully and this approach is adaptable for various shapes of weld joints.

All-order celestial OPE in the MHV sector

On-shell kinematics for gluon scattering can be parametrized with points on the celestial sphere; in the limit where these points collide, it is known that tree-level gluon scattering amplitudes exhibit an operator product expansion (OPE)-like structure. While it is possible to obtain singular contributions to this celestial OPE, getting regular contributions from both holomorphic and anti-holomorphic sectors is more difficult. In this paper, we use twistor string theory to describe the maximal helicity violating (MHV) sector of tree-level, four-dimensional gluon scattering as an effective 2d conformal field theory on the celestial sphere. By organizing the OPE between vertex operators in this theory in terms of soft gluon descendants, we obtain all-order expressions for the celestial OPE which include all regular contributions in the collinear expansion. This gives new, all-order formulae for the collinear splitting function (in momentum space) and celestial OPE coefficients (in the conformal primary basis) of tree-level MHV gluon scattering. We obtain these results for both positive and negative helicity gluons, and for any incoming/outgoing kinematic configuration within the MHV sector.

The Collins Asymmetry in Λ Hyperon Produced SIDIS Process at Electron–Ion Colliders

We investigate Collins asymmetry in the Λ hyperon produced semi-inclusive deep inelastic scattering (SIDIS) process based on the kinematical region of Electron-ion collider in China (EicC) and Electron–ion collider (EIC) within the transverse momentum dependence (TMD) factorization framework at next-to-leading-logarithmic order. The asymmetry is contributed by the convolution of the target proton transversity distribution function and the Collins function of the final-state Λ hyperon. The TMD evolution effect of the corresponding parton distribution functions (PDFs) and fragmentation functions (FFs) is considered with the help of parametrization of the non-perturbative Sudakov form factors for the proton PDFs and Λ fragmentation functions. We apply the parametrization of the collinear proton transversity distribution function and the model results of Λ Collins function from the diquark spectator model as the inputs of the TMD evolution to numerically calculate Collins asymmetry in Λ produced SIDIS process at the kinematical configurations of EIC and EicC. It can be shown that the asymmetry is significant and can be measured at EIC and EicC. The flavor dependence of transversity distribution functions could be further constrained by studying the Λ hyperon produced SIDIS process in the future to improve our understanding of the spin structure within nucleons.

Algorithms for minimal Picard–Fuchs operators of Feynman integrals

In even space-time dimensions the multi-loop Feynman integrals are integrals of rational function in projective space. By using an algorithm that extends the Griffiths--Dwork reduction for the case of projective hypersurfaces with singularities, we derive Fuchsian linear differential equations, the Picard--Fuchs equations, with respect to kinematic parameters for a large class of massive multi-loop Feynman integrals. With this approach we obtain the differential operator for Feynman integrals to high multiplicities and high loop orders. Using recent factorisation algorithms we give the minimal order differential operator in most of the cases studied in this paper. Amongst our results are that the order of Picard--Fuchs operator for the generic massive two-point $n-1$-loop sunset integral in two-dimensions is $2^{n}-\binom{n+1}{\left\lfloor \frac{n+1}{2}\right\rfloor }$ supporting the conjecture that the sunset Feynman integrals are relative periods of Calabi--Yau of dimensions $n-2$. We have checked this explicitly till six loops. As well, we obtain a particular Picard--Fuchs operator of order 11 for the massive five-point tardigrade non-planar two-loop integral in four dimensions for generic mass and kinematic configurations, suggesting that it arises from $K3$ surface with Picard number 11. We determine as well Picard--Fuchs operators of two-loop graphs with various multiplicities in four dimensions, finding Fuchsian differential operators with either Liouvillian or elliptic solutions.

