text:
|Publication number
|Publication type
|Application number
|Publication date
|May 16, 1989
|Filing date
|Jul 28, 1987
|Priority date
|Jul 28, 1987
|Fee status
|Also published as
|Publication number
|Walter E. Red, Brady R. Davies, Xuguang Wang, Edgar R. Turner
|Original Assignee
|Brigham Young University
|Export Citation
|BiBTeX, EndNote, RefMan
|Patent Citations (9), Referenced by (170), Classifications (22), Legal Events (4)
|External Links: USPTO, USPTO Assignment, Espacenet
1. Field of Invention:
The present invention relates to a device and method for enabling off-line programming of robot tasks. More particularly, the present invention relates to a method of mapping and accommodating robot inaccuracy which enables off-line programming with a high degree of accuracy and flexibility with respect to robot tasks being performed.
2. Prior Art
Robot mechanisms are being increasingly used within the manufacturing industry for performing repetitive tasks in an assembly line configuration. Such use of robots extends from automobile production lines to manufacture of microchips within the computer industry. At present, the primary factor limiting increased market expansion of robotics is the inability of conventional robot systems to perform within very limited tolerances. Inherent robot inaccuracy is a major contributor to this obstacle and has been the object of investigation for many years.
Robot inaccuracy describes the inability of a robot to move to a command pose, defined by position and/or orientation, within the working volume of the robot. For example, a robot control program may direct the movement of a robot arm to a specific point in space based on mechanical specifications of the robot structure and a perceived reference frame to which the robot is oriented. Despite the best of care in manufacture and positioning, however, actual performance of the commanded movement will not place the robot arm precisely at the desired location and/or orientation. This condition, known as robot inaccuracy, is the result of our inability to manufacture and assemble each of the respective robot components to conform to a perfect or ideal robot model. Instead, slight deviations in component length, compliance under stress, imperfect gear matching, and a host of other structural limitations contribute to robot task performance inconsistent with ideal mathematical models. Accordingly, the existence of robot inaccuracy has posed a major obstacle with respect to preprogramming robot movement within a task oriented work cell. Simply stated, the inability to predict the exact position or movement of a robot limits the ability to preprogram an exact path of robot movement. Accordingly, industry has had to turn to alternative forms of programming of robot task performance, despite the numerous advantages that off-line programming offers.
Two of the principal alternative methods for programming robots include the use of sensory systems and teach pendant methods. The teach pendant programming method is the dominant process applied in current robotics relating to performance of a repetitive task. This method is accomplished by leading the robot through a series of necessary intermediate configurations or joint states and then storing such joint states in a robot computer memory. Because the robot is able to reproduce these configurations or joint states, based on the stored data, the robot task can be performed within customary tolerance limits. The end result is that the robot is "taught" the exact task to be performed along a dictated path of movement. The control driver of the robot simply reproduces the sequence of joint states and movements which were programmed by the teach pendant method.
A number of serious limitations exist with respect to this form of robot task programming. For example, programs the same model. In fact, each separate robot has distinct structural and manufacturing deviations due to joint misalignment, joint compliance, gear train errors, standard tolerance deviations, etc. In addition, complex paths of movement may require many intermediate joint poses which are very tedious to program and usually inefficient in operation. Furthermore, robot movement paths in a dynamic or congested work space can be very difficult to teach. In addition, the probability of inadvertent collision with work space hardware is greatly increased.
From a practical point of view, teach pendant methods severely limit the flexibility of robot task performance in an assembly line operation. For example, unacceptable deviations or changes in task performance require the total assembly line to be shut down, even though modification of only one robot element is required. Where robots perform many assembly line tasks, lost production time due to required reprogramming by teach pendant methods can be very costly. Such teach pendant programming must be practiced in the actual work cell because any attempt to move the robot following programming results in changed frames of reference with a concurrent loss of orientation. It is well known to those skilled in the art that these teach pendant limitations consume numerous hours of personnel time and severely constrain the utility of robot task performance within many lines of manufacture.
A second method of robot programming depends on the use of sensor systems to move the robot end-effectors into appropriate interaction with a target object or other feature. This method is typically used when the object parts in the work cell are not delivered in the same orientation or position, or such part has some physical characteristic which is dynamically changing. In this instance, the ability of the robot to repeat actual movements offers no flexibility to adapt to parts with new orientations or position. Accordingly, the sensing device such as a camera or imaging system may be coupled to the distal link of the robot and may be programmed to adapt robot movements in response to a servo system which directs the robot to a detected target location. Unfortunately, sensory guide systems are extremely expensive and require special fixtures, substantial computer support and extensive programming effort. Therefore, economic limitations have severely limited commercial applications for sensor drive systems in robotics.
In addition, several hybrid approaches of these two methods have been applied. For example, in some tasks most global moves may be taught by teach pendant methods, whereas movements within localized areas are accomplished with sensor systems. In other tasks, sensor systems may be used to recognize small deviations in part delivery, with the teach pendant method being applied to maintain the deviated path. This method adapts the robot for changes in the rigid body pose of the part, but is only effective if the part experiences small changes or if the task does not demand tight robot-part interaction tolerances.
In summary, it is apparent that robot repeatability and robot inaccuracy constitute positioning factors which pose critical limitations to the programming of robots. The on-line teach pendant mode utilizes robot repeatability to overcome the robot inaccuracy problem, but is severely limited in its flexibility and requires expensive tooling and an on-going commitment of personnel time. Sensor based systems use feedback to overcome repeatability and accuracy limitations, but are complicated and require significant computational power which tends to slow the process and reduce reliability.
These limitations have prompted further research and development in an effort to realize a more flexible robot application which can accommodate changes in work cell, including variations in part delivery, work cell operating environments and varying throughput demands. Although some attempts have been made to build reference frames which serve as a basis for manipulating robot movement, such reference frames have relied on global techniques, as opposed to localized task areas. Global methods seek to determine the robot inaccuracy over the entire working volume of the robot and use modeling methods to predict or measure kinematic and dynamic hardware sources of robot error. For example, such errors include improper orientations, errors in joint location, transmission system errors, robot compliance under loads, encoder sensor reading error, etc. Once these errors are determined, the methods suggest that mathematical correction models can be implemented to correct the deviations from the ideal robot model.
Such global techniques have not proved successful for measurement of robot inaccuracy because they attempt to accurately define a specific point in space, and then attempt to conform the robot path to that point. Such steps require a knowledge of the exact robot base reference frame is located relative to the robot chassis. This concept is difficult to manage because it is an imaginary rather than actual physical position on the robot. In addition, the complexity of defining given points in a global environment becomes unmanageable. The complexity of programming, the extensive memory storage requirements and the experimental complexity have frustrated all attempts to make global methods the basis for accommodating changes in robot characteristics and robot inaccuracy.
Other related approaches for improvement in robot accuracy have included definition of the kinematic parameters of the robot, with an attempt to compensate in software for any kinematic error. Hayati, S., "Robot Arm Geometric Link Parameter Estimation," Proceedings of the 22nd IEEE Conference on Decision and Control, pp. 1477-1483, December 1983. Other researchers have shown that joint axis misalignment can greatly affect robot positioning accuracy and have developed methods to identify axis position and orientation errors. Mooring, B. W., "An Improved Method for Identifying the Kinematic Parameters in a Six Axis Robot," Texas A & M University. These simulation methods have not fully accounted for measurement error. Furthermore, these measurements have been conducted in global coordinates. Other published literature presents an improved and involved calibration method but still does not overcome measurement errors necessary to achieve acceptable accuracy data. Whitney, D. E., C. A. Lozinski, and J. M. Rourke, "Industrial Robot Calibration Method and Results," Proceedings of the ASME on Computers in Engineering Conference, pp. 92-100, Las Vegas, Nev., August, 1984. Finally, attempts have been made to define a mathematical model which would allow the robot controller to compensate for second order non-linear kinematic effects; however, this has again been related to absolute space and does not account for any manipulator dynamic effects in predicting positioning accuracy. More importantly, all of these techniques attempt to define the robot inaccuracy utilizing global methods.
It is an object of the present invention to provide a method for compensating for robot inaccuracy.
It is a further object of the present invention to describe a method which enables off-line programming of robot tasks.
Yet another object of this invention is to provide a method for improving orientation and/or location accuracy of a programmable robot with respect to a target object.
