Kinematic Mapping Research Articles

A novel planar motion generation method based on the synthesis of planetary gear train with noncircular gears

Four-bar linkage has been used in motion generation synthesis for a long time, but there are inevitably some shortcomings such as order defects and poor design flexibility. In this work, a planetary gear train with noncircular gears is proposed to realize planar motion generation synthesis. Compared with the four-bar linkage, it has the advantages of a compact structure, full rotatability, and flexible design. The planetary gear train with noncircular gears is composed of two interrelated parts: a two-stage noncircular gear pair and the RR dyad. The synthesis method is divided mainly into three steps: First, the constraint equation of RR dyad for planar motion generation is established, and a solution region of the double revolute joint (RR) dyads is calculated by kinematic mapping theory. Second, after the full rotatability identification of RR dyads and the determination of each transmission ratio, the centrodes of two-stage noncircular gear pairs, which correspond to the specific RR dyad, are obtained. Finally, the planetary gear train with noncir-cular gears is established to pass the given poses. This method has a universal significance and can be applied to many practical cases.

Modeling and simulation of cooperative transport of an object by two mobile manipulators on an uneven terrain using KSOM network

ABSTRACT In this paper, a learning-based method for cooperative load transport by two 16 DOF wheeled mobile manipulators (MM) on a rough surface is proposed. Each MM has a 10 DOF mobile platform with a six DOF manipulator on top of it. As the MM system is redundant, the standard pseudo inverse or Jacobian methods for finding the inverse kinematics solution cannot be used in real time. Thus, an advanced Kohonen self-organizing map (KSOM) network is used to learn the inverse kinematic mapping and resolve the redundancy of the MMs. Considering the nonholonomic constraints of the vehicle and manipulability measure of the manipulator, the forward kinematic model of the MM system is used to train the network. A user defined object path governs the end effector paths of the two MMs for carrying the object and the trained network resolves the redundancy of the MMs to follow the respective end effector paths. The advantage of the proposed method is that once a terrain is learned, multiple MMs can be simulated to carry an object together in real time, without complex inverse kinematics. Simulation results show the usefulness of the proposed method.

Robotic hand-arm system for on-orbit servicing missions in Tiangong-2 Space Laboratory

PurposeThe purpose of this study is to develop a robotic hand–arm system for on-orbit servicing missions at the Tiangong-2 (TG-2) Space Laboratory.Design/methodology/approachThe hand–arm system is mainly composed of a lightweight arm, a dexterous hand, an electrical cabinet, a global camera, a hand–eye camera and some human–machine interfaces. The 6-DOF lightweight arm and the 15-DOF dexterous hand adopt the modular design philosophy that greatly reduces the design cycle and cost. To reduce the computational burden on the central controller and simplify system maintenance, an electrical system which has a hierarchical structure is introduced.FindingsThe prototypical operating experiments completed in TG-2 space laboratory demonstrate the performance of the hand–arm system and lay foundations for the future applications of space manipulators.Originality/valueThe main contributions of this paper are as follows a robotic hand–arm system which can perform on-orbit servicing missions such as grasping the electric drill, screwing the bolt, unscrewing J599 electrical connector has been developed; a variable time step motion plan method is proposed to adjust the trajectories of the lightweight arm to reduce or eliminate the collision force; and a dexterous hand uses the coordinated grasp control based on the object Cartesian stiffness to realize stable grasp. To solve the kinematic mapping from the cyber glove commands to the dexterous hand, a fingertip-position-based method is proposed to acquire precise solutions.

