Beno Benhabib

A complete generalized solution to the inverse kinematics of robots

The kinematic transformation between task space and joint configuration coordinates is nonlinear and configuration dependent. A solution to the inverse kinematics is a vector of joint configuration coordinates that corresponds to a set of task space coordinates. For a class of robots closed form solutions always exist, but constraints on joint displacements cannot be systematically incorporated in the process of obtaining a solution. An iterative solution is presented that is suitable for any class of robots having rotary or prismatic joints, with any arbitrary number of degrees of freedom, including both standard and kinematically redundant robots. The solution can be obtained subject to specified constraints and based on certain performance criteria. The solution is based on a new rapidly convergent constrained nonlinear optimization algorithm which uses a modified Newton-Raphson technique for solving a system nonlinear equations. The algorithm is illustrated using as an example a kinematically redundant robot.

Three-dimensional location estimation of circular features for machine vision

A closed-form analytical solution to the problem of 3D estimation of circular-feature location is presented. Two different cases are considered: 3D orientation and position estimation when the radius is known and when it is not known. Extension of the method to general 3D quadratic features is also addressed. Simulated experimental results obtained for all three cases verified the analytical method. In the case of real experiments, a set of circles located on a calibration plate, whose locations were known with respect to a reference frame, were used for camera calibration as well as for the application of the method. A sequential compensation procedure was applied to the input gray-level image to compensate for distortion. These results also showed the validity of the process and the applicability of the analytical method. >

A Unifying Framework for Classification and Interpretation of Mechanism Singularities

This paper presents a generalized approach to the singularity analysis of mechanisms with arbitrary kinematic chains and an equal number of inputs and outputs. The instantaneous kinematics ofa mechanism is described by means of a velocity equation, explicitly including not only the input and output velocities but also the passive-joint velocities. A precise definition of singularity of a general mechanism is provided. On the basis of the six types of singular configurations and the motion space interpretation of kinematic singularity introduced in the paper, a comprehensive singularity classification is proposed.

Identification and classification of the singular configurations of mechanisms

This paper presents a novel method for finding and classifying all the singularities of an arbitrary non-redundant mechanism. The proposed technique is based on the velocity-equation formulation of kinematic singularity and the singularity classification introduced earlier by the authors. Criteria for singularity are derived and used to formulate a method for computing the singularity set and revealing its division into singularity classes. As an example, the comprehensive singularity analysis of a spatial mechanism is presented.

Robotic interception of moving objects using an augmented ideal proportional navigation guidance technique

Presents an approach to online, robot-motion planning for moving-object interception. The proposed approach utilizes a navigation-guidance-based technique, that is robust and computationally efficient for the interception of fast-maneuvering objects. Navigation-based techniques were originally developed for the control of missiles tracking free-flying targets. Unlike a missile, however, the end-effector of a robotic arm is connected to the ground, via a number of links and joints, subject to kinematic and dynamic constraints. Also, unlike a missile, the velocity of the robot and the moving object must be matched for a smooth grasp, thus, a hybrid interception scheme, which combines a navigation-based interception technique with a conventional trajectory tracking method is proposed herein for intercepting fast-maneuvering objects. The implementation of the proposed technique is illustrated via numerous simulation examples.

Singularity analysis of mechanisms and robots via a velocity-equation model of the instantaneous kinematics

This paper presents a new generalized approach to the singularity analysis of a general mechanism (arbitrary kinematic chain), considered as a non-redundant input-output device with equal number of inputs and outputs. The instantaneous kinematics of a mechanism is described by means of a velocity equation, explicitly including not only the input and output velocities but also the passive-joint velocities. A precise definition of singularity of a general mechanism is provided. On the basis of the six types of singular configurations introduced in the paper singularity classifications are proposed.<<ETX>>

Development of an inspection process for ball-grid-array technology using scanned-beam X-ray laminography

An inspection process based on scanned-beam X-ray laminography (SBXLAM) is proposed herein for quantitatively monitoring the quality of ball-grid-array (BGA) joints. The long-term reliability of the BGA joints depends on the component-assembly process producing joints with sufficient solder volume and proper alignment. Inspection algorithms were developed to measure the critical BGA-joint characteristics, including the alignment between the ball and the PCB pad, the solder thickness, and the average joint-diameter, and thus, determine whether the joints are defective. The performance of the inspection algorithms was evaluated by inspecting samples with defects that were independently verified.

Singularity analysis of mechanisms and robots via a motion-space model of the instantaneous kinematics

This paper investigates the kinematic singularities of a general mechanism (arbitrary kinematic chain), considered as a non-redundant input-output device with equal number of inputs and outputs. The instantaneous kinematics of a mechanism is described by the orientation of a linear subspace, the motion space, inside the velocity space of all potential instantaneous motions. The definition of singularity for a general mechanism is provided. On the basis of the six types of singular configurations introduced in the paper a comprehensive singularity classification is developed.<<ETX>>

Accurate parameter estimation of quadratic curves from grey-level images

Abstract Accurate estimation of the parameters of a curve present in a grey-level image is required in various machine-vision and computer-vision problems. Quadratic curves are more common than other curve types in these fields. The accuracy of the estimated parameters depends not only on the global interpolation technique used, but, as well, on compensation of major sources of error. In this paper, first, as a preliminary step in accurate parameter estimation of quadratic curves, a sequential distortion-compensation procedure is formulated. This procedure addresses the major distortion factors involved in the transformation of a curve from the object space to the image space. Subsequently, as a means for accurate estimation of the coordinates of edge points, a new subpixel edge detector based on the principle of the sample-moment-preserving transform (SMPT) is developed. A circular-arc geometry is assumed for the boundary inside the detection area. The new arc-edge detector is designed as a cascade process using a linear-edge detector and a look-up table. Its performance is compared with that of a linear subpixel edge detector. Then, as a part of the main theme of the paper, the estimation of the five basic parameters of an elliptical shape based on its edge-point data is addressed. To achieve the desired degree of accuracy, a new error function is introduced and as the basis for a comparative study, an objective and independent measure for “goodness” of fit is derived. The proposed new error function and two other error functions previously developed are applied to six different situations. The comparative performance of these error functions is discussed. Finally, as the basis for evaluation of the total process, a 3D location estimation problem is considered. The objective is to accurately estimate the orientation and position in 3D of a set of circular features. The experimental results obtained are significant in two separate ways: in general, they show the validity of the overall process introduced here in the accurate estimation of 3D location; in particular, they demonstrate the effectiveness of the sub-pixel edge detector and the global interpolation technique, both developed here.

Application of moment and Fourier descriptors to the accurate estimation of elliptical-shape parameters

Abstract Accurate estimation of the parameters of an elliptical shape is required in various machine-vision and computer-vision problems. In our previous work, we have addressed this problem by proposing to optimize a weighted minimum-squares-error (MSE) function. As a continuation of this work, we have studied other techniques for elliptical-parameter estimation, ones applying elliptical-Fourier descriptors, moments of area, and moments of perimeter. A study, to be reported here, was carried out to evaluate the comparative performance of the above-mentioned three techniques and the one based on the weighted MSE function. The limitation and degree of accuracy of each technique was determined. It was found that different elliptical-parameter-estimation techniques must be applied depending on acceptable computational cost, number of parameters to be estimated, the required degree of accuracy, and the specific conditions under which the estimation must be performed.