A still further object of this invention is to provide a method for calibrating the position of a terminal control frame attached at a distal link of the robot as part of a robot movement control system.
Yet another object of this invention is to provide a method for mapping features on a target object for improving accuracy of manipulation and processing as part of the robot task.
These and other objects are realized in a method which is characterized by the following orientation steps. First, the robot is positioned with respect to the target object, with a terminal end-effector having a range of movement which includes the target area. A plurality of reference positions are identified and identification data with respect to such positions is developed and stored in the data processing unit. The robot end-effector is then moved near a reference position, which is referred to as the calibration position. Here, a sensor coupled to the robot detects the presence of the calibration position or feature. This position is compared with the originally stored information data relating to the same calibration position. A rigid body error correction based on position differences is developed and stored within the data processing unit. The end-effector is then moved to a second reference position based on originally stored identification data which is modified by applying the rigid body correction to more accurately predict proper placement of the robot with respect to the second reference position. Other related steps involving inaccuracy mapping and calibration of the robot terminal control frame are disclosed.
Other objects and features of the present invention will be apparent to those skilled in the art from the following detailed description taken in combination with the accompanying drawings.
FIG. 1 depicts a graphic representation of a robot performing manipulations with respect to a calibration plate or other target part.
FIGS. 2a, 2b and 2c represent position calibration steps for the terminal control frame.
FIG. 3 graphically illustrates determination of TCF orientation within the calibration procedure disclosed herein.
FIG. 4 graphically illustrates a calibration path segment in Cartesian space.
FIG. 5 depicts a robot with terminal control and sensor components.
FIG. 6 illustrates a robot configuration with respect to a calibration table.
FIG. 7 is a graph representing position error convergence.
FIG. 8 discloses an exemplary calibration table for use with the present invention.
FIG. 9 is a data summary based on performed experiments regarding robot inaccuracy.
FIG. 10 is a graphic plot of robot inaccuracy measurements.
FIG. 11 discloses data with respect to error correction or orientation.
FIG. 12 is a graphic flow chart summarizing the integrated steps of the present invention.
FIG. 13 is a graphic flow chart illustrating the calibration procedures integrated with the present invention.
FIG. 14 graphically illustrates the use of control points in preprogramming methods.
FIG. 15 graphically illustrates the use of deviated path for avoiding unintended contact between the robot arm and obstacles.
The present inventors have discovered that off-line programming of a robot task can be implemented where a relative frame of reference is utilized as opposed to a global reference frame. Specifically, the inventive methods disclosed herein are based on spatial relationships and orientations which are compared on a relative basis to local features or reference frames, rather than attempting to relate robot movements to a global reference frame. This method assumes that the geometry of the target parts on which the robot is to operate or use is known within some acceptable tolerance. Indeed, a significant aspect of this invention is characterized by the premise that successful off-line programming is enabled with methodologies that are based on relative information, as opposed to global reference frames. Such a premise relies on the fact that most robots are repeatable to within satisfactory tolerances and that target parts on which the robot operates have been previously manufactured to a satisfactory tolerance. In view of this premise, it will be apparent to those skilled in the art that the repeatability of the robot must be less than the desired tolerance of the robot task. It is also essential that the geometry specifications for the part on which the robot will operate can be accessed and passed to the robot work cell as needed.
Generally, the present methods incorporate the use of sensors such as vision systems and touch probes to view or probe known features on the target part(s). The sensor systems and work cell layout are designed so that these features can be accessed by either manual control of the robot or by using off-line planned paths. This choice is made depending on factors such as the capacity of the sensor system and the accuracy of the original geometrical layout of the work cell.
In implementing the disclosed methods, it is generally assumed that the parts are delivered in a repeatable manner to the work cell within acceptable tolerances, and that the geometry of the part remains within such tolerances. Where these conditions are satisfied, the methodology involves use of sensor systems to access known geometric features which are located on the target part. The difference between the actual and sensor measured geometry is the robot inaccuracy measured relative to the part. Once this inaccuracy is known at selected features, the robot can be commanded to move more accurately to other part interaction points using interpolated and extrapolated predictions of the robot inaccuracy. Based on this predicted robot inaccuracy, an error correction algorithm can be applied to deviate the off-line planned path and improve the effective robot accuracy by as much as an order of magnitude or more.
In simple context, the general method involves identification of a first reference feature on a target part or at a target position. This feature is utilized to make a rigid body pose correction relative to the robot. Other reference features or positions will generally be determined relative to the first reference feature, but may be determined relative to each other as well. The feature relative geometry is then utilized to determine the robot inaccuracy that occurs, based on relative rather than global moves This method provides a major advantage over the prior art in that robot inaccuracy need not be determined globally, but is only determined in localized regions. Typically, these regions would be volumes of space in which the robot is actually performing interactions with a target part. Furthermore, inaccuracy measurements need not be made by independent measurement devices which may require global positioning.
With reference to applications to manufacturing, this provides a significant advantage in that parts which are delivered repeatably and within tolerance may be initially mapped or measured for robot inaccuracy relative to the part. After mapping, the sensor system can be turned off and the robot task can be repeatedly performed. Occasional mapping can be implemented to verify that the parts and robot are operating within required tolerances. In this mode, the method can be used for statistical process control.
The off-line programming techniques disclosed herein assume that the work cell and robot tool geometry are known relative to the robot base frame for any robot configuration. Generally, this information is supplied by the manufacturer or can be otherwise determined. Global off-line techniques fail because robots cannot be commanded to move to global positions in space accurately due to joint misalignment, joint compliance, gear train errors, etc. Target parts separate from the robot frame are located by a sensor such as a vision system. Such parts are located relative to a vision camera frame (also referred to as frame of reference) using relative joint transformations. Once these parts are located in the robot base frame, inverse kinematic solutions determine robot joint values which move the robot tools or end-effectors to the desired operation points.
Calibration techniques are applied with respect to the various elements of the robot including the base frame, intermediate links, distal link (including distal link frame) and terminal control frame which is associated with the end-effector. The object of such calibration techniques is to establish exact relative position and orientation measurements along the robot components. Obviously, once such relative position and orientation measurements are known, a determination of any specific position orientation of a robot component enables the determination of specific positions and orientations for all other robot components from the base frame through the terminal control frame.
The present invention discloses two levels of robot calibration, namely off-line calibration and on-line calibration. Off-line calibration techniques are used to precisely locate the terminal control frames (TCF) for end-effectors which are attached to the robot distal link or last link in the robot arm. Robot teach terminal readout is used to determine the end-effector TCF location. On-line calibration is used to position the robot TCF relative to the parts in the work space and thereby compensate for robot inaccuracy in localized regions of the robot's work space. Because these calibration methods utilize localized reference features, the robot inaccuracy is less than the desired tolerances required for assembly. In addition, statistical averaging of the calibration data can be utilized to compensate for some of the robot position errors.
A simulation of manipulator and robot tasks (SMART) has been developed with simulation software for off-line planning of both calibration tasks and working tasks. The calibration path is a set of robot configurations which, when integrated, downloaded to the robot controller, and executed, will cause the robot to move the vision system such as a camera near to the desired calibration feature being identified for part location. The working path is a set of robot configurations, speed settings, pick/place commands, etc. which, when integrated, downloaded to the robot controller, and executed, will cause the robot to move the robot tool to the desired operation points
Because of robot inaccuracy and work cell geometry uncertainties, the off-line path planned by a computer simulation must be modified to account for errors. These errors are measured by the vision system or other sensing means. Conformed path deviation algorithms are developed which use appropriate control points within the pre-planned paths to perturb or adjust the predicted working path, and yet maintain similar Cartesian path shape. Such procedures are discussed in greater detail hereafter.
The first of the disclosed calibration methods relates to calibration of the TCF position, which relates to end-effectors and sensors attached to the distal link of the robot. These relationships will be better understood with reference to FIG. 1. This figure discloses a robot 10 having a base reference frame 11, intermediate links 12, 13 and 14. A distal link 15 comprises the last link of the robot arm and includes a distal frame 16. An end-effector such as a camera, gripper or tool 17 is coupled to the distal link 16. A terminal control frame (TCF) 18 is associated with the end-effector and provides its frame of reference. These frames are graphically identified as the manipulator global frame (XYZ)m, the end-effector or vision TCF frame (XYZ)T and the robot terminal frame or distal frame (XYZ)e.