The Milky Way bar/bulge in proper motions: a 3D view from VIRAC and Gaia

Abstract We have derived absolute proper motions of the entire Galactic bulge region from VVV Infrared Astrometric Catalogue (VIRAC) and Gaia. We present these both as integrated on-sky maps and, after isolating standard candle red clump (RC) stars, as a function of distance using RC magnitude as a proxy. These data provide a new global, 3D view of the Milky Way barred bulge kinematics. We find a gradient in the mean longitudinal proper motion, $\langle \mu _ l^\star \rangle $, between the different sides of the bar, which is sensitive to the bar pattern speed. The split RC has distinct proper motions and is colder than other stars at similar distance. The proper motion correlation map has a quadrupole pattern in all magnitude slices showing no evidence for a separate, more axisymmetric inner bulge component. The line-of-sight integrated kinematic maps show a high central velocity dispersion surrounded by a more asymmetric dispersion profile. $\sigma _{\mu _l} / \sigma _{\mu _b}$ is smallest, ≈1.1, near the minor axis and reaches ≈1.4 near the disc plane. The integrated $\langle \mu_b\rangle$ pattern signals a superposition of bar rotation and internal streaming motion, with the near part shrinking in latitude and the far part expanding. To understand and interpret these remarkable data, we compare to a made-to-measure barred dynamical model, folding in the VIRAC selection function to construct mock maps. We find that our model of the barred bulge, with a pattern speed of 37.5 $\mathrm{ \mathrm{ km \, s^{-1}} \, kpc^{-1} }$, is able to reproduce all observed features impressively well. Dynamical models like this will be key to unlocking the full potential of these data.

The impact of AGN on stellar kinematics and orbits in simulated massive galaxies

ABSTRACT We present a series of 10 × 2 cosmological zoom simulations of the formation of massive galaxies with and without a model for active galactic nucleus (AGN) feedback. Differences in stellar population and kinematic properties are evaluated by constructing mock integral field unit maps. The impact of the AGN is weak at high redshift when all systems are mostly fast rotating and disc-like. After z ∼ 1 the AGN simulations result in lower mass, older, less metal rich, and slower rotating systems with less discy isophotes – in general agreement with observations. 2D kinematic maps of in situ and accreted stars show that these differences result from reduced in-situ star formation due to AGN feedback. A full analysis of stellar orbits indicates that galaxies simulated with AGN are typically more triaxial and have higher fractions of x-tubes and box orbits and lower fractions of z-tubes. This trend can also be explained by reduced late in-situ star formation. We introduce a global parameter, ξ3, to characterize the anticorrelation between the third-order kinematic moment h3 and the line-of-sight velocity (Vavg/σ), and compare to ATLAS3D observations. The kinematic correlation parameter ξ3 might be a useful diagnostic for large integral field surveys as it is a kinematic indicator for intrinsic shape and orbital content.

The Fornax3D project: Tracing the assembly history of the cluster from the kinematic and line-strength maps

The 31 brightest galaxies (mB ≤ 15 mag) inside the virial radius of the Fornax cluster were observed from the centres to the outskirts with the Multi Unit Spectroscopic Explorer on the Very Large Telescope. These observations provide detailed high-resolution maps of the line-of-sight kinematics, line strengths of the stars, ionised gas reaching 2–3 Re for 21 early-type galaxies, and 1–2 Re for 10 late-type galaxies. The majority of the galaxies are regular rotators, with eight hosting a kinematically distinct core. Only two galaxies are slow rotators. The mean age, total metallicity, and [Mg/Fe] abundance ratio in the bright central region inside 0.5 Re and in the galaxy outskirts are presented. Extended emission-line gas is detected in 13 galaxies, most of them are late-type objects with wide-spread star formation. The measured structural properties are analysed in relation to the galaxies’ position in the projected phase space of the cluster. This shows that the Fornax cluster appears to consist of three main groups of galaxies inside the virial radius: the old core; a clump of galaxies, which is aligned with the local large-scale structure and was accreted soon after the formation of the core; and a group of galaxies that fell in more recently.

