Inverse Kinematic Transformation Research Articles

Postprocessor for Verification of Robot Movements with Additional Axis after Toolpath Optimization

This paper discusses a postprocessor for milling robots connected to additional linear machine axes where toolpath is optimized with respect to variable properties of the robot in its workspace. A toolpath optimization method is proposed based on an experimentally verifiedrobot stiffness model. After postprocessor distribution of the movements between the robot and the linear axes, the collision states during machiningcannot be verified in common CAM. Therefore, a solution enabling simulation of movements after optimization is proposed. The tool center point coordinates are used to control the robot and additional machine axes, while the joint coordinates calculated by inverse kinematic transformation are used to verify the movements.

Real-time walking pattern generation for a lower limb exoskeleton, implemented on the Exoped robot

Lower extremity exoskeletons have been developed as a motion assistive technology in recent years. Walking pattern generation is a fundamental topic in the design of these robots. The usual approach with most exoskeletons is to use a pre-recorded pattern as a look-up table. There are some deficiencies with this method, including data storage limitation and poor regulation relating to the walking parameters. In addition, the walking parameters can be taken in hand very hard. Therefore modeling the human walking pattern is required. The few existing models provide piece by piece walking patterns, only generating at the beginning of each stride. In this paper, a real-time walking pattern generation method is provided which enables changing the parameters during the stride. For this purpose, two feedback controlled third order systems are proposed as real-time trajectory planners for generating the trajectories of the x and y components of each joint’s position. The boundary conditions of the trajectories are determined to prevent backward balance loss by appropriate displacement of the center of mass. In addition, a cost function is intended for each trajectory planner in order to increase the smoothness of trajectories. Optimization technique is used to design the feedback controller for tracking the boundary conditions in such a way that the cost function is minimized. Finally, the proper joint angles are generated using inverse kinematics transformation. The performance of the proposed pattern generator is verified via real experiments on the Exoped robot.

Influence of manufacturing errors in a metal-cutting machine with parallel kinematic structure on its machining precision

Possible manufacturing and assembly errors in a metal-cutting machine with parallel kinematic structure that affect its kinematic model are analyzed. On the basis of the manufacturing tolerances for the metal-cutting machine, the equations of the direct and inverse kinematic transformations are refined. An algorithm is derived for simulating the influence of geometric errors on the positioning precision of the actuator in the metal-cutting machine.

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.

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.

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.

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.

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.

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.

A New 2T-2R Hybrid Parallel Manipulator

Though computer technology has brought about virtual manufacturing to expedite design and analysis through simulation and visualization, machines remain essential, as ultimately products need to be made. There is a need for equipment providing more than three degrees of freedom (DOF) arranged in parallel and based on simpler arrangements than 6-DOF arrangements in application. This paper presents a new 4-DOF hybrid parallel platform manipulator with fixed-leg lengths and base mounted prismatic actuators. The movable platform of the manipulator can translate along two directions and rotate around two axes respectively (2T-2R). The kinematics model is formulated, which describes the inverse and forward kinematics transformation. It is very easy to develop a 5-axis NC machine-tool which is of large-workspace based on the 2T-2R, 4-DOF parallel mechanism presented in this paper.

A Four Degrees of Freedom Parallel Manipulator for Machining

In the past decades, a number of parallel manipulators have been extensively studied. However, most efforts are dedicated to six degrees of freedom (DOF) or three-DOF manipulators. There is a need for equipment providing more than three DOF's arranged in parallel and based on simpler arrangements than six-DOF arrangements in application. This paper presents a novel four-DOF parallel platform manipulator with base mounted prismatic actuators. The manipulator is driven by four linear actuators. The movable platform of the manipulator can translate along two directions and rotate around two axes respectively. The kinematics model is formulated, which describes the inverse and forward kinematics transformation. It is very easy to develop a five-axis NC machine-tool which is of large-workspace based on the four-DOF parallel mechanism presented in this paper.