The object of calibrating the TCF position is to define this frame 18 with respect to the distal frame 16. Because the relative position of the distal frame with respect to the manipulator frame 11 is known, this calibration technique will tie all three reference frames together. The computer data processing and storage unit of the robot can readily calculate relative positions of any of these elements, given the position of any one element.
The method is practiced by attaching a pointing means such as an elongate pointer 19 to the robot distal link 15 such that the pointing means 19 is aligned parallel with the Z axis of the distal frame 16. A first reference point is selected at a space removed from the robot but within the operational distance. This reference point in FIG. 1 is represented as item 20 and may comprise an etched mark on a calibration plate 21. The robot is then moved to a first pose wherein the pointing end of the pointing means is located at the first reference point. The robot positioning data representing this first pose is stored in the robot computer for later recall and comparison. An end-effector such as a camera 17 is coupled to the distal link and includes a reference point (not shown).
The robot is then moved to a second pose wherein the end-effector reference point is located at the first reference point. Although item 20 is shown as a large rectangle, the reference point would be a single point which could be made coincident with the pointer 19. The robot positioning data for the second robot pose of this last step is also stored in the computer means for later recall and comparison.
The next step in the calibration for TCF position involves comparing the stored positioning data representing the first and second pose for detection of differences. These differences are processed within the robot computer to define an offset position of the TCF with respect to the robot distal frame. This step is accomplished using the following equations which can be derived by merging the configurations of FIGS. 2(b) and 2(c). From this sequence of steps it is possible to generate a set of equations which can be solved for X and Y, the TCF origin position coordinates in the robot distal link frame as follows:
X=(X2 -X1) S2 -(Y2 -Y1) C2 Equation (1)
Y=(X2 -X1) C2 +(Y2 -Y1) S2 Equation (2)
Where Si =Sin θi ; Ci =Cos θi ; and X1, Y1, X2, Y2, θ1 and θ2 are the robot teach terminal readout values.
Due to the robot inaccuracy from sources such as visual inspection, robot encoder and decoder errors, gear backlash, controller error, etc., the same calibration procedure is conducted for a number of randomly selected work space locations 22 (others not shown). The statistical average is then used to determine the best TCF transformation matrix. Such procedures are incorporated within the following method steps. An additional reference point 22 is selected and the robot is moved to a first pose position wherein the pointing end 19 is located at the additional reference point. The robot positioning data representing the first robot pose in this additional procedure is stored in the computer for later recall and comparison. The robot is then moved to a second pose wherein the end-effector reference point is located at the additional reference point 22. The positioning data is again stored and the comparison of data is made, with an appropriate processing of signals to define an offset position of the terminal control frame. The referenced statistical average is derived by repeating the above procedure to develop a substantial statistical base of difference values which can be processed to find the best TCF transformation matrix.
Once the TCF position is defined, calibration of the TCF orientation is necessary. This information is required when assembly or robot use requires both position and orientation determination. This orientation is determined by selecting a second reference point in a space removed from the robot but within the operating distance of the end-effector. The robot is then moved to a first pose wherein the pointing end of the pointing means 19 is located at this second reference point 22. The positioning data representing the first robot pose at this second reference point is stored in the computer memory. The robot computer then processes the stored positioning data for the first and second reference points to identify an orientation vector for a line connecting the first and second reference points. This line and vector have a defined orientation with respect to the TCF. This orientation data is stored in the computer means for later recall and processing.
The robot is then moved to a third pose such that the orientation of the vector relative to the TCF can be defined. This third pose information is also stored and the computer processes the cumulated data to define the relative orientation of the TCF with respect to the terminal distal frame. These steps are more specifically described with respect to FIG. 3 as follows.
Using the TCF position coordinates found in the previous calibration method, two arbitrary points are selected at spots p and q. This is accomplished by moving the robot to a position such that the center of the end-effector TCF is at the arbitrarily selected spot p. This current robot position is then read from the robot teach terminal. The position of q in robot global coordinates can be similarly identified. The orientation vector pq=p-q in the robot global frame is represented by α, using the information obtained in step 1 above. This angle is represented by the following expression wherein xp, yp, xq, yq are the position coordinates of p and q in the robot global frame:
α=arctan (Yq -Yp, Xq -Xp) Equation (3)
The robot arm is then moved to a position such that the orientation of vector pq relative to the end-effector (angle gamma as shown in FIG. 3) can be obtained. Again, the current robot position is read from the robot teach terminal. For a vision camera and effector, angle gamma can be determined from Equation (4) as follows:
γ=arctan (Yqv -Ypv, Xqv -Xpv) Equation (4)
where Xpv, Ypv =position of p in vision screen coordinates, and Xqv, Yqv =position of q in vision screen coordinates. From this sequence a set of equations can be generated, and TCF orientation, β can be determined by:
β=arctan [Cos (α-θ-γ), Sin (α-θ-γ]Equation (5)
For other end-effectors that are not axisymmetric the end-effector's TCF space X-axis is aligned with vector pq such that γ=zero. The TCF orientation calibration procedures set forth above can be used for any end-effector attached to the robot distal link. Statistical averaging for the best TCF orientation can be conducted using the procedures previously outlined.
On-line robot calibration is conducted at run time. By using a vision camera, the calibrated TCF geometry information and the work piece geometry information from a pre-processed data base, on-line calibration will determine the relative locations of work pieces in the work space. This permits correction of rigid body and robot position errors which are detailed in other parts of this disclosure.
The relative approaches developed use the calibration features shown in FIG. 1 and a vision system to capture the relative geometry information between parts and the robot end-effectors. Using the relative frames shown in FIG. 1, the component pose with respect to the robot global frame can be represented by the transformation equation as follows:
Tm c =CTm e Te v Tv f Tf c Equation (6)
Tm c =transformation from the component frame to the robot global frame.
cTm c =transformation from the robot terminal frame to the robot global frame when the vision camera acquires the calibration feature.
Te v =transformation from the vision camera frame to the robot terminal frame, as determined by the off-line robot calibration.
Tv f =transformation from the calibration feature frame to the vision camera frame, as determined by the image analysis [6].
Tf c =transformation from the component frame to the calibration feature frame, and determined from pre-processed workpiece geometry data bases.
With the TCF position and orientation now defined with respect to the distal frame, it is possible to establish relative position and/or orientation of any target object or part with respect to the computer. This is accomplished by defining reference frames on a relative basis, as opposed to endeavoring to define robot position with respect to a global reference frame. From a practical sense, the use of relative reference frames between the part and the robot position are preferable, because most manufacturing operations are specified relative to a local frame of reference or part datum. Utilization of the present method enables robot poses to be referenced and robot inaccuracy to be characterized relative to the part datum, rather than a more complex global reference frame.
This invention includes a description of methodology which can be applied to a kinematic model and stochastic model, as well as other analytical forms. The general procedure is represented by the following steps:
The robot is positioned with respect to a target object or position and a plurality of separated reference positions or features are identified. Typically, these features will be located on the target object and will be characterized by specific geometries and spatial data. The next step is to identify data defining these geometries, as well as spatial data of the separated reference positions relative to the target. This identification data is stored for each respective reference position within a data processing unit such as the computer system of the robot. This information will be utilized in a comparison operation by the robot upon later excursion to a location near this reference position.
The robot end-effector is then moved to a first location near one of the reference positions. For example, in FIG. 4, the robot end-effector is moved to an initial reference position 41 which is defined as the calibration position or calibration feature. In this position, the end-effector detects the presence of the calibration feature This detected calibration position is compared with the originally stored information data relating to that position. A rigid body error correction is developed based on position differences detected in the previous comparison step. This correction will be used with respect to later moves of the robot relative to this calibration position. The rigid body error correction data is then stored within the robot computer for later use.
The end-effector 42 is then moved to a second reference position 43. This movement is developed based on identification data regarding this reference position 43 as it was loaded into the robot computer with the originally stored identification data regarding this reference position In addition, however, the movement of the end-effector to the second position includes a correction factor developed by application of the rigid body correction defined from the previous step. This more accurately predicts proper placement of the robot in approximate vicinity to the second reference position 43. Accordingly, the present invention defines a rigid body correction with respect to a first calibration feature 41 and applies this correction with respect to subsequent moves, thereby modifying the originally stored identification data for the second position.
