End-effector Frame Research Articles

Oscillating Saw Calibration for Mandibular Osteotomy Robots

Accurate oscillating saw tool calibration is an important task for mandibular osteotomy robots to perform precise cutting operations. However, in contrast to traditional tool calibration which just calibrates the tool center position (TCP) or the tool feed axis, both the position and the plane orientation of the saw should be carefully calibrated. