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A new kinematic modeling convention for robot manipulators is proposed. The kinematic model is termed after its "completeness and parametric continuity" (CPC) properties. Parametric continuity of the CPC model is achieved by adopting a singularity-free line representation consisting of four line parameters. Completeness is achieved through adding two link parameters to allow arbitrary placement of link coordinate frames. The transformations from the world frame to the base frame and from the last link frame to the tool frame can in the CPC model be modeled with the same modeling convention as that used for internal link transformations. Since all the redundant parameters in the CPC model can be systematically eliminated, a linearized robot error model can be constructed in which all error parameters are independent and span the entire geometric error space. These properties make the CPC model particularly useful for robot calibration. The paper focuses on model construction, mappings between the CPC model and the Denavit-Hartenberg model, study of the model properties, and its application to robot kinematic calibration.

Abstrucr-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,X = YB,, 1 = 1 2 . rv. 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 rewlting solution algorithm is noniterative, fast and robust.

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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 forcehorque 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 plate's pose in world coordinates and then solve the individual leg lengths. The accuracy of the robot critically depends on accurate knowledge of the device's kinematic parameters. This article focuses on the accuracy improvement of Stewart platforms by means of calibration.Calibration 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 leg's 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.

An estimate of the probability density function of a random vector is obtained by maximizing the output entropy of a feedforward network of sigmoidal units with respect to the input weights. Classification problems can be solved by selecting the class associated with the maximal estimated density. Newton's optimization method, applied to the estimated density, yields a recursive estimator for a random variable or a random sequence. A constrained connectivity structure yields a linear estimator, which is particularly suitable for "real time" prediction. A Gaussian nonlinearity yields a closed-form solution for the network's parameters, which may also be used for initializing the optimization algorithm when other nonlinearities are employed. A triangular connectivity between the neurons and the input, which is naturally suggested by the statistical setting, reduces the number of parameters. Applications to classification and forecasting problems are demonstrated.

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