This method can be further extended to apply statistical averaging by measuring additional reference positions, comparing the detected new reference position with respect to the predicted value of this position. The difference between the predicted position and the actual position of the robot is detected and processed to define the amount of correction necessary to position the end-effector at subsequent reference positions with greater accuracy. This defined correction is stored within the computer for later processing. This is accomplished by repeating the movement, detection, storing and processing steps with respect to each additional reference such as items 44 and 45 of FIG. 4.
This procedure ha been applied with respect to a vision camera 51 and touch probe 52 mounted adjacent to the robot end-effector 53 as shown in FIG. 5. In conjunction with the vision 51 and touch sensors 52, a calibration plate or table 61 containing reference features 62 serve as a template to measure robot position. For example, feature 63 may be identified as the calibration feature, which is the first feature to which the pointer 52 is positioned. The remaining feature such as 62 offer additional reference points which can assist in building a statistical average to improve determination of the kinematic model. In this instance, the position of the reference feature is referenced to the calibration table datum (which is predetermined in construction) and robot poses are measured with respect to the calibration table datum.
The application of this methodology to measurement of the kinematic model of the robot is a slight modification of procedures described by Mooring, B. W., "The Effect of Joint Axis Misalignment on Robot Positioning Accuracy", Proceedings of the ASME Conference on Computers in Engineering, Chicago, Illinois, 1983 [1], and Tang, G., "Calibration and Accuracy Analysis of a Six-Axis Industrial Robot", Doctoral Dissertation, Dept. of Mechanical Engineering, Texas A & M University, December, 1986 [2]. Using these procedures, the kinematic model of a robot manipulator can be calculated from measured pose data. The calculated kinematic model is formulated by determining the location and orientation of each joint axis comprising the robot. This kinematic formulation is based on the generalized screw displacement matrix, formulation described by Suh, C. and Radcliffe, C. W., Kinematics and Mechanism Design, New York: John Wiley & Sons, 1978 [3], where a location vector p and an orientation vector u defines each joint. Once the actual joint model parameters are determined, a calibrated kinematic model is developed. This model is defined with respect to the part datum referenced during pose measurements as shown in FIG. 6.
When the robot kinematic model is accurately known and each robot joint value is specified, the robot pose can be accurately predicted. Inverse kinematic models can be developed which calculate joint values necessary to accurately position the robot at specified poses. Inverse kinematic formulations can be based on Denavit-Hartenburg parameters or any valid formulation of robot kinematics. Most robot controllers utilize such an inverse-kinematic transformation and many robot models are published in the literature. The subject inventors have developed algorithms which are based on predictor-corrector and inverse Jacobian formulations.
The simple predictor-corrector method utilizes the calibrated kinematic model of the robot to predict robot position. Robot pose joint value are estimated using a nominal inverse-kinematics model. The resulting poses and predicted using the calibrated model. The difference between the target pose and the predicted pose is pose inaccuracy. The target position is then corrected to account for pose inaccuracy. The process is repeated until the predicted robot inaccuracy is sufficiently reduced. The inverse-Jacobian method incorporates the inverse-Jacobian into a predictor-corrector iteration scheme by again using the calibrated kinematic model to predict robot position and the inverse-kinematic transformation. The mathematical formulation is similar to the calibrated kinematic model formulation. The partial derivatives of the robot position with respect to each joint value are determined and differential joint correction is estimated by solving the following linear matrix equation for delta q:
(∂T/∂qi) Δq=ΔT Equation (7)
where ∂T/∂qi denotes the partial derivative of the robot pose with respect to the ith joint value qi, Δq denotes the differential joint value and ΔT is the difference between the robot position predicted by the calibrated joint model parameters and the target robot pose. Thus, the kinematically corrected joint values are obtained by successive iteration of equation (7).
A slightly different inverse-Jacobian formulation was also developed for kinematic compensation. This formulation is contained in Paul, R., Robot Manipulators: Mathematics, Programming, and Control, Boston, Mass., M.I.T. Press, 1982 [5]. Both inverse-Jacobian formulations were based on the approximation:
(∂T/∂qi)c ≈(∂T/∂qi)n Equation (8)
where (∂T/∂qi)c denotes the change in robot position with respect to joint value qi from the calibrated robot model, and (∂T/∂qi)n denotes the change in robot position with respect to joint value qi from the ideal or nominal robot model. Convergence of the predictor-corrector and inverse-Jacobian methods for typical robot configuration is shown in FIG. 7. The rms positioning error shown on the vertical axis of FIG. 7 represents the root-mean-square location error of the simulated robot with successive iterations.
Stochastic modeling provides additional inaccuracy compensation capability to further reduce robot inaccuracy. The method of stochastic modeling used in this research is based on the Response Surface Methodolofy (RSM). RSM is used to plan the robot poses necessary to develop a comprehensive statistical model of robot inaccuracy. The design space applicable to a 6 degree-of-freedom robot manipulator is a 2 or 3 level, 6 factor space. The number of levels in the design space determines the order of the statistical model (2 level for a linear model and 3 level for a quadratic model). The number of factors reflects the number of robot joints. The factors represent the independent variables of the linear or quadratic model of robot inaccuracy.
Developing the statistical compensation models requires another set of target part relative measurements as previously described. Before the statistical calibration poses are sent to the robot controller or computer, they are corrected using kinematic compensation as previously discussed. The robot then moves to the corrected poses and the residual inaccuracy is measured. This residual inaccuracy is transformed to differential joint values by again applying the kinematic compensation algorithms (predictor-corrector or inverse-Jacobian). The residual differential joint perturbations are determined from the statistical compensation equations as follows:
qi =a+bi1 q1 +ci1 q1 2 +bi2 q2 +ci2 q22 + . . .+bi6 q6 +ci6 q6 2 Equation (9)
where a, b, and c represent quadratic model coefficients obtained from regression analysis, q represents the joint values, and qi denotes a differential joint perturbation. The first subscript of the model coefficients designates the joint compensated (ith), an the second coefficient subscript designates the joint. Likewise, the joint value subscript designates the joint.
A typical compensation process utilizing this methodology is as follows. The calibration poses are planned off-line on a simulator. The robot moves and positions itself in the calibration poses required by the calibrated kinematic model, and the inaccuracy is then measured. The robot moves and positions itself in the calibration poses required by the statistical model (as determined by RSM), and the inaccuracy is measured. The desired task is then planned off-line relative to the part datum. The off-line planned task is corrected using the models developed with respect to the calibration poses for the kinematic model and the statistical model. The compensated task information is then sent to the robot controller. Once the initial steps of planning calibration poses off-line and measuring the calibrated kinematic model poses need only be repeated infrequently . Measurement of the statistical model calibration poses are repeated periodically and the remaining procedures are repeated for each robot position planned on an off-line simulator.
As has been previously indicated, off-line programming in accordance with the present methodology is based on relative information, relying on the fact that most robots are repeatable with acceptable tolerances, and on the additional fact that parts on which the robot operates have been previously manufactured to some satisfactory tolerance. By guaranteeing that the part to be worked on will reach the robot work cell with some predetermined tolerance, it is possible to use off-line programming to command the robot to move to a reference calibration feature on the part, thereby capturing the rigid body inaccuracy information. With the establishment of a reference feature (item 41 in FIG. 4 and item 63 in FIG. 6) the robot can now be commanded to move to other predetermined features on that part. Knowing the relative geometry between the part features, procedures may be implemented to define the inaccuracy of the robot relative to the part on which it operates. Correction routines are then implemented which correct for the inaccuracy of the robot in the localized regions, thus allowing the practical application of off-line programming methods.
This enables the mapping of localized inaccuracy of the robot. Such mapping would not be necessary for each part which enters the work space if the part is positioned repeatedly within a predetermined tolerance. When parts enter the work space with the stated repeatability, the sensor equipment may be turned off during assembly operations, thus speeding the assembly process by compensating for robot inaccuracy utilizing software modification in the off-line programs.
A general method for mapping robot inaccuracy with respect to a target object is set forth as follows. First, the target object is identified, including a plurality of identifiable features thereon which can serve as reference points. A feature data base is developed defining the geometries and spatial relationships of the features on the object in sufficient detail to enable individual recognition of each feature by the computer sensing means. Feature data base information is then stored within the robot computer for later recall and comparison. The target object is placed within operational reach of a distal link of the robot and sensing means are attached to the distal link which include a capability of detecting the stored features of the target object. This detection is usually based on a comparison of (i) sensory data developed by the sensing means with respect to the feature and (ii) the stored feature data base information.