A Computational Fluid Dynamics Investigation of a Flapping Hydrofoil as a Thruster

The paper features a computational fluid dynamics study of a flapping NACA0015 hydrofoil moving with a combination of sinusoidal heaving and pitching. Several kinematic configurations are explored, varying sequentially pitch and heave amplitude, Strouhal number and phase angle, in an attempt to determine the influence of each parameter on the propulsive performance. To optimize efficiency the angle of attack should assume the highest value that also avoids the arise of the leading edge vortex generated in the dynamic stall state. At low Strouhal number optimum is reached at high heave amplitudes, which correspond to the configurations minimizing the hysteresis in the (Cy,Cx) plane. The same outcome in terms of hysteresis minimization has been verified to occur when optimal phase shift was considered. Differently, when the Strouhal number and the angle of attack become higher, to exploit efficiently the lift increment owed to dynamic stall it emerged the necessity of adopting low heave amplitude to improve separation resistance, avoiding the occurrence of deep stall.

A Concurrent Framework for Constrained Inverse Kinematics of Minimally Invasive Surgical Robots.

Minimally invasive surgery has undergone significant advancements in recent years, transforming various surgical procedures by minimizing patient trauma, postoperative pain, and recovery time. However, the use of robotic systems in minimally invasive surgery introduces significant challenges related to the control of the robot's motion and the accuracy of its movements. In particular, the inverse kinematics (IK) problem is critical for robot-assisted minimally invasive surgery (RMIS), where satisfying the remote center of motion (RCM) constraint is essential to prevent tissue damage at the incision point. Several IK strategies have been proposed for RMIS, including classical inverse Jacobian IK and optimization-based approaches. However, these methods have limitations and perform differently depending on the kinematic configuration. To address these challenges, we propose a novel concurrent IK framework that combines the strengths of both approaches and explicitly incorporates RCM constraints and joint limits into the optimization process. In this paper, we present the design and implementation of concurrent inverse kinematics solvers, as well as experimental validation in both simulation and real-world scenarios. Concurrent IK solvers outperform single-method solvers, achieving a 100% solve rate and reducing the IK solving time by up to 85% for an endoscope positioning task and 37% for a tool pose control task. In particular, the combination of an iterative inverse Jacobian method with a hierarchical quadratic programming method showed the highest average solve rate and lowest computation time in real-world experiments. Our results demonstrate that concurrent IK solving provides a novel and effective solution to the constrained IK problem in RMIS applications.

Boomerang Algorithm based on Swarm Optimization for Inverse Kinematics of 6 DOF Open Chain Manipulators

In this study, a feasible swarm intelligence algorithm is proposed that computes the inverse kinematics solution of 6 degree of freedom (DOF) industrial robot arms, which are frequently used in industrial and medical applications. The proposed algorithm is named as Boomerang algorithm due to its recursive structure. The proposed algorithm aims to reduce the computation time to feasible levels without increasing the position and orientation errors. In order to reduce the computational time in swarm optimization algorithms and increase feasibility, an alternative definition method was used instead of the DH method in defining the robot arm kinematic configuration. The effect of the proposed alternative definition method in reducing the computational time is presented through example inverse kinematic analysis. The proposed algorithm was compared with 3 different particle swarm optimization (PSO) variants that include orientation in the inverse kinematic solution of 6 DOF robot arms. Comparative simulation studies were carried out with 20 randomly selected position and orientation data from the workspaces of PUMA 560 and ABB IRB120 manipulators to measure performance of the algorithms. Using the error and computation time values obtained from the simulation results, the algorithms are compared using the Wilcoxon nonparametric statistical test. When the simulation results are analysed by considering the calculation time, positioning accuracy and solution finding rates, it is seen that the Boomerang algorithm is more feasible than the other PSO variants. Verification of the simulation results, and the physical applications were carried out with the ABB IRB120 6 DOF robot arm. Simulation studies and experimental studies showed that the proposed algorithm may be an efficient method for inverse kinematics of time-critical applications.

