Zvi S. Roth

An overview of robot calibration

An overview is given of the existing work on robot calibration, and some of the basic issues are identified in calibration and improvement of robot precision. Modeling, measurement, identification, and correction issues in robot calibration are discussed, and some of the unresolved questions are identified.

Simultaneous robot/world and tool/flange calibration by solving homogeneous transformation equations of the form AX=YB

The paper presents a linear solution that allows a simultaneous computation of the transformations from robot world to robot base and from robot tool to robot flange coordinate frames. The flange frame is defined on the mounting surface of the end-effector. It is assumed that the robot geometry, i.e., the transformation from the robot base frame to the robot flange frame, is known with sufficient accuracy, and that robot end-effector poses are measured. The solution has applications to accurately locating a robot with respect to a reference frame, and a robot sensor with respect to a robot end-effector. The identification problem is cast as solving a system of homogeneous transformation equations of the form A/sub i/X=YB/sub i/,i=1, 2, ..., m. Quaternion algebra is applied to derive explicit linear solutions for X and Y provided that three robot pose measurements are available. Necessary and sufficient conditions for the uniqueness of the solution are stated. Computationally, the resulting solution algorithm is noniterative, fast and robust. >

Simultaneous calibration of a robot and a hand-mounted camera

A popular configuration widely used in a variety of robotic applications is to mount a camera on the robot manipulator hand. Before performing a measurement task using such a system, both the camera and the robot need to be calibrated. In this paper, a procedure is developed for simultaneous calibration of a robot and a monocular camera. Unlike conventional approaches based on first calibrating the camera and then calibrating the robot, the algorithm solves for the kinematic parameters of the robot and camera in one stage, thus eliminating error propagation and improving noise sensitivity. Only two parameters are added to a robot calibration model to represent camera geometry. With this addition, different levels of calibration can be done under a unified framework. An error model relating-image measurement residuals to kinematic parameter deviations is derived. Simulation and experimental studies have been conducted to assess the effectiveness of the proposed procedure. >

A complete and parametrically continuous kinematic model for robot manipulators

A kinematic modeling convention for robot manipulators is proposed. The kinematic model has complete and parametrically continuous (CPC) properties. The parametric continuity of the CPC model is achieved by adopting a singularity-free line representation. Completeness is achieved through adding two link parameters which allow arbitrary placement of link coordinate frames. The transformation from the base frame to the world frame and from the tool frame to the last link frame can be modeled with the same convention as that used for internal link transformations. These parameters make the CPC model particularly useful for robot calibration.<<ETX>>

Method for kinematic calibration of stewart platforms

A Stewart platform is a six degrees of freedom parallel manipulator composed of six variable-length legs connecting a fixed base to a movable plate. Like all parallel manipulators, Stewart platforms offer high force/torque capability and high structural rigidity in exchange for small workspace and reduced dexterity. Because the solution for parallel manipulators forward kinematics is in general much harder than their inverse kinematics, a typical control strategy for such manipulators is to specify the plates pose in world coordinates and then solve the individual leg lengths. The accuracy of the robot critically depends on accurate knowledge of the devices kinematic parameters. This article focuses on the accuracy improvement of Stewart platforms by means of calibration. n n n nCalibration of Stewart platforms consists of construction of a kinematic model, measurement of the position and orientation of the platform in a reference coordinate frame, identification of the kinematic parameters, and accuracy compensation. A measurement procedure proposed in this article allows a great simplification of the kinematic identification. The idea is to keep the length of the particular leg, whose parameters are to be identified, fixed while the other legs change their lengths during the measurement phase. By that, redundant parameters can be eliminated systematically in the identification phase. The method also shows the estimation of each legs parameters separately because the measurement equations are fully decoupled, which results in a drastical reduction of the computational effort in the parameter identification. Simulation results assess the performance of the proposed approach.