As with previous methods of kinematic and stochastic modeling, the sensing means is calibrated with respect to the distal link to accurately define relative positioning of the distal frame with respect to a terminal control frame of the sensing means. This calibrated terminal control frame position is stored within the computer for later recall and comparison. A routine or program is prepared which correlates stored feature data base information with the calibrated terminal control frame position. This routine provides drive commands to the robot for moving the sensing means sequentially to predicted positions of the respective features to be mapped on the target object.
The next step is to activate the routine with the robot, thereby moving the sensing means to a calibrated feature which is one of the stored reference features on the target object. For example, this could be item 41 in FIG. 4 or item 63 in FIG. 6. The relative pose error of the actual position of the sensing means with respect to the predicted position i defined and provides rigid body correction data. This data is stored within the computer for later recall and comparison. For example, the stored rigid body correction data is correlated with the prepared routine or program to define a new predicted position for an additional or subsequent feature to which the sensing means will be moved (items 43, 44, and 62). The sensing means is then moved to the new predicted location and the relative pose error of the actual position with respect to the new predicted position is defined. This error data is stored within the computer. By repeating these steps with respect to each remaining feature, a map of the target object is developed providing a statistical base for robot inaccuracy.
This general procedure was applied with respect to a calibrated plate machined to a tolerance of +0.0005 inches. The dimensions of the calibration plate are shown in FIG. 8 in graphic form.
Once the TCF is determined, inverse kinematic routines can be implemented to correctly position the camera frame near the part feature. An Automatix AV-3 vision system was calibrated with respect to the plate illustrated in FIG. 8. The relative pixel size of the y-pixel to the x-pixel was determined by location two dots on the calibration plate within the vision system camera frame. Their respective locations in pixel coordinates were then determined by statistically averaging over a number of tests to obtain the ratio of the y-pixel distance to the x-pixel distance. The distance between pixels in real world coordinates was also required. By using the same two dots and by knowing the physical distance separating the dots, a statistical average was obtained from the tests.
The origin of the coordinate frame of vision system was located at an x-pixel of 192.0 and a y-pixel of 127.5. Because the vision system was used, a coordinate frame was determined which related the feature captured by the vision system to the TCF frame of the camera which was attached to the robot distal link. The method used to determine this frame was the calibration method disclosed in the initial part of this specification for the TCF. This transformation involved getting the calibration plate coordinate frame and the vision system coordinate frame in the coordinate frame of the camera TCF, equation (10).
Tv f =Tv c *Tc f Equation (10)
Tv f =transformation from the calibration feature frame to the vision system frame;
Tv c =transformation from the camera TCF frame to the vision system coordinate frame;
Tc f =transformation from the calibration feature frame to the camera TCF frame.
The utilization of a "relative" positioning method represents a significant improvement over prior art techniques because an understanding of robot inaccuracy is only needed in the localized part area on which the robot operates. When the robot is making sweeping moves between work stations, the inaccuracy of the robot is not critical. However, because great accuracy is required in actual assembly or other for of robot task such as a pick or place move, the inaccuracy of the robot needs to be defined within this small area. These procedures were successfully demonstrated on a SEIKO RT-3000 series robot which is repeatable to +0.001 inches.
By using the calibration plate of FIG. 8, the robot inaccuracy propagation over a localized area was determined by first moving the camera over the reference calibration feature 81. From this feature the necessary information was captured which allowed for a part rigid body error correction for all subsequent moves of the robot. The rigid body error correction applies the same translation and orientation correction to all the features used in inaccuracy mapping of the robot relative to the part. Once the rigid body error transformation was determined, the robot was commanded in the vision system software to move to the next feature 82. By accessing a data base, all eight features 81-88 were mapped by the vision system. FIG. 9 lists the test data obtained in determining the robot inaccuracy. As seen in FIG. 10, the robot error increases proportionally (near linear) with distance from the reference calibration feature 81.
Since the localized position inaccuracy is a near linear function of distance, the following linear equations were developed to compensate for robot inaccuracy:
Ex=A1 x+B1 y Equation (11)
Ey=A2 x+B2 y Equation (12)
To solve for the constants it is necessary to capture the inaccuracy information from two independent points in the workspace area. This was accomplished by first moving the camera to a reference calibration feature to determine the rigid body error correction and then the camera was moved to two other features, designated i and j, from which all the necessary information was obtained to solve equations (11) and (12). The error equations at object i are:
Exi =A1 xi +B1 yi Equation (13)
Eyi =A2 xi +B2 yi Equation (14)
where xi and yi are the Cartesian moves of the robot and Exi and Eyi are the position errors captured by the vision system at object i. Similarly, the same information was captured at object j. Next Kramess rule was applied to solve for the constants A1, B1, A2 and B2. In this experiment, features 2 and 6 represented objects i and j respectively.
Next, the database information was modified to correct for predicted positional errors in location of each feature as the robot was commanded to move to all the features. FIG. 11 lists the error after the robot has been corrected for inaccuracy. Comparing FIGS. 9 an 11, it can be seen that the maximum robot inaccuracy of 0.0172" was improved to 0.0025" at a distance of 14.142" away from the reference feature. This is near the camera resolution and not realistically attainable. A statistical analysis of tolerance stack-up would imply that these techniques could be applied to processes not requiring greater than 0.005" of positional accuracy.
Robot orientation compensation presents greater difficulty. The orientation inaccuracy of the robot is not a function of distance from the reference calibration feature. Such orientation inaccuracy can be attributed to sources such as gear backlash, joint compliance, vision system algorithm limitations, etc. Experimentation has demonstrated that the orientation inaccuracy after a linear equation for orientation correction similar to the premise that successful off-line programming is enabled with methodologies that are based on relative information, as opposed to global reference frames. Such a premise relies on the fact that most robots are repeatable to within satisfactory tolerances and that target parts on which the robots operates have been previously manufactured to a satisfactory tolerance. In view of this premise, it will be apparent to those skilled in the art that the repeatability of the robot must be less than the desired tolerance of the robot task. It is also essential that the geometry specifications for the part on which the robot will operate can be accessed and passed to the robot work cell as needed.
Referring to FIG. 12, a flow chart illustrates the information flow and data base structure representing implementation of the subject invention within a typical manufacturing process. This flow chart integrates the calibration steps regarding TCF with the other forms of error correction based on relative rather than global reference frames. FIGS. 12 and 13 illustrate the integration of the present methodology from the calibration state through error determination and mapping stages. Referring specifically to FIG. 12, geometric features of targeted parts are usually well specified by design engineering and can be accessed at the robot task-planning stage of software preparation. Transformation software can be utilized to make the appropriate conversions to load geometric descriptions of features into the robot controller. Off-line calibration rules as set forth in the initial part of this disclosure can be integrated into the part design so that sufficient reference features can be identified or placed on the part for use by the robot feature acquisition system. For example, a vision or camera system has been described as useful for mapping the target part during the dynamic calibration stage. It is apparent from the preceding disclosure that the parts on which the robotic system operates must have the calibration reference features processed on them before they enter the robot work cell. These features may be resident geometry which can be easily processed by the feature acquisition subsystems or simply add-on features, either permanently placed on the part or placed on a temporarily attached template 26. Note that if the part is delivered in a consistent fashion, the accessing of features only needs to be conducted periodically. The integration of these procedures is represented by the initial box 110 of FIG. 11.
The planning process can be developed off-line in both the calibration tasks and the actual process tasks. These tasks are filed as a set of robot configurations with sufficient information to specify pick or place, speed settings, sensor read, etc. This planning involves both the calibration moves to be stored in calibration task files and the process moves to be stored in process task files. This aspect of the process is represented by box 111.
The path/task files can be downloaded to the work cell controller of the robot by file transfer software, using as a minimum serial RS232 communications. These interfaces are represented as item 112 in FIG. 12. Item 113 represents the work cell controller which maintains the software to convert the path file configurations into robot task macros. This software has both general algorithms applicable to most robots and device driver-type algorithms which are robot specific. At calibration, software is activated to correct the robot inaccuracy as observed by the sensor system, such as the camera. In its simplest form, this software consists of interpolation algorithms which operate on a matrix of position and orientation errors observed during the calibration phase. More complex software develops distortion transformations which map object geometries as distorted by the robot inaccuracies. Using these transformations, the robot operates on perceived part geometries.
