A dynamic quasi-Newton method for uncalibrated, vision-guided robotic tracking control with fixed imaging is developed and demonstrated. This method does not require calibrated kinematic and camera models. Robotic control is achieved at each step through minimizing a nonlinear objective function by taking quasi-Newton steps and estimating the composite Jacobian at each step. The Jacobian is estimated using a dynamic recursive least squares algorithm. Experimental results demonstrate the validity of this approach.
The Kutzbach–Grübler mobility criterion calculates the degrees of freedom of a general mechanism. However, the criterion can break down for mechanisms with special geometries, and in particular, the class of so-called overconstrained parallel mechanisms. The problem is that the criterion treats all constraints as active, even redundant constraints, which do not affect the mechanism degrees of freedom. In this paper we reveal a number of screw systems of a parallel mechanism, explore their inter-relationship and develop an original theoretical framework to relate these screw systems to motion and constraints of a parallel mechanism to identify the platform constraints, mechanism constraints and redundant constraints. The screw system characteristics and relationships are investigated for physical properties and a new approach to mobility analysis is proposed based on decompositions of motion and constraint screw systems. New versions of the mobility criterion are thus presented to eliminate the redundant constraints and accurately predict the platform degrees of freedom. Several examples of overconstrained mechanisms from the literature illustrate the results.
Three necessary conditions derived from classical geometry are proposed to evaluate formulations for the simultaneous twist and wrench control of rigid bodies, and for any theory to be meaningful it must be invariant with respect to (1) Euclidean collineations, (2) change of (Euclidean) unit length, and (3) change of basis. It is demonstrated in this paper that a previously established theory of hybrid control for robot manipulators is in fact based on the metric of elliptic geometry and is thus noninvariant with respect to (1) and (2). A new alternative invariant formulation based on the metric of Euclidean geometry and an induced metric of projective geometry is presented in terms of screw theory. An example of insertion illustrates both the invariant and noninvariant methods.
The structure of nonsingular robot compliance is investigated by applying screw theory to two eigenvalue problems. For the first problem the eigenscrews are demonstrated to be Ball’s (1990) principal screws of the potential. Several new propositions are presented characterizing compliance matrix eigenstructure. Using a novel formulation, the second eigenvalue problem generalizes the three wrench-compliant axes of Dimentberg (1965) to include three twist-compliant axes. These two types of compliant axes are shown to be reciprocal and define conjugate screw systems. The wrench- and twist-compliant axes are demonstrated to the general elements of a compliant axis hierarchy.
In this paper we present new uncalibrated control schemes for visionguided robotic tracking of a moving target using a moving camera. These control methods are applied to an uncalibrated robotic system with eye-in-hand visual feedback. Without a priori knowledge of the robot's kinematic model or camera calibration, the system is able to track a moving object through a variety of motions and maintain the object's image features in a desired position in the image plane. These control schemes estimate the system Jacobian as well as changes in target features due to target motion. Four novel strategies are simulated and a variety of parameters are investigated with respect to performance. Simulation results suggest that a GaussNewton method utilizing a partitioned Broyden's method for model estimation provides the best steady-state tracking behavior.
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