Harvey Lipkin

Mobility of Overconstrained Parallel Mechanisms

The Kutzbach-Grubler 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.

Uncalibrated dynamic visual servoing

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.

Uncalibrated Eye-in-Hand Visual Servoing

In this paper we present new uncalibrated control schemes for vision-guided 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 robots kinematic model or camera calibration, the system is able to track a moving object through a variety of motions and maintain the objects 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 Gauss-Newton method utilizing a partitioned Broydens method for model estimation provides the best steady-state tracking behavior.

Synthesis of Cartesian stiffness for robotic applications

A new, systematic approach to the synthesis of Cartesian stiffness by springs is presented using screw (spatial vector) algebra. The space of solutions is fully characterized for all stiffnesses realizable by springs. The main result shows that a rank r stiffness can always be synthesized by r springs. Further, it can also be synthesized by an arbitrarily large number of springs greater than r. Synthesis algorithms are presented and numerical results support the theory.

A dynamic Jacobian estimation method for uncalibrated visual servoing

A dynamic Broydens method is presented for use in a quasi-Newton control scheme for model-independent vision guided robotic control. Model independent visual servo control is defined as using visual feedback to control a robot without precisely calibrated kinematic and camera models. The control problem is formulated as a nonlinear least squares optimization. For the moving target case, this results in a time-varying objective function which is minimized using a dynamic Newtons method. The dynamic Jacobian estimation scheme is used to estimate the combined robot and image Jacobians. Experimental results for a two-degree-of-freedom system demonstrates the success of the algorithm.

A new method of robotic rate control near singularities

A novel method of controlling robotic manipulators near singularities is introduced. In traditional rate control, a local first-order approximation of the robot kinematics is used, which may fail at a singularity. However, if the approximation is extended to the second order, it becomes possible to solve for the joint rates. The proposed method uses a multidimensional Newton-Raphson technique to solve the resulting set of coupled, quadratic equations. The method is presented in conjunction with a description of rate control in the complex domain, which allows for end-effector locations outside the manipulators workspace. Two examples employing quadratic rate control are presented for a 6R robot in a singular configuration, and one example applying the method to a closed trajectory is shown.<<ETX>>

Tracking a moving target with model independent visual servoing: a predictive estimation approach

Target tracking by model independent visual servo control is achieved by augmenting quasi-Newton trust region control with target prediction. Model independent visual servo control is defined using visual feedback to control the robot without precise kinematic and camera models. While a majority of the research assumes a known robot and camera model, there is a paucity of literature addressing model independent control. In addition, most researches have focused primarily on static targets. The work presented here demonstrates the use of predictive filters to improve the performance of the control algorithm for linear and circular target motions. The results show a performance of the same order of magnitude as compared to some model based visual servo control research. Certain limitations to the algorithm are also discussed.

Lagrangian wrench distribution for cooperating robotic mechanisms

A systematic method for analysis of cooperating robotic mechanisms is investigated using constrained optimization. The wrench distribution problem is formulated as a quadratic optimization problem with a linear constraint. This leads to the definition of the Lagrangian screw, which is shown to be an important geometrical tool for analysis. The geometrical meaning of the distributed wrench field is explained in terms of the Lagrangian screw. Examples show that several previous investigations in the literature may be included as special cases.<<ETX>>

Generalized center of compliance and stiffness

The elastic characteristics of many robot systems can be modeled by a 6*6 stiffness or compliance matrix. Three results are presented via screw theory. First, stationary values of compliance and stiffness are determined. Second, linear and rotational properties are characterized by dual ellipsoids in three-dimensional space. Third, a generalized center-of-elasticity (compliance and stiffness) is proposed. If a compliant axis exists, it is shown to pass through the center. These elements simplify the understanding of complex elastic properties.<<ETX>>

Uncalibrated eye-in-hand visual servoing

This paper presents uncalibrated control schemes for vision-guided 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 robots kinematic model or camera calibration, the system is able to track a moving object and maintain the desired features. 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.