Using the corrected transformations, software is activated to modify the pre-processed paths. This requires that the robot configurations be modified in the vicinities of the interaction situations using control points. These control points maintain the path shapes near critical assembly interaction points and correct for surface feature distortions due to the robot positioning inaccuracy. The simulation user will have insured that the intermediate configurations are sufficiently removed from work space obstacles as to avoid collision even after a path has been locally modified. Accordingly, these procedures not only relate to box 113 of FIG. 12, but also to box 111.
The use of control points is illustrated in FIG. 7. During the calibration off-line path planning, the user enters a set of generalized set of generalized displacement matrices in global coordinates to describe a set of desired calibration poses for the vision system TCF. FIG. 7 illustrates the calibration path segments 1, 2, 3 and 4 as they are connected to form a path in Cartesian space. During working path simulation planning, the gripper TCF is used as the robot end-effector TCF and the user enters displacement matrices to describe a set of desired poses of the gripper TCF relative to the components on which the gripper acts. FIG. 14 illustrates the concatenated working path segments in Cartesian space and the critical path nodes. After planning the calibration and working paths, the planned path segments are filed for later use in path segment integration and path deviation. The path file contains the number and sequence of path configurations, pick/place activation flags and other information relating to robot speed settings. At this stage, path files exist; however, they may not represent the exact form of the final path. To determine the exact form, integration procedures are applied which integrate the preplanned tasks and converts them to control languages used in work cell controllers such as those in the vision system or robot. Integration software has been developed that will allow the user to combine the preplanned path segment files by adding or deleting path segments from the total task file or by changing the sequence of path segments. Additionally, the user can enter commands in the robot control language during the integration process.
The off-line path planned by computer simulation must be modified to account for calibration errors measured by the vision system or other sensors and to account for geometric modeling uncertainties. There are various ways that off-line paths can be modified; however, for purposes of illustration, the Cartesian path shape or path conformity of critical path segments will be maintained by deviating the path while maintaining consistent relative Cartesian motions of the robot end-effector terminal control frame.
It is impractical to deviate the entire assembly task path to maintain the path conformity. Path segments near critical points such as pick and place locations are candidates for conformed path segment deviation by specifying three control points. The first point is the control pose point (CPP) which is a critical point where calibration error affects the effectiveness of the robot end-effector interaction with the part. The second point is the control point next (CPN) which is a point after which there will be a critical point (CPP). The Cartesian shape of the deviated path segment between CPP and CPN must conform to the shape of the Cartesian path planned by simulation. Finally, control point last (CPL) is a point before which there has been a critical point (CPP). Path conformity after path deviation must be maintained between CPP and CPL.
In a Cartesian work space, the task of modifying a path segment to maintain path conformity can be described as deviating each off-line planned pose of an end-effector TCF between the control points exactly the same amount of translational and rotational error detected during calibration. In other words, the displacement matrix of the end-effector TCF for every node on the simulated path segment is post multiplied by the same error correction transform matrix to get a new displacement matrix from which the conformed deviated path segment results. This is illustrated in FIG. 15 wherein poses 1, 2, 3 and 4 have been deviated by the software to points b, c, d, and e. This deviation method represents a novel approach to avoiding collision between the end-effector and obstacles within the work cell which might fall within the path of a modified planned pose.
The practical off-line programming techniques developed and illustrated in this disclosure have been applied to microelectronics assembly tasks in accordance with the following steps. Microelectronic chips of different sizes were picked up by the robot end-effector from a component feeder. Deviation path planning was developed to avoid work space collisions during transitional paths. The microelectronic chips were inserted into a designated IC board location. These tasks have been successfully accomplished and the off-line programming techniques developed have been shown to improve the robot position accuracy to +0.1 mm. within small areas of work space using rigid body error correction.
It will be apparent to those skilled in the art that the foregoing description and specific reference to examples are exemplary. The basic concepts and methods set forth in this disclosure are not to be construed as limiting with respect to the definition of invention set forth in the following claims.
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|Intuitive Surgical Operations, Inc.
|Medical robotic system providing sensory feedback indicating a difference between a commanded state and a preferred pose of an articulated instrument
|Aug 24, 2015
|Apr 25, 2017
|Intuitive Surgical Operations, Inc.
|Method and system for moving an articulated instrument back towards an entry guide while automatically reconfiguring the articulated instrument for retraction into the entry guide
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|Apr 25, 2017
|Industrial Perception, Inc.
|Detection and reconstruction of an environment to facilitate robotic interaction with the environment
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|Apr 25, 2017
|Industrial Perception, Inc.
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|Sep 28, 2001
|Apr 4, 2002
|J.G. Walacavage
|Method of part flow model for programmable logic controller logical verification system
|Sep 28, 2001
|Jun 6, 2002
|Walacavage J. G.
|Method of logical modeling of operator interaction with programmable logic controller logical verification system
|Dec 14, 2001
|Jun 27, 2002
|Madsen David D.
|Camera with improved illuminator
|Oct 30, 2001
|Aug 29, 2002
|Sankar Jayaram
|Computational geometry system, interrupt interface, and method
|Jul 26, 2001
|Oct 3, 2002
|Hwei-Min Lu
|3-D kinematics and tolerance variation analysis
|Nov 27, 2001
|Dec 19, 2002
|Ntn Corporation
|Workshop facility design and operation support system enabling verification of the entire workshop to be performed easily
|Oct 30, 2001
|Jul 17, 2003
|Sankar Jayaram
|Geometric model comparator and method
|Mar 3, 2003
|Nov 27, 2003
|Siemens Aktiengesellschaft
|Method for calibrating of machine units located in machine tools or robotic devices
|Dec 9, 2002
|Jan 15, 2004
|Samsung Electronics Co., Ltd.
|Method of calibrating robot
|Oct 15, 2002
|Jan 29, 2004
|Red Walter E.
|Systems and methods for representing complex n-curves for direct control of tool motion
|Oct 27, 2003
|May 6, 2004
|Fanuc Ltd.
|Object conveying system and conveying method
|Jan 21, 2004
|Aug 19, 2004
|Guenter Herrmann
|Method of and apparatus for operating a work robot
|Mar 4, 2004
|Nov 25, 2004
|Madsen David D.
|Camera with improved illuminator
|Dec 24, 2003
|Dec 16, 2004
|Fisher Lance K.
|Board align image acquisition device with improved interface
|Oct 26, 2004
|May 5, 2005
|Fanuc Ltd
|Simulation apparatus
|Dec 22, 2004
|Jun 30, 2005
|Japan Aerospace Exploration Agency
|Method of controlling redundant manipulator
|Jul 26, 2005
|Dec 1, 2005
|Robotic Workspace Technologies, Inc.
|Automation equipment control system
|Nov 23, 2005
|May 25, 2006
|Denso Wave Incorporated
|Automated manufacturing system
|Dec 17, 2003
|Aug 17, 2006
|Abb Ab
|Method and a system for programming an industrial robot to move relative to defined positions on an object, including generation of a surface scanning program
|May 16, 2005
|Nov 16, 2006
|Intuitive Surgical Inc.
|Methods and system for performing 3-D tool tracking by fusion of sensor and/or camera derived data during minimally invasive robotic surgery
|Nov 16, 2006
|Mar 29, 2007
|Toshio Takahashi
|Multi-axis ac servo control system and method
|Dec 21, 2006
|Jul 12, 2007
|Behzad Dariush
|Reconstruction, Retargetting, Tracking, And Estimation Of Pose Of Articulated Systems
|Apr 12, 2007
|Nov 1, 2007
|Honda Motor Co., Ltd.
|Control Of Robots From Human Motion Descriptors
|Jun 12, 2007
|Dec 20, 2007
|Fanuc Ltd
|Robot simulation apparatus
|Jun 29, 2006
|Jan 3, 2008
|Intuitive Surgical Inc.
|Tool position and identification indicator displayed in a boundary area of a computer display screen
|Jun 13, 2007
|Mar 13, 2008
|Intuitive Surgical, Inc.
|Preventing instrument/tissue collisions
|Oct 16, 2007
|Jun 5, 2008
|Toshiba Kikai Kabushiki Kaisha
|Robot system
|Feb 16, 2005
|Sep 25, 2008
|Thomas Pagel
|Method for Calibrating a Tool Center Point of Tools for Industrial Robots
|Oct 24, 2008
|Mar 19, 2009
|Honda Motor Co., Ltd.