Characterization of 3D surface topography in 5-axis milling

Within the context of 5-axis free-form machining, CAM software offers various ways of tool-path generation, depending on the geometry of the surface to be machined. Therefore, as the manufactured surface quality results from the choice of the machining strategy and machining parameters, the prediction of surface roughness in function of the machining conditions is an important issue in 5-axis machining. The objective of this paper is to propose a simulation model of material removal in 5-axis based on the N-buffer method and integrating the Inverse Kinematics Transformation. The tooth track is linked with the velocity giving the surface topography resulting from actual machining conditions. The model is assessed thanks to a series of sweeping over planes according to various tool axis orientations and cutting conditions. 3D surface topography analyses are performed through the new areal surface roughness parameters proposed by recent standards.

Optimal grids for five-axis machining

This paper presents a new grid generation method for tool path planning for five-axis machining based on minimization of the kinematics error. First, the procedure constructs a space-filling curve so that the scallops between the resulting tracks of the tool do not exceed a prescribed tolerance. At the second stage (which is the subject of this paper) a one-dimensional grid along the space-filling curve is generated using direct minimization of the kinematics error. A closed form representation of the kinematics error as a function of locations cutter contact points is derived from the inverse kinematics transformations associated with a particular five-axis machine and obtained through automatic symbolic calculations. The grid of cutter location points is generated so that it minimizes the kinematics error. Numerical and cutting experiments demonstrate that the proposed procedure outperforms distribution of points based on the equi-arc-length principle. Finally, we show that our optimization routine requires less points than that based on sequential point insertion and numerical evaluation of the cost function, such as bisection.

A new format for 5-axis tool path computation, using Bspline curves

This article presents a new format of tool path polynomial interpolation in 5-axis machining. The linear interpolation usually used produces tangency discontinuities along the tool path, sources of decelerations of the machine tool whereas polynomial interpolation reduces the appearance of such discontinuities. The new format involves a faster tool path and a better surface quality. However, it imposes a modification of the process so as to take the interpolation format and the inverse kinematics transformation (necessary to 5-axis machining) into account. This article deals with the geometrical problem of tool path calculation. Validation tests are detailed. They show that profits concern the reduction of machining time as well as the quality of the machined surfaces. Indeed, the trajectory continuity avoids the appearance of marks and facets.

Avoiding 5-axis singularities using tool path deformation

This paper deals with a topical method for avoiding the tool to traverse singular positions in 5-axis machining. It is well known that the inverse kinematics transformation generates singular positions for which incoherent movements of rotary axes appear. However, in the paper, we show that due to uncertainties on the positioning, the singular position is actually characterized by a cone. We thus adopt the concept of singular cone. Following, we propose a method to deform the tool path so that the tool does not traverse the singular cone during machining. This method takes advantage of the description of the tool trajectory as B-spline curves. Therefore, the deformation corresponds to the displacements of certain control points wisely chosen. As the corrected tool path must still verify the machining tolerance, the displacement is limited by the admissible displacement which can be calculated in function of the geometrical characteristics of the tool and of the specified machining tolerance. The deformation method we propose can be extended so that the contact point is preserved. Our purpose is illustrated through the example of the machining of a surface in 5-axis high-speed machining (HSM). This illustration shows the efficiency of our method: incoherent movements are eliminated after tool path deformation and the dynamic performance of the machine tool is improved.

Performance Analysis of Drive‐Line Steering Methods in Excavator‐Mounted Sheet‐Piling Systems

Sheet‐piling processes pose the problem of guiding the pile to follow a fixed trajectory in order to drive it correctly into the ground. Since the complete system consists of the supporting excavator boom with hydraulic actuators, the gripper, and the vibratory unit, the large number of system variables implies the use of servo control to allow a human operator to handle the operation. An exact inverse kinematic transformation from Cartesian workspace to boom joint space variables allows the pile penetration to be guided, keeping the valve input of the main boom actuator as the free parameter, while the remaining actuators are governed automatically by the control computer. The penetration record of the pile differs based on whether a constant valve input is used in semiautomatic steering mode or, alternatively, the desired penetration speed is governing the valve input in a feedback loop in full‐automatic steering mode. A numerical model representing an actual industrial system has been developed. Variable results from computer simulations have led the manufacturer to realize the steering system. It has been verified in real piling tests that the steering system may be tuned to be stable and fast enough for practical working conditions. In particular, the performance of trajectory control in terms of tracking error is much better than in the conventional manual steering method, as expected.

