Kinematic Transformation Research Articles

Open Solution for Humanoid Attitude Estimation through Sensory Integration and Extended Kalman Filtering

In this paper an Extended Kalman Filter (EKF) is used in order to estimate the real state of a humanoid robot (HRP-2 robot in our case study) using the combination of the information coming from the encoders (kinematics) and from the Inertial Measurement Unit (IMU). The integration of the kinematic information into the Kalman filtering process allows a good estimation of the attitude and reduces the complexity of the problem to the use of simple kinematic transformations, even considering the existence of accelerations and mechanical flexibilities in the robot. The EKF estimator presented here is an open solution directly applicable to any humanoid robot, which is the main contribution of our approach. Experimental results are given showing the good performance of the method.

Modeling and experimental validation of cutting forces in five-axis ball-end milling based on true tooth trajectory

The accurate prediction of cutting forces plays an important role in high performance cutting of free-form surfaces which are widely used in automotive, die/mold, and aerospace industries. The purpose of this paper is to present a novel model of cutting forces in five-axis ball-end milling based on true tooth trajectory. The model can be implemented in three steps. First, the representation of the five-axis machine configuration and kinematic transformations is given as the basis of the geometry analysis of five-axis milling operations. Second, through analysis of the true tooth trajectories during the five-axis ball-end milling process, the bisection method can be applied to calculate the true instantaneous undeformed chip thickness. Meanwhile, the start and exit rotation immersion angles and the two limit axial positions can be modeled to determine the exact engagement region. Finally, a method to identify cutting force coefficients is proposed, and the model is then utilized to predict the cutting forces. All experiments carry out under different cutting parameters and cutter positions to prove its effectiveness. Comparisons of the predicted cutting forces and the experimental results show the reliability of the proposed model.

Kinematics and Interfacing of ModRED: A Self-Healing Capable, 4DOF Modular Self-Reconfigurable Robot

Modular self-reconfigurable robots (MSRs) are systems which rely on modularity for maneuvering over unstructured terrains, while having the ability to complete multiple assigned functions in a distributed way. An MSR should be equipped with robust and efficient docking interfaces to ensure enhanced autonomy and self-reconfiguration ability. Genderless docking is a necessary criterion to maintain homogeneity of the robot modules. This also enables self-healing of a modular robot system in the case of a failed module. The mechanism needs to be compact and lightweight and at the same time have sufficient strength to transfer loads from other connected modules. This research focuses on the design of a modular robot with four degrees of freedom (4DOF) per module and with the goal of achieving higher workspace flexibility and self-healing capability. To explain the working principle of the robot, forward kinematic transformations were derived and workspace and singularity analysis were performed. In addition, to address the issues of interfacing, a rotary plate genderless single-sided docking mechanism—RoGenSiD—was developed. The design methodology included considerations for minimal space and weight as well as for fault tolerance. As a result, this docking mechanism is applicable for multifaceted docking in lattice-type, chain-type, or hybrid-type MSR systems. Several locomotion gaits were proposed and bench-top testing validated the system performance in terms of self-healing capability and generation of locomotion gaits.

Numerical controlled robot crawler: new resource for industries with large scale products

This paper introduces a novel mobile automation resource for industries with large scale products. The inherent challenges of large structures for an automation system are discussed and requirements for a mobile machine are derivated. Based on the kinematic investigation, a hybrid kinematic mechanical structure is developed to fulfill the requirements. The characteristics of hybrid kinematics especially for the kinematic transformation and the resulting advantages are introduced. The necessary adhesion system to enable a safe and reliable movement on different surfaces is described. Additionally, the control concept is presented and the intrinsic challenges of using an industrial machine tool control for a mobile robot are shown. Finally, first results of the experimental application are presented.