The MASSIVE Survey XIII. Spatially Resolved Stellar Kinematics in the Central 1 kpc of 20 Massive Elliptical Galaxies with the GMOS-North Integral Field Spectrograph

Abstract We use observations from the GEMINI-N/GMOS integral field spectrograph (IFS) to obtain spatially resolved stellar kinematics of the central ∼1 kpc of 20 early-type galaxies (ETGs) with stellar masses greater than 1011.7 M ⊙ in the MASSIVE survey. Together with observations from the wide-field Mitchell IFS at McDonald Observatory in our earlier work, we obtain unprecedentedly detailed kinematic maps of local massive ETGs, covering a scale of ∼0.1–30 kpc. The high (∼120) signal-to-noise ratio of the GMOS spectra enables us to obtain two-dimensional maps of the line-of-sight velocity and velocity dispersion σ, as well as the skewness h 3 and kurtosis h 4 of the stellar velocity distributions. All but one galaxy in the sample have σ(R) profiles that increase toward the center, whereas the slope of σ(R) at one effective radius (R e ) can be of either sign. The h 4 is generally positive, with 14 of the 20 galaxies having positive h 4 within the GMOS aperture and 18 having positive h 4 within 1R e . The positive h 4 and rising σ(R) toward small radii are indicative of a central black hole and velocity anisotropy. We demonstrate the constraining power of the data on the mass distributions in ETGs by applying Jeans anisotropic modeling (JAM) to NGC 1453, the most regular fast rotator in the sample. Despite the limitations of JAM, we obtain a clear χ 2 minimum in black hole mass, stellar mass-to-light ratio, velocity anisotropy parameters, and circular velocity of the dark matter halo.

Transverse bar/bulge kinematics with Gaia and VVV

AbstractWe present new results on the Galactic bar/bulge transverse velocity structure using Gaia and the VISTA Variables in Via Lactea (VVV) survey. Gaia is complemented in high extinction regions by the multi-epoch infrared VVV observations for which derived relative proper motions can be tied to Gaia’s absolute frame. We extract kinematic maps (both 2D and 3D) of the Galactic bar/bulge, from which we measure the pattern speed of the bar using a novel technique. We focus on the evidence of an X-shaped bulge from the kinematic maps.

Revisiting the innermost kinematics of M31 galaxy with the OMM Fabry-Perot interferometer

AbstractWe present observations on optical emission lines acquired with the scanning Fabry-Perot interferometer of the observatoire du Mont Mégantic, of the Andromeda galaxy (M31). A 765 order Fabry-Perot were used with a fast readout EM-CCD. From data obtained, kinematic maps and data points for the rotation curve of the innermost part of the galaxy are derived. Several dozen of regions have been scanned with the Fabry-Perot interferometer and narrow band interference filters. The central 10’x10’ were scanned with five different filters. Observations have been made in order to get better Hα data for kinematics purposes.

Outflows, inflows, and young stars in the inner 200 pc of the Seyfert galaxy NGC 2110

ABSTRACT We present a 2D mapping of stellar population age components, emission-line fluxes, gas excitation, and kinematics within the inner ∼200 pc of the Seyfert 2 galaxy NGC 2110. We used the Gemini North Integral Field Spectrograph (NIFS) in the J and K bands at a spatial resolution of ∼22 pc. The unresolved nuclear continuum is originated in combined contributions of young stellar population (SP; age ≤ 100 Myr), a featureless AGN continuum and hot dust emission. The young-intermediate SP (100 < age ≤ 700 Myr) is distributed in a ring-shaped structure at ≈140 pc from the nucleus, which is roughly coincident with the lowest values of the stellar velocity dispersion. In the inner ≈115 pc the old SP (age > 2 Gyr) is dominant. The [Fe ii] $\lambda \, 1.2570\, \mu$m emission-line flux distribution is correlated with the radio emission and its kinematics comprise two components, one from gas rotating in the galaxy plane and another from gas in outflow within a bicone-oriented along north–south. These outflows seem to originate in the interaction of the radio jet with the ambient gas producing shocks that are the main excitation mechanism of the [Fe ii] emission. We estimate: (1) an ionized gas mass outflow rate of ∼0.5 M⊙ yr−1 at ∼70 pc from the nucleus; and (2) a kinetic power for the outflow of only 0.05 per cent of the AGN bolometric luminosity implying weak feedback effect on the galaxy.

