We propose a novel implementation of visual servoing whereby a human operator can guide a robot relative to the coordinate frame of an eye-in-hand camera. Among other applications, this can allow the operator to work in the image space of the eye-in-hand camera. This is achieved using a gamepad, a time-of-flight camera (an active sensor that creates depth data), and recursive least-squares update with Gauss-Newton control. Contributions of this paper include the use of a person to cause the control action in a visual-servoing system, and the introduction of uncalibrated position-based visual servoing. The system's efficacy is evaluated via trials involving human operators in different scenarios.

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.

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 robot's 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.

Target tracking and obstacle avoidance are demonstrated for uncalibrated visual servoing. An objective function is designed that encourages target following by a robotic end-effector while discouraging movements near an obstacle. The objective function incorporates the error between the target and the end-effector and a potential function related to the obstacle. This objective function is minimized using a dynamic nonlinear least squares optimization method in conjunction with a recursive least squares Jacobian estimation algorithm. The approach is generic and can be applied to a variety of systems. Calibration is unnecessary after a reconfiguration or disturbance to the robotic workcell. This type of control has the potential to provide a low-cost, low-maintenance automation solution for unstructured industries and environments. Experimental results demonstrate both target tracking and obstacle avoidance for an uncalibrated robotic system.

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.

Tracking of a moving target by uncalibrated model independent visual servo control is achieved by developing a new "dynamic" quasi-Newton approach. 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 new dynamic Newton's method. A second-order convergence rate is established, and it is shown that the standard method is not guaranteed convergence for a moving target. The algorithm is extended to develop a dynamic Broyden update and subsequently a dynamic quasi-Newton method. Results for both one- and six-degree-of-freedom systems demonstrate the success of the algorithm and shows dramatic improvement over previous methods.

Remote center-of-compliance devices have long been used to facilitate insertion for assembly operations. A new analysis with a more accurate model better characterizes the interesting properties of remote compliance. The center location and stiffiness are presented as nondimensional ratios that are functions of geometrical properties. New results describe: i) the high sensitivity of the center location and ii) the inverse relationship between linear and angular lateral stiffnesses.

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.>

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.>

For unconstrained manipulation, the linear compliance and stiffness models are equivalent. The equivalence does not hold for constrained manipulation, but leads to two dual models. These are analyzed using screw theory and a novel duality is explicitly demonstrated. The eigenstructure of the singular compliance and singular stiffness matrices is determined and several new dual propositions are developed.>

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.>

A method for using complex numbers in the kinematic solution of robotic manipulators is presented. The inverse kinematics algorithm of a manipulator produces complex joint angles if it is given an end effector location outside its workspace. Although complex joint angles cannot be implemented physically, they can be converted to real numbers through a suitable mapping, and the robot approximates the configuration required to produce the desired location within the limits of its workspace. It is shown that for certain manipulators, the real-part mapping produces a minimization of the end effector location error. Examples of the technique using 2R and 3R manipulators are presented.>

A technique for analyzing robots with fourth-order inverse kinematic solutions is introduced. The solution of the inverse kinematics problem is restated as a pencil of conics. In this representation, the order of the solution reduces when one of the conics in the pencil becomes degenerate and noncentral. Properties of conics are exploited to define and develop special manipulator geometries. The method is illustrated by a detailed examination of all revolute (R) robots which have a three-axis wrist (i.e. 3R regional manipulators). All criteria for reduction of the inverse kinematics of this type of robot are determined, resulting in some new robot designs. These designs constitute all regional robots with kinematics that require the solution of only quadratic equations.>