Optimal selection of measurement configurations for robot calibration using simulated annealing

Measuring robot positions and orientations is a crucial step in a robot calibration process. Off-line optimal selection of measurement configurations can significantly improve the accuracy of kinematic identification. Since the dimension of the parameter space is very large and the cost function is highly nonlinear, this selection process could be well beyond the capacity of todays computers if a global optimal solution is sought by an exhaustive search. On the other hand, gradient-based algorithms are often trapped into local minima. A simulated annealing (SA) approach is adopted in this paper to obtain optimal or near optimal measurement configurations for robot calibration. Simulated annealing is capable of overcoming local minimum points. It is also very convenient for the inclusion of joint travel limits. The SA algorithm is costly computationally; however, since optimal configuration selection can be performed off-line, this may not be a serious problem. To accelerate the convergence rate, a suitable cooling schedule is devised. Practical implementation considerations are discussed. Experimental results are presented to demonstrate the feasibility of the proposed approach.<<ETX>>

Robot calibration with planar constraints

Investigates robot calibration with planar constraints, and in particular the conditions for the parameters of the robot kinematic model to be observable. Mainly multiple-plane constraints for robot calibration are considered. It is first shown that a single-plane constraint is normally not sufficient to calibrate a robot. It is also proven that by using a three-plane constraint, the constrained system is equivalent to an unconstrained point-measurement system under certain conditions. The significance of this observation is that one can use the three-plane constraint setup to successfully calibrate a robot. Simulations have been conducted to verify the theory presented in the paper.

Self-calibration and mirror center offset elimination of a multi-beam laser tracking system

Abstract New methods for the self-calibration of a laser tracking coordinate measuring machine are reported in this paper. Proper calibration of a laser tracking system is essential prior to using such a device for coordinate measuring. The task is nontrivial in the absence of other measurement systems of comparable accuracy. One has to rely on a self-calibration strategy. Two calibration methods, one based on a four-tracker system and the other based on three trackers combined with precision planes to constrain the target motion, are proposed. Iterative optimization algorithms are developed. A basic assumption for these calibration methods is that there is no tracking mirror center offset. Error analysis presented in this paper reveals that measurement errors due to mirror center offsets are significant. Therefore before calibrating the laser tracking system, the mirrors must be adjusted so that the laser beams hit the mirror centers. The adjustment is a tedious manual task. In the FAU laser tracking machine, an adjustment procedure which employs a four quadrant detector has been devised for the elimination of tracking mirror center offsets. Simulation and experimental results are presented to demonstrate the effectiveness of the suggested methods.

A closed form solution to the kinematic parameter identification of robot manipulators

A linear method for identifying the unknown kinematic parameters of a manipulator directly from the forward kinematic model is presented. The method requires the use of neither a nominal model nor a linearized error model of the robot. Such a solution is made possible by the use of a special robot kinematic modeling convention known as the complete and parametrically continuous (CPC) model, in which the independent CPC link parameters appear linearly in the system of equations to be solved, and the use of a particular sequence of robot pose measurements. The CPC orientation parameters of the revolute joints are first determined recursively under the condition that the pose measurements of the robot are taken while releasing each revolute joint one at a time and successively. The remaining CPC parameters are then computed in terms of the orientation parameters obtained earlier. Some practical issues related to kinematic parameter identification with the proposed approach are addressed through simulation studies. >

Modeling gimbal axis misalignments and mirror center offset in a single-beam laser tracking measurement system

The calibration of robots and machine tools normally requires external pose measuring devices to provide precision cal ibration measurement data. Among the various coordinate measuring techniques, laser tracking systems based on in terferometry offer the potential for continuously producing noninvasive and highly accurate measurements over a large work volume. This article addresses the error modeling is sue for laser tracking coordinate measuring systems, which is crucial in the accuracy enhancement of such systems. Relative distance measurements provided by laser interfer ometers have an extremely high resolution. However, accuracy errors of a coordinate measuring machine based on laser tracking are dominated by geometric errors in the tracking mir ror system. Major geometric error sources include gimbal axis misalignments and mirror center offset. In this article a kine matic model for the single-beam tracker is developed in which a necessary and sufficient number of kinematic parameters are used to represent these two types of error sources for ar bitrary target positions. This model, together with its error model, which is also presented in this article, can be used for design, calibration, and control of single-beam laser tracking measurement systems.