Distinguishing Mergers and Disks in High-redshift Observations of Galaxy Kinematics

Abstract The majority of massive star-forming galaxies at z ∼ 2 have velocity gradients suggestive of rotation, in addition to large amounts of disordered motions. In this paper, we demonstrate that it is challenging to distinguish the regular rotation of a disk galaxy from the orbital motions of merging galaxies with seeing-limited data. However, the merger fractions at z ∼ 2 are likely too low for this to have a large effect on measurements of disk fractions. To determine how often mergers pass for disks, we look to galaxy formation simulations. We analyze ∼24,000 synthetic images and kinematic maps of 31 high-resolution simulations of isolated galaxies and mergers at z ∼ 2. We determine if the synthetic observations pass the criteria commonly used to identify disk galaxies and whether the results are consistent with their intrinsic dynamical states. Galaxies that are intrinsically mergers pass the disk criteria for anywhere from 0% to 100% of sightlines. The exact percentage depends strongly on the specific disk criteria adopted and weakly on the separation of the merging galaxies. Therefore, one cannot tell with certainty whether observations of an individual galaxy indicate a merger or a disk. To estimate the fraction of mergers passing as disks in current kinematics samples, we combine the probability that a merger will pass as a disk with theoretical merger fractions from a cosmological simulation. Taking the latter at face value, the observed disk fractions are overestimated by small amounts: at most by 5% at high stellar mass (1010–11 M ⊙) and 15% at low stellar mass (109–10 M ⊙).

Real-time humanoid whole-body remote control framework for imitating human motion based on kinematic mapping and motion constraints

ABSTRACTIn this paper, we propose a whole-body remote control framework that enables a robot to imitate human motion efficiently. The framework is divided into kinematic mapping and quadratic programming based whole-body inverse kinematics. In the kinematic mapping, the human motion obtained through a data acquisition device is transformed into a reference motion that is suitable for the robot to follow. To address differences in the kinematic configuration and dynamic properties of the robot and human, quadratic programming is used to calculate the joint angles of the robot considering self-collision, joint limits, and dynamic stability. To address dynamic stability, we use constraints based on the divergent component of motion and zero moment point in the linear inverted pendulum model. Simulation using Choreonoid and a locomotion experiment using the HUBO2+ demonstrate the performance of the proposed framework. The proposed framework has the potential to reduce the preview time or offline task computation time found in previous approaches and hence improve the similarity of human and robot motion while maintaining stability.

The kinematics of local thick discs do not support an accretion origin

Thick discs are nearly ubiquitous components of the discs of present-day galaxies. It has been proposed that a fraction of their stars have been accreted. Here, we aim to find whether accretion of satellites is the main formation mechanism of thick discs. To do so, we observed a sample of eight nearby edge-on galaxies with the Multi-Unit Spectroscopic Explorer (MUSE) integral field unit at the Very Large Telescope (VLT). Six of the galaxies have a distinct thick disc. We derived thick-disc velocities and velocity dispersions for the galaxies in our sample. We devise a formalism to estimate the fractions of retrograde material in the thick discs by using kinematical maps and thin/thick disc decompositions. None of the galaxies in our sample show strong evidence for retrograde material at large distances from the centre. Including those found in the literature, there are seventeen thick discs with studied kinematics, with only one showing unambiguous signatures of retrograde material. Literature numerical studies of dynamical friction allow us to estimate that at the current cosmic time about one in six mergers for which the stars of the accreted galaxy ended in a thick disc were retrograde. This is in tension with the observed fraction of galaxies with a partly retrograde thick disc (one in seventeen). We conclude that satellite accretion is not favoured by observations to be the main formation mechanism of thick discs.