On Mathematical Foundations of Quantum Collisions and Nuclear Reactions and Outcome of Certain Physical Phenomena from Them

I. Analytical structure of the non-relativistic unitary and non-unitary S-matrix is reviewed for the cases of any interactions with any motion equations inside a sphere of radius a, enclosed by centrifugal and rapidly decreasing (exponentially or by the Yukawian law or by the more rapidly decreasing) potentials. Some kinds of the symmetry conditions are imposed. The Schroedinger equation for the particle motion in the external region where r > a and the completeness of the correspondent wave functions are assumed. The connection of the obtained results with the causality is examined. Partially some analytical properties for the multi-channel S-matrix are reviewed and the sum rules for mean compound-nucleus time delays and the density of compound-nucleus levels. Sometimes (as physical manifestations of the profound general methodic and in very good consistent accordance with the experiment) observable physical effects, such as parity violation enhancement and time resonances or explosions, are appeared. Finally a scientific program of future search is presented as a clear continuation and extension of the obtained results. II. It is already known the appearance of time advance (due to distortion by the non-resonant background) instead of the expected time delay in the region of a compound-nucleus resonance in the center-of-mass (C-) system. Here at the same conditions we study cross sections and durations of the neutron-nucleus scattering in the laboratory (L-) system. Here it is shown that such time advance is a virtual paradox but in the L-system the time-advance phenomenon does not occur and only the trivial time delay is observed. At the same time the transformations from C-system into the L-system appeared to be different from the standard kinematical transformations because in the C-system the motion of a compound nucleus is absent but it is present in the L-system. We analyze the initial wave-packet motion (after the collision origin) and the cross section in the laboratory (L-) system. Also here (as physical revelations of profound general methodic and in very good consistent accordance with the experiment) several results of the calculated cross sections for the neutron-nucleus in comparison with the experimental data in the L-system at the range of one or two overlapped compound resonances are presented. It is shown in the space-time approach that the standard kinematical transformations of cross sections from the C-system to the L-system are not valid because it is necessary to consider the center-of-mass motion in the L-system. Finally on a correct self-consistent base of the space-time description of the nuclear processes in the laboratory system with 3 particles in the final channel, it is shown the validity of the former approach, obtained for the space-time description of the nuclear processes with 2-particle channels earlier.

Developing A Surface Roughness Model for End-Milling of Micro-Channel

Micro-milling operations are one of the common manufacturing processes that are used primarily to produce miniaturized components within the range of less than a millimeter. The surface roughness of the channel plays an important role in the motion of fluid in the channel. Since most traditional finishing operations cannot be performed easily on micro-channels, the study of relationship between micro-milling parameters and surface roughness is of extreme importance. In this work, the geometrical features of cutting edge, along with the concept of minimum chip thickness, are taken into consideration for constructing the micro-channel surface texture using kinematic rules and transformation operators. ACIS, a 3D B-rep geometric kernel, is used as a geometric engine for simulation of surface texture produced in the micro-milling process. In addition, the relationship between cutting conditions and surface roughness is investigated using DOE method and a regression model. All micro-channel experiments were performed on stainless steel 316. Finally, simulation and regression results are compared with measured surface roughness and the validity of these two models is approved. Depending on the available data, one of these two approaches can be used to predict the surface roughness of the channel's floor.

Design and implementation of five-axis transformation function in CNC system

To implement five-axis functions in CNC system, based on domestic system Lan Tian series, an improved design method for the system software structure is proposed in this paper. The numerical control kernel of CNC system is divided into the task layer and the motion layer. A five-axis transformation unit is integrated into the motion layer. After classifying five-axis machines into different types and analyzing their geometry information, the five-axis kinematic library is designed according to the abstract factory pattern. Furthermore, by taking CA spindle-tilting machine as an example, the forward and the inverse kinematic transformations are deduced. Based on the new software architecture and the five-axis kinematic library, algorithms of RTCP (rotation tool center point control) and 3D radius compensation for end-milling are designed and realized. The milling results show that, with five-axis functions based on such software structure, the instructions with respect to the cutter’s position and orientation can be directly carried out in the CNC system.

Scattering Amplitudes Interpolating Between Instant Form and Front Form of Relativistic Dynamics

Among the three forms of relativistic Hamiltonian dynamics proposed by Dirac in 1949, the front form has the largest number of kinematic generators. This distinction provides useful consequences in the analysis of physical observables in hadron physics. Using the method of interpolation between the instant form and the front form, we introduce the interpolating scattering amplitude that links the corresponding time-ordered amplitudes between the two forms of dynamics and provide the physical meaning of the kinematic transformations as they allow the invariance of each individual time-ordered amplitude for an arbitrary interpolation angle. We discuss the rationale for using front form dynamics, nowadays known as light-front dynamics (LFD), and present a few explicit examples of hadron phenomenology that LFD uniquely can offer from first-principles quantum chromodynamics. In particular, model-independent constraints are provided for the analyses of deuteron form factors and the N Δ transition form factors at large momentum transfer squared Q2. The swap of helicity amplitudes between the collinear and non-collinear kinematics is also discussed in deeply virtual Compton scattering.