|Real-time self collision and obstacle avoidance
|Sep 30, 2007
|Apr 2, 2009
|Intuitive Surgical, Inc.
|Methods and systems for robotic instrument tool tracking
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|May 7, 2009
|Honda Motor Co., Ltd.
|Real-time self collision and obstacle avoidance using weighting matrix
|Mar 31, 2009
|Jul 30, 2009
|Intuitive Surgical, Inc.
|Synthetic representation of a surgical instrument
|Mar 31, 2009
|Jul 30, 2009
|Intuitive Surgical, Inc.
|Synthetic representation of a surgical robot
|Feb 13, 2009
|Aug 13, 2009
|Landsnes Oeyvind A
|System And Method For Visualization Of Process Errors
|May 19, 2009
|Nov 26, 2009
|Aljosa Vrancic
|Controlling or Analyzing a Process by Solving A System of Linear Equations in Real-Time
|Jun 23, 2009
|Dec 31, 2009
|Intuitive Surgical, Inc.
|Medical robotic system providing an auxilary view including range of motion limitations for articulatable instruments extending out of a distal end of an entry guide
|Jun 27, 2008
|Dec 31, 2009
|Intuitive Surgical, Inc.
|Medical robotic system providing an auxiliary view of articulatable instruments extending out of a distal end of an entry guide
|Dec 17, 2008
|Dec 31, 2009
|Intuitive Surgical, Inc.
|Medical robotic system providing computer generated auxiliary views of a camera instrument for controlling the positioning and orienting of its tip
|Jul 1, 2008
|Aug 5, 2010
|Aldebaran Robotics S.A
|Method for Editing Movements of a Robot
|Apr 12, 2010
|Aug 5, 2010
|Translation Technologies, Inc.
|Feature-Based Translation System and Method
|Mar 10, 2009
|Sep 16, 2010
|Gm Global Technology Operations, Inc.
|Method for dynamically controlling a robotic arm
|May 14, 2010
|Oct 28, 2010
|Intuitive Surgical Operations, Inc.
|Medical robotic system with coupled control modes
|Nov 25, 2008
|Jan 27, 2011
|Andersson Bjoern E
|method and an apparatus for calibration of an industrial robot system
|Dec 15, 2008
|Jan 27, 2011
|Lorenz Bewig
|Method for error recognition in a control system of a medical treatment and/or diagnosis device
|Nov 5, 2009
|Feb 17, 2011
|Intuitive Surgical, Inc.
|Controller assisted reconfiguration of an articulated instrument during movement into and out of an entry guide
|Sep 15, 2009
|Mar 17, 2011
|Harris Corporation, Corporation Of The State Of Delaware
|Robotic apparatus implementing collision avoidance scheme and associated methods
|Nov 10, 2010
|May 5, 2011
|Intuitive Surgical Operations, Inc.
|Real-Time Generation of Three-Dimensional Ultrasound image using a Two-Dimensional Ultrasound Transducer in a Robotic System
|Apr 16, 2008
|Jun 30, 2011
|Tim Fielding
|Frame Mapping and Force Feedback Methods, Devices and Systems
|Feb 12, 2010
|Aug 18, 2011
|Intuitive Surgical Operations, Inc.
|Medical robotic system providing sensory feedback indicating a difference between a commanded state and a preferred pose of an articulated instrument
|Jan 25, 2011
|Jun 7, 2012
|Industrial Technology Research Institute
|Robot positioning method and calibration method
|Feb 6, 2013
|Jun 13, 2013
|Harris Corporation
|Robotic apparatus implementing collision avoidance scheme and associated methods
|Feb 25, 2013
|Sep 12, 2013
|Canon Kabushiki Kaisha
|Information processing apparatus and information processing method
|Jul 10, 2013
|Jan 30, 2014
|Seiko Epson Corporation
|Robotic system and robot control device
|Oct 8, 2013
|May 22, 2014
|Tim Fielding
|Frame Mapping and Force Feedback Methods, Devices and Systems
|Feb 11, 2014
|Aug 14, 2014
|Canon Kabushiki Kaisha
|Robot system and method for controlling the same
|Mar 10, 2014
|Sep 18, 2014
|Kabushiki Kaisha Yaskawa Denki
|Robot system, calibration method, and method for producing to-be-processed material
|Mar 19, 2014
|Sep 25, 2014
|Kabushiki Kaisha Yaskawa Denki
|Robot system and calibration method
|Apr 6, 2006
|Oct 18, 2007
|Kuka Roboter Gmbh
|Gear`s transmission ratio determining method, involves determining difference of positions of engine during positioning of forcipate units in two known relative positions, and changing positions of engine in defined intervals
|Nov 21, 2002
|Sep 17, 2003
|Robert Bosch Gmbh
|Method for calibrating a sensor and circuit arrangement for using a sensor
|Nov 21, 2002
|Aug 26, 2009
|Robert Bosch Gmbh
|Method for calibrating a sensor and circuit arrangement for using a sensor
|Oct 30, 2001
|May 10, 2002
|Translation Technologies, Inc.
|Computational geometry system, interrupt interface, geometric model comparator, and method
|Dec 20, 2001
|Jul 11, 2002
|Robotic Workspace Technologies, Inc.
|Versatile robot control system
|Oct 14, 2003
|Apr 29, 2004
|Brigham Young University
|Systems and methods for representing complex n-curves for direct control of tool motion
|Oct 14, 2003
|Apr 14, 2005
|Robert M Cheatham
|Systems and methods for representing complex n-curves for direct control of tool motion
|Sep 29, 2006
|Apr 12, 2007
|Honda Motor Co., Ltd.
|Motor and controller inversion: commanding torque to position-controlled robots
|Sep 29, 2006
|Jun 28, 2007
|Behzad Dariush
|Motor and controller inversion: commanding torque to position-controlled robots
|U.S. Classification
|700/254, 901/16, 901/2
|International Classification
|Cooperative Classification
|European Classification
|Nov 9, 1992
|Fee payment
Year of fee payment: 4
|Dec 26, 1996
|Maintenance fee reminder mailed
|May 18, 1997
|Lapse for failure to pay maintenance fees
|Jul 29, 1997
|Expired due to failure to pay maintenance fee
Effective date: 19970521


text:
"I am fearless and therefore I do, what I do."
"Don't look at the obstacles and go for your dreams."
"Everyone needs a little Nikki Bella in their life."
Nikki Bella (born Stephanie Nicole Garcia-Colace in San Diego, California on November 21, 1983) is an American model, actress, and professional wrester who is currently signed to WWE. Nikki's twin, Brie Bella is also a professional wrestler for WWE and together the twins are a wrestling tag team under the ring names Brie and Nikki Bella, or the Bella Twins. Both women are former WWE Divas Champions, with Nikki's second reign of 301 days being the longest in the title's history. In November 2015, Nikki was ranked number one in Pro Wrestling Illustrated's Female 50 in 2015. The twins are also reality stars on Total Divas, a television series that premiered on E! in 2013.
Best Known For:
Nikki Bella is best known for being a WWE powerhouse and starring in the reality television series, Total Divas.
Personal Life:
Nikki Bella is dating fellow professional wrestler John Cena after she previously dated Nick Nemeth, who is known on-screen as Dolph Ziggler. After more than four years of dating, John proposed to Nikki at WrestleMania 33 on April 2, 2017. In May 2014, Nicole revealed on Total Divas that she had married her high school sweetheart at the age of 20, however, the marriage was annulled three years later. Nicole also announced on Total Divas in 2014 that she is a qualified real-estate agent.
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text: "You will rattle the stars" - Elena (Throne of glass, by Sarah J. Maas Hi, I'm Sara, or as other people know me as Black flame on Movellas, I am on Wattpad by the name of Maree-grace2000. I just like to make other people smile and laugh, I like to write books. To read, the colour purple and a bunch of other colours. You will find that I'm very easy to talk to and will take time to listen to you (Well I must correct myself there, I mean read) when you need me to. I am a very protective person and will jump to the defence of anyone, especially any one in need of help. I dislike bullying, I don't approve of hate comments. Anyway, that's just me. NICE TO MEET YOU!!