Nuclear ionised outflows in a sample of 30 local galaxies

AbstractUnderstanding active galactic nuclei (AGN) feedback is essential for building a coherent picture of the evolution of the super massive black hole and its host galaxy. To that end we have analysed the inner kiloparsec of a sample of 30 local AGN with spatially resolved optical spectroscopy. In this talk I will review the analysis of the ionised gas for the galaxies in our sample, including kinematical maps, emission line ratios and fluxes. The W80 kinematical index is used to trace outflows, and also to provide an estimate for the outflowing velocity. Electron densities, derived from the [S II] ΛΛ6716, 6731Å lines, along with Hα luminosities and the sizes of the outflowing regions are employed in estimates of the outflowing gas mass. We find a median mass outflow rate of Ṁ = 0.3 M⊙ yr-1 and median outflow power of log [P/(erg s-1)] = 40.4.

Novel approach for planetary gear train dimensional synthesis through kinematic mapping

The synthesis of a kinematic trajectory traversed by an output link (planet gear) and posture of a planetary gear train with noncircular gears can be divided into two phases: dimensional synthesis of the open-chain 2R mechanism (planetary carrier) and optimization of the transmission ratio of noncircular gear pairs. According to kinematic mapping theory, more than one closed coupler trajectory can be obtained by five preset poses. Simultaneous consideration of the trajectory shape, posture, and gear ratio is difficult during planetary gear train synthesis. This work therefore proposes a new method for the synthesis of planetary gear train in which different path segments in different trajectories are selected and a group of same-type 2R mechanisms is employed to pass through them in order to rebuild a new, closed trajectory. Subsequently, the transmission ratio of noncircular gear pairs can be determined using the relative angular displacement of the 2R mechanism. To improve the roundness of the pitch curves of noncircular gears, two optimization steps are implemented using a genetic algorithm without alternating the data points of the requisite open trajectories. For example, a mechanism for rice pot seedling transplanting is obtained by using the method.

Modeling the robotic manipulation of woven carbon fiber prepreg plies onto double curved molds: A path-dependent problem

This paper investigates the behavior of woven prepreg plies being placed on a weakly double curved mold by a robot. It is essential that the draped configuration is free from wrinkles. The baseline is a virtual draping environment that can plan and simulate robot draping sequences. It consists of a kinematic mapping algorithm for obtaining target points for the grippers on the mold surface. A simple motion planner is used to calculate the trajectories of the grippers. Here, two conceptually different draping strategies are employed. Finally, the two generated draping sequences are simulated using a transient, non-linear finite element model and compared w.r.t. their predicted wrinkle formations. Material data are obtained by means of tension, bias-extension and cantilever tests. The numerical examples show that the virtual draping environment can aid in developing the automatic draping system but that the generation of feasible draping sequences is highly path dependent and non-trivial.

Deep Neural Network Approach in Human-Like Redundancy Optimization for Anthropomorphic Manipulators

Human-like behavior has emerged in the robotics area for improving the quality of Human-Robot Interaction (HRI). For the human-like behavior imitation, the kinematic mapping between a human arm and robot manipulator is one of the popular solutions. To fulfill this requirement, a reconstruction method called swivel motion was adopted to achieve human-like imitation. This approach aims at modeling the regression relationship between robot pose and swivel motion angle. Then it reaches the human-like swivel motion using its redundant degrees of the manipulator. This characteristic holds for most of the redundant anthropomorphic robots. Although artificial neural network (ANN) based approaches show moderate robustness, the predictive performance is limited. In this paper, we propose a novel deep convolutional neural network (DCNN) structure for reconstruction enhancement and reducing online prediction time. Finally, we utilized the trained DCNN model for managing redundancy control a 7 DoFs anthropomorphic robot arm (LWR4+, KUKA, Germany) for validation. A demonstration is presented to show the human-like behavior on the anthropomorphic manipulator. The proposed approach can also be applied to control other anthropomorphic robot manipulators in industry area or biomedical engineering.