Tool orientation planning for five-axis CNC machining of open free-form surfaces

For the geometry characteristics of open free-form surfaces, it is hard to consider global interference during the planning of feasible domains. Therefore, the optimal kinematic orientation of tool axis will no longer be confined to the boundary of feasible domains. In this paper, according to the principle demanding that the tool should be fitted to a surface as close as possible and relevant processing parameters, a feasible domain of tool orientation for each cutter contact is planned in the local feed coordinates system. Then, these feasible domains of the tool orientation are transformed into the same coordinates system of the machine tool by the inverse kinematics transformation. The linear equations based feasible domain method and Rosen gradient projection algorithm are used to improve the optimization process in precision and efficiency of the algorithm. It constructs the variation of tool orientation optimization model and ensures the smoothness of tool orientation globally. Simulation and analysis of examples show that the proposed method has good kinematics performance and greatly improves the efficiency.

Implicit and Explicit Representations of Hand Position in Tool Use

Understanding the interactions of visual and proprioceptive information in tool use is important as it is the basis for learning of the tool's kinematic transformation and thus skilled performance. This study investigated how the CNS combines seen cursor positions and felt hand positions under a visuo-motor rotation paradigm. Young and older adult participants performed aiming movements on a digitizer while looking at rotated visual feedback on a monitor. After each movement, they judged either the proprioceptively sensed hand direction or the visually sensed cursor direction. We identified asymmetric mutual biases with a strong visual dominance. Furthermore, we found a number of differences between explicit and implicit judgments of hand directions. The explicit judgments had considerably larger variability than the implicit judgments. The bias toward the cursor direction for the explicit judgments was about twice as strong as for the implicit judgments. The individual biases of explicit and implicit judgments were uncorrelated. Biases of these judgments exhibited opposite sequential effects. Moreover, age-related changes were also different between these judgments. The judgment variability was decreased and the bias toward the cursor direction was increased with increasing age only for the explicit judgments. These results indicate distinct explicit and implicit neural representations of hand direction, similar to the notion of distinct visual systems.

Interpolating scattering amplitudes between the instant form and the front form of relativistic dynamics

Among the three forms of relativistic Hamiltonian dynamics proposed by Dirac in 1949, the instant form and the front form can be interpolated by introducing an interpolation angle between the ordinary time $t$ and the light-front time $(t+z/c)/\sqrt{2}$. Using this method, we introduce the interpolating scattering amplitude that links the corresponding time-ordered amplitudes between the two forms of dynamics and provide the physical meaning of the kinematic transformations as they allow the invariance of each individual time-ordered amplitude for an arbitrary interpolation angle. In particular, it exhibits that the longitudinal boost is kinematical only in the front form dynamics, or the light-front dynamics (LFD), but not in any other interpolation angle dynamics. It also shows that the disappearance of the connected contributions to the current arising from the vacuum occurs when the interpolation angle is taken to yield the LFD. Since it doesn't require the infinite momentum frame (IMF) to show this disappearance and the proof is independent of reference frames, it resolves the confusion between the LFD and the IMF. The well-known utility of IMF usually discussed in the instant form dynamics is now also extended to any other interpolation angle dynamics using our interpolating scattering amplitudes.

Studies on the Exchangeability of Different APT Interpreters for 5-Axis Machine Tool Applications