Model Predictive Leg Configuration Control for Leg/Wheel Mobile Robots that Adapts to Changes in Ground Level

Leg/wheel mobile robots, which have articulated legs ending in a wheel, can walk on legs as well as drive on wheels by switching between those two motive mechanisms in response to the terrain. However, effective control of the redundant degrees of freedom of leg/wheel mobile robots is complex. In this study, we propose a model predictive controller for leg configuration control that achieves both driving along the ground surface and climbing over a step. The proposed method simultaneously optimizes the robot pose, wheel positions, and joint angles. To consider the kinematic configuration of the legs explicitly, we formulate constraints on the relative position between the body and wheels. The ground contact condition of the wheels is approximately expressed as a continuous function with respect to each wheel’s relative position to the ground. This formulation induces smooth lifting of the wheels when the ground level abruptly changes, as when climbing a step. To prevent overturning, we evaluate the load distribution between each grounded wheel and constrain the body position to form a support polygon consisting of the grounded wheels. We conducted numerical simulations to verify that the proposed method achieves both driving on wheels and climbing over a step.

Quasi-Coordinates-Based Closed-Form Dynamic Modeling and Analysis for a 2R1T PKM with a Rigid–Flexible Structure

This work derives a closed-form dynamic model for a two rotational and one translational degrees-of-freedom (2R1T) parallel kinematic mechanism (PKM) with a hybrid rigid–flexible structure for force-control applications. Based on the three-prismatic-prismatic-spherical (3PPS) kinematic configuration of the 2R1T PKM and its zero-torsion motion characteristics, a symbolic formulation approach is proposed to establish closed-form kinematic models for both forward and inverse kinematics analysis. As the moving platform pose of the 2R1T 3PPS PKM can be readily determined by the three active prismatic joint variables and the three passive prismatic joint variables, these six joint variables are selected as the quasi-coordinates so as to systematically develop the closed-form dynamic model with a Lagrangian formulation, in which the stiffness and deformation of the three flexure-based passive prismatic joints are uniformly taken into consideration. Through eliminating the three passive prismatic joint variables based on the principle of virtual work and the relationships between the active and passive prismatic joint variables, a closed-form dynamic model for the 2R1T 3PPS PKM with a rigid–flexible structure is finally obtained. The correctness of the closed-form dynamic model was validated with the commercial dynamic simulation software. Utilizing the closed-form dynamic model, the effects of different flexure stiffness in driving directions on the required active joint force were investigated, which indicated that little flexure stiffness in driving directions is desired.

Harnessing elastic energy to overcome singularity issues in four-bar mechanisms with a crank link

The ability to convert reciprocating, i.e., alternating, actuation into rotary motion using linkages is hindered fundamentally by their poor torque transmission capability around kinematic singularity configurations. Here, we harness the elastic potential energy of a linear spring attached to the coupler link of four-bar mechanisms to manipulate force transmission around the kinematic singularities. We developed a theoretical model to explore the parameter space for proper force transmission in slider-crank and rocker-crank four-bar kinematics. Finally, we verified the proposed model and methodology by building and testing a macro-scale prototype of a slider-crank mechanism. We expect this approach to enable the development of small-scale rotary engines and robotic devices with closed kinematic chains dealing with serial kinematic singularities, such as linkages and parallel manipulators.

Assessment of a RANS Transition Model with Flapping Foils at Moderate Reynolds Numbers

Numerical simulations based on a high-order discontinuous Galerkin solver were performed to investigate two-dimensional flapping foils at moderate Reynolds numbers, moving with different prescribed harmonic motion laws. A Spalart–Allmaras RANS model with and without an algebraic local transition modification was employed for the resolution of multiple kinematic configurations, considering both moderate-frequency large-amplitude flapping and high-frequency small-amplitude pure heaving. The propulsive performance of the airfoils with the two modelling approaches were tested by referring to experimental and (scale-resolving) numerical data available in the literature. The results show an increase in effectiveness in predicting loads when applying the transition model. This is particularly true at low Strouhal numbers when, after laminar separation at the leading edge, vorticity dynamics appears to have a strong effect on the forces exerted on the profile. Specifically, the transition model more accurately predicts the wake topology emerging in the flow field, which is the primary influence on thrust/drag generation.