Gaia-DR2 extended kinematical maps

Context. The Gaia Collaboration has used Gaia-DR2 sources with six-dimensional (6D) phase space information to derive kinematical maps within 5 kpc of the Sun, which is a reachable range for stars with relative error in distance lower than 20%. Aims. Here we aim to extend the range of distances by a factor of two to three, thus adding the range of Galactocentric distances between 13 kpc and 20 kpc to the previous maps, with their corresponding error and root mean square values. Methods. We make use of the whole sample of stars of Gaia-DR2 including radial velocity measurements, which consists in more than seven million sources, and we apply a statistical deconvolution of the parallax errors based on the Lucy’s inversion method of the Fredholm integral equations of the first kind, without assuming any prior. Results. The new extended maps provide lots of new and corroborated information about the disk kinematics: significant departures of circularity in the mean orbits with radial Galactocentric velocities between −20 and +20 km s−1 and vertical velocities between −10 and +10 km s−1; variations of the azimuthal velocity with position; asymmetries between the northern and the southern Galactic hemispheres, especially towards the anticenter that includes a larger azimuthal velocity in the south; and others. Conclusions. These extended kinematical maps can be used to investigate the different dynamical models of our Galaxy, and we will present our own analyses in the forthcoming second part of this paper. At present, it is evident that the Milky Way is far from a simple stationary configuration in rotational equilibrium, but is characterized by streaming motions in all velocity components with conspicuous velocity gradients.

A Computational Geometric Approach for Motion Generation of Spatial Linkages With Sphere and Plane Constraints

This paper studies the problem of spatial linkage synthesis for motion generation from the perspective of extracting geometric constraints from a set of specified spatial displacements. In previous work, we have developed a computational geometric framework for integrated type and dimensional synthesis of planar and spherical linkages, the main feature of which is to extract the mechanically realizable geometric constraints from task positions, and thus reduce the motion synthesis problem to that of identifying kinematic dyads and triads associated with the resulting geometric constraints. The proposed approach herein extends this data-driven paradigm to spatial cases, with the focus on acquiring the point-on-a-sphere and point-on-a-plane geometric constraints which are associated with those spatial kinematic chains commonly encountered in spatial mechanism design. Using the theory of kinematic mapping and dual quaternions, we develop a unified version of design equations that represents both types of geometric constraints, and present a simple and efficient algorithm for uncovering them from the given motion.

Key technologies of TianGong-2 robotic hand and its on-orbit experiments

With the development of robotics in recent years, space robotic manipulators have become a research focus on space technologies. In the TianGong-2 (TG-2) spacelab mission, a human-robot collaborative on-orbit servicing experiment was planned as one of the three key tasks. The central component of this task is the TG-2 robotic manipulator, which is a multisensory in-vehicle space robot with multiple control modes, including a 6-DOF robotic arm, a five-fingered humanoid hand, hand-eye and global cameras, and on-orbit human-machine interfaces(space mouse and cyber glove). The design purpose of TG-2 robotic task is to complete various prototypical experiments under micro-g environment to validate key technologies of space robots and on-orbit human-robot collaboration and gain experience and experimental data about robotic on-orbit servicing by assisting or cooperating with human astronauts. A variable time-scale motion plan method, which could adjusts the trajectories of the robot to reduce or eliminate the collision force between the robot collide with the environment, is developed for safe human-robot collaboration. The five-fingered hand grasp control is based on an approach coined as “coordinated grasp control based object Cartesian stiffness” for the adaptation of external forces and robust grasp. To solve the kinematic mapping from cyber glove commands to five-fingered robotic hand, a fingertip-position-based method is proposed to acquire precise solutions. The TG-2 robotic manipulator was launched to space in Sep. 15, 2016. From Oct. 27 to Nov. 13, 2016, all the planned experiments, including dynamic parameter identification, grasping floating objects and prototypical on-orbit servicing, were carried out successfully under the supervision and assistance of the two astronauts, laying foundations for the future applications of space robots.