Coordinate transformation learning of hand position feedback controller with time delay

The speed, accuracy, and adaptability of human movement depends on the brain performing an inverse kinematics transformation—i.e., a transformation from visual to joint angle coordinates—based on learning from experience. In human visually guided motion control, it is important to learn a feedback controller for the hand position error. This paper proposes two novel models that learn coordinate transformations of the human visual feedback controller with time delay. The proposed models redress drawbacks in current models because they do not rely on complex signal switching, which does not seem neurophysiologically plausible.

Kinematic Control of Redundant Manipulators with On-Line End-Effector Path Tracking Capability Under Velocity and Acceleration Constraints

Kinematic control techniques are based on an inverse kinematic transformation which feeds the reference values to the joints corresponding to the assigned end-effector trajectory. In this paper, a inverse kinematics algorithm for redundant robots is developed which takes into account joint velocity and acceleration limits while ensuring tracking of the assigned end-effector path. The desired end-effector trajectory is supposed to be given on-line. Numerical simulation results are reported to demonstrate the application of the proposed technique.

Adaptive tracking control of manipulators: Theory and experiments

This paper considers the trajectory tracking problem for uncertain robot manipulators and proposes two adaptive controllers as solutions to this problem. The first controller is derived under the assumption that the manipulator state is measurable, while the second strategy is developed for those applications in which only position measurements are available. The adaptive schemes are very general and computationally efficient since they do not require knowledge of either the mathematical model or the parameter values of the manipulator dynamics, and are implemented without calculation of the robot inverse dynamics or inverse kinematic transformation. It is shown that the control strategies ensure uniform boundedness of all signals in the presence of bounded disturbances, and that the ultimate size of the tracking errors can be made arbitrarily small. Experimental results are presented for a PUMA 560 manipulator and demonstrate that accurate and robust trajectory tracking can be achieved by using the proposed controllers.

Neuro-Fuzzy System for Robotics Applications

Over the last two decades several advances have been made in the areas of fuzzy logic and artificial neural networks. It is interesting to note that fuzzy logic and neural networks complement each other, and their fusion provides the benefits of both the technologies. Neural networks can deal with imprecise data and ill-defined activities; thus, they offer low-level computational features. On the other hand, fuzzy logic provides higher-level cognitive features as it can deal with issues such as approximate reasoning and natural language processing. The merging of these two fields results in an emerging paradigm called ‘neuro-fuzzy systems’. These are believed to have considerable potential in the areas of robotics, expert systems, medical diagnosis, control systems, pattern recognition and system modeling. The intent of this paper is to describe a Neuro-Fuzzy System (NFS) for on-line computation of inverse kinematic transformations of a robot manipulator. The NFS is comprised of a conventional fuzzy logic controller in the feedback configuration and a recurrent neural network in the inverse mode (feedforward) configuration. It is envisaged that the integration of fuzzy logic-and neural networks—based systems will encompass the merits of both the techniques, and thus provide an intelligent and a robust mechanism. The NFS uses minimum fuzzy rules for a given task, thus, overcoming the problem of designing an elaborate Knowledge Base for the Fuzzy Logic Controller. The proposed scheme is implemented for computing inverse kinematic transformations of a two-linked robot. It should be noted, however, that the NFS is not to be considered as a ‘Fuzzy Neural Network’; but it is a synthesis of neural networks and fuzzy logic based control techniques.