text:
Queen's Inn by the River
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- Free High-Speed Internet
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- Bar/lounge
- Wheelchair accessibility
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- Bar/lounge
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Travel Blogs from Oakhurst
Back to Yosemite
Woke to sunshine again - yep, while we are loving the warm weather I think most people are after a cool change and lots of rain.
We had a slow start, which wasn't unpleasant and over breakfast planned the day.
A trip to Bass Lake where there were some caches to try for, and then back to Yosemite National Park to Wawona to explore a waterfall and find a covered bridge.
We had a pleasant half hour wandering to a cache under a ...
The long and winding road
... was impressive with a line up to pay our entrance fee ($30 - that's around fifty bucks Australian!)
Our first plan was a disappointment. The road to the original Mariposa Grove of Sequoias was closed for renovation and would be for the next 18 months or more. It is the home of some of the biggest and oldest living things on earth, but we weren't able to visit it.
However, the disappointment was soon forgotten as scenery opened up which was beautiful and ...
Road trip to Yosemite
... and on messaging the owner (who had asked us to correspond back on the condition of his pond) he told us we could use the Weber with caution as the surrounding area was tinder dry. On second thought, Jonathan ended up cooking on the frying pan inside (we couldn't find any matches to light the BBQ anyhow).
Bellies full, we sat down and planned the next two days, our much anticipated venture into Yosemite Valley.
Yosemite National Park: Beauty Beyond Belief
... McCoy, a hydrographer for the Los Angeles Department of Water and Power. As a member of the Eastern Sierra Ski Club, McCoy noticed that Mammoth Mountain consistently had more snow than other mountains in the Sierras. He bought a portable rope tow from the club in 1941, usually keeping it at Mammoth. In 1953, the US Forest Service awarded a permit to McCoy to operate the ski area, and he built it into one of the largest in California – ...
Day 65 - Yosemite is an Awesome Park!
... I just gave it a pass. Someday, I'll have to take Jody to Maryland for some real Maryland Lump Crab Cakes!
Tomorrow we are off to check out the Kings Canyon and Sequoia National Park. The Giant Sequoias of Mariposa Grove in Yosemite were closed being renovated, so we should be able to see some big trees tomorrow.
135.3 miles today
11,889.4 miles total
0.0 gallons today
284.941 gallons total


text:
Suspect Arrested In Denton Drive-By ShootingPolice said Trestin Clyde Durante, 21, was taken into custody at 2:20 p.m. Wednesday without incident.
Police Investigate Drive-By Shooting Outside Elementary SchoolSomeone in a car shot a man in the parking lot of Evers Park Elementary School after hours Tuesday night.
Dallas Drive By Injures Child, Rattles NeighborhoodPolice confirmed a 9-year-old was riding in a vehicle that was sprayed with bullets and taken to Dallas Children's Medical Center in good condition.
2 People Hurt In Dallas Drive-By ShootingTwo people are being treated at the hospital on Thursday morning after being injured during a drive-by shooting near Fair Park.
Man Killed In Shooting At Lancaster ParkPolice in Lancaster are searching for three suspects connected to a deadly drive-by shooting at a city park. The incident left 23-year-old Sheldon Earl dead.
Teenaged Girl Shot In Drive-By In Fort WorthPolice say it happened on Meadowbrook Drive when someone in a white SUV drove by and started shooting.
Arlington Road Rage Incident Ends With Gunfire & ArrestAn Arlington Independent School District teaching assistant is shaken, after police say a man shot into her minivan in an apparent case of road rage.
3 People Hurt In Arlington Drive-By ShootingAuthorities in Arlington are investigating a drive-by shooting at a nightclub early Monday. The incident left three people hurt, but all of the victims are expected to be okay.
Gang Member Arrested For Shooting 80-Year-Old GrandmaFort Worth police say a gang member has been arrested after an 80-year-old woman was shot in her sleep during a drive-by shooting.
80-Year-Old Grandma Hurt In Drive-By ShootingAn 80-year-old grandmother was wounded late Tuesday night in a drive-by shooting that narrowly missed striking a 1-year-old child.
Dallas Man Hospitalized After Drive-By ShootingDallas police are investigating a drive by shooting in Oak Cliff.
One Injured In Northeast Dallas Drive-By ShootingOne man was injured in a drive-by shooting at a laundromat in northeast Dallas late Monday night. A 15-year-old was shot and killed at the same shopping center three weeks ago.


text:
Kaiari: I'm Sorry! I Don't know What Came Over Me...
As I went downstairs, and made to go back into the kitchen, Strong hands pulled me round. "Shhhh...there's a hunter somewhere in the house. Searching, not for vampires. But for you and Matthew." Raven hissed in my ear. I was suddenly scared. I turned to face him. Since he was still holding onto me, it meant we were no almost nose to nose. Great. Just what I needed. I was addicted to his blood, and I was hopelessly in love with him. I slid and arm roun his neck, and stood on my tiptoes. I kissed his neck, then bit in. Raven wrapped his arms round me. I bit in harder, not on purpose. "Kaiari..." he warned.
I pulled away quickly, ripping his neck. He gave a little cry, and fell to the floor. I gasped. "Raven, I won't be able to kiss your neck better for this. This is serious. Do you want me to save you?" I asked softly. He nodded. I pushed a strand of his hair back behind his ear. "Trust me." I whispered, and wrapped my arms round the back of his neck. I kissed his lips. I felt his breath catch slightly with the shock. I opened my eyes, and saw the wound begin to heal. The blood returned, and the cut sealed up. I closed my eyes again, holding Raven to me. I felt his arms slide round my waist. I pulled away, bowing my head slightly. Raven touched one of his hands to his neck, and feeling it dry and uncut, and pulled me into a hug.
He pulled back slightly, and pushed his lips against mine. "Mmmn!" I mumbled, and pulled away. "I..I'm sorry! I didn't know what came over me...I guess it was just a thanks for healing me." He said softly. He bit his lip. He still had his arms round my waist, and my arms round his neck. I raised an eyebrow.
"What?" he asked grumpily, begining to pull away. I shook my head slightly, and gave him a kiss on the cheek. "And that was a thnks for my thanks." I giggled. We untangled ourselves, and he helped me up. I felt a tear roll down my cheek.
"What's up?" Raven asked. I cover his eyes with my hands. "Forgive and forget." I whispered. I took my hands off, and let, leaving Raven staring after me, slightly confused. I went up to my room, and smiled at Matthew. I plonked myself beside him. He rolled over, and opened his eyes. He reached up, and touched his fingers to my forehead. "Argh!" I cried out, as Matthew scrolled through my memories, searching my aura. It pained me a little. Ana ran in, followed by her sister. Matthew pulled away after seeing the memory of Raven and I. "You really need to control your lust for blood." Matthew said seriously, and left the room. He picked up Ana, and flew with her, away around the house somewhere. Ema stared after them. She turned to me. "Damn pixie powers. He could show those memories to anyone!" I growled. Ema laughed.
"If its the one where you ripped Raven's neck then used a Ultimate Healing Kiss, then there's nothing to worry about. No one minds. You healed him. That's it. I saw nothing after that. It went all blurry." She laughed. I smiled inwardly. Matthew had blocked the embarresing bit. Thank whoever's there. I looked out the window. I wondered if it was the last day of the year, and if I was still bound to Luna. Luna was my sister. She had black hair, icey blue eyes, and she was trapped, not far away from here. I would have to save her on New Year's Day, before one of us is exterminated.


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The 4-star Torremaura Hotel by the sea in Milano Marittima gives guests the possibility to spend dream holidays along the Adriatic Coast of Emilia-Romagna. This prestigious 4-star hotel in Milano Marittima gathers modern comforts and excellent services and facilities, what gives guests the possibil...
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3333 Abingdon Road
Bel Air South, Maryland, 21009
Commute to Downtown Edgewood
Almost all errands require a car.
About your score
3333 Abingdon Road has a Walk Score of 12 out of 100. This location is a Car-Dependent neighborhood so almost all errands require a car.
This location is in Bel Air South.
Explore how far you can travel by car, bus, bike and foot from 3333 Abingdon Road.
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1.2 mi
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This location is in the city of Bel Air South, MD. Bel Air South has an average Walk Score of 21 and has 47,709 residents.Learn More About Bel Air South


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FTF at 7:55 am. Quick grab.
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