Generally, the NC format is the description for the positioning and/or the movement of its linear and rotary axes. As the multi-axis machine tools have a variety of configurations, their NC codes are not exchangeable. This issue leads to some inconvenience and confounding in the manufacturing processing schedule. Furthermore, when the specifications of tool such as length, diameter or shape are reset, the NC program must be regenerated accordingly. That is to say, the exchangeability of NC program among different five-axis machine configurations is an important issue in making better usage of industrial five-axis machine tools for efficient applications. An APT program records the tool path, tool vector and cutting information, etc. In particular, the recent development of APT format can provide the capability recording the motion posture of the tool such as the tool orientation, the position and its normal vector of the tool contact point. Therefore, it can solve the problems of the exchangeability for the different machine tools as well as the online resetting of tool specifications, even the tool posture. In this paper, a new method was proposed to interpret the APT code into tool movement data including toolpath, location, tool orientation, the contact point and its contact vector, etc., which can be applied to the conversion of different NC codes, or be connected to the controller of the machine tool so as to proceed the interpolation calculation for directly machining control. Moreover, the application scope can be extended to the verification of machining and to drive a virtual machine tool for previewing. Since the APT format varies according to different CAD/CAM systems, a common intermediate interchange standard (CMIS) was proposed, designed and verified in this paper as a feasible solution for the exchangeability of different APT formats. The process of the proposed method includes interpreting a variety of APT program into a common standard format, and then transforming this intermediate standard code into various NC programs for the corresponding machine configurations. An example was used to demonstrate how to convert an APT generated by CATIA software into intermediate code for a Table-Table five-axis machine tool with two rotary axes attached on table (XYZAC configuration). As the APT contains the definition of inclined plane, so the homogeneous coordinate transformation was adopted to transform the coordinate system of the inclined plane into the work coordinate system; it was further transformed into the corresponding NC program via an inverse kinematics transformation. This example has shown the feasibility of the method proposed. Moreover, the research can be applied not only to the exchangeability of different APT format but also to the other related applications such as the verification of machining error and the drive of virtual machine tool.

Towards mastery of complex visuo-motor transformations.

In this paper we review and integrate a set of findings on learning the transformation of a sliding first-order lever, a type of tool with a prominent role in minimal access surgery. Its kinematic transformation is characterized by the so-called fulcrum effect, the inversion of the movement direction of the tip of the lever relative to that of the hand for rotations. A second characteristic is gain anisotropy, which results in curved paths of the tip of the lever for straight paths of the hand and vice versa. An internal model of the kinematic transformation is acquired during practice, the accuracy of which can be assessed in visual open-loop test trials. The accuracy of the acquired internal model is enhanced when visual closed-loop control during practice is impeded, and the accuracy of the internal model is reduced when closed-loop control during practice is facilitated. The internal model consists of a rapidly acquired line-symmetric approximation to the transformation of the sliding lever and a slowly acquired fine tuning. The fine tuning is local, that is, it is specific for the region of the workspace encountered during practice. The internal model is transferred to other regions of the workspace, but not adjusted to the fine tuning appropriate for these regions. Whereas the symmetry approximation is most likely explicit, the fine tuning seems to be represented implicitly. Findings on the straightness of the paths of the tip of the lever and the hand suggest that the internal model of the transformation is confined to initial and final positions of aimed movements, whereas their path is not strictly controlled, but affected by the dynamic transformation of the tool. Only when visual closed-loop control is possible, the path of the effective part of the tool is straightened. These characteristics of the internal model of the sliding first-order lever and its acquisition may be partly specific to sufficiently complex extrinsic transformations that arise from mechanical or electronic extensions of the body.

Loading Excavator Analysis for Trajectory Control Improvement

Automatic control assistance to improve the digging and bucket-filling trajectory of loading excavators is moving from concept to industrial applications. Directly controlling the path of the bucket instead of controlling individual hydraulic joints by human operators is possible using robotics. The task may be achieved by redefining the excavator kinematics and enhancing it with a software-controlled “virtual kinematics.” It is necessary to determine what type of kinematics transformation of the excavator would be best from its “as-built” motion pattern to an “as-desired” machine for the loading tasks. If known, this loading kinematics then can be programmed into the machine motion control system. Since no loading movement and bite is exactly the same as the previous one, a man-machine interface is needed for easy access for adjustment. Such loading task is analyzed for cycle time, energy consumption, and machine wear. Static and dynamic forces, torques, energy, and power consumption is evaluated for any given digging bucket trajectory for an EX3500 Hitachi excavator. Typical digging trajectories from published data are used to evaluate the potential benefits of a new bucket loading kinematics by “bucket steering,” a motion kinematics which requires two joysticks control actions only. One joystick serves for interactive adjustment to the trajectory shape, and the other is for loading velocity control. The paper describes the potential benefit to mining front shovel operations.

A Five-Axis CNC Machine Postprocessor Based on Inverse Kinematics Transformation

This paper presents a postprocessor for five-axis milling machine that capable of converting CL (cutter location) data to machine control data (NC program). The proposed postprocessor method is based on inverse kinematics transformation and postprocessor module is programmed in Visual Basic language. The Deckel Maho DMU 50 eVoluion five-axis machine with two rotary axes (B and C) on the table is modeled and verified in software VERICUT® to validate the NC data generated by proposed postprocessor.

Kinematics Analysis for a PRRR Manipulator

The PRRR manipulator of the kinematic equation transformation matrix is worked out by using D-H method, the kinematics solutions are derived ；The coordinate transform method and inverse transform method of the robot kinematics equations are derived, the inverse kinematics is derived and a example is given.

A Strain-Induced Martensite Transformation Model for TRIP Steels in Cyclic Loading Condition

TRIP-assisted steels are ideal for lightweight automotive applications due to not only its high strength and ductility but also the fatigue resistance, which result from the special strengthening mechanism of phase transformation in deformation processes. In this paper, a kinematic transformation model is developed, based on shear-band intersections, to reasonably evaluate the transformation from austenite into martensite with cyclic loading. The transformation process is controlled by parameters, such as, increase temperature, transformation driving force, shear-band formation rate and shear-band intersection volume fraction, by which the influences of cyclic loading variables (such as, number of cycles, strain amplitude and frequency) on transformation from austenite into martensite are predicted. The microstructure volume fraction is tested by X-Ray to verify the model.

Deficient Use of Visual Information in Estimating Hand Position in Cerebellar Patients

We tested cerebellar degeneration in human patients in a task designed to isolate different aspects of motor planning and found a specific relationship between their ability to do inverse kinematic transformation and sparing of Crus I. Our approach was based on an experimental design introduced by Sober and Sabes (2003, 2005). Their paradigm allows behavioral deficits in planning of movement direction to be dissociated from deficits in generation of motor commands and also allows for the relative role played by visual and proprioceptive information to be quantified. Perturbation of visual information about hand position affected cerebellar degeneration patients (N = 12) and age-matched controls equally in determining movement direction, but had less of an effect in both groups in the transformation of movement direction to motor command. However, when provided with vision of the joints, control participants were more affected in generating the motor command in perturbed trials, and cerebellar degeneration participants were not. Thus, cerebellar patients were less able to use visual information about the joints in generating motor commands. Voxel-based morphometric analysis showed that this inability was primarily correlated with degeneration of Crus I. These results show that the cerebellum plays a role in motor planning, and specifically in the generation of inverse kinematic models for sensorimotor processing. The involvement of Crus I is consistent with an emerging picture in which increasingly posterior lobules of the anterior cerebellar cortex are associated with increasingly complex and abstract aspects of motor behavior.

Machining tests to identify kinematic errors of machine tool table rotation axis based on sensitive directions

Machining tests based on homogeneous transformation matrix approach are relatively complex and time resuming in the mathematical modeling and the implementation of measurement and calculation. A new method is proposed to identify the kinematic errors of the rotation axis of machine tool table by machining tests based on sensitive directions. In order to identify the kinematic errors in the sensitive direction conveniently, a simple mathematical model of the kinematic errors is developed by optimizing the coordinate system settings based on basic kinematic transformation, and the sensitive direction vector was adopted to identify the kinematic errors from the machining errors of the finished workpiece. Experimental results demonstrate that the proposed method can reduce the complexity and time resuming substantially.

Eccentric universal joints for parallel kinematic machine tools: variants and kinematic transformations

In the 1990’s enhanced capabilities of parallel kinematic machine tools (PKM) regarding stiffness, motion accuracy and dynamics have been announced generously. Extensive research and development has been done in this area to date. Regarding this, the application range of PKMs is still small. Looking for reasons often yields inadequate motion accuracy as well as insufficient workspace. In either case the passive joints of the kinematic chains pose essential weak points. This article is about eccentric universal joints as an alternative approach that can avoid drawbacks of conventional universal joints and finally enhance the application range of PKMs. However, one of the consequences is a more complex and no longer unique kinematic transformation. This is significant in a control context, where iterative calculations should be avoided when possible due to real-time demands and the uniqueness of the solution has to be guaranteed in any case. Though the general inverse kinematic problem of industrial robots is identical, no generic closed-form (non-iterative) solution is known so far. But often closed-form as well as unique solutions are possible yet by considering particular features of the kinematic chain. In this paper after an introduction types of joint eccentricity are discussed and corresponding inverse kinematic transformations are derived with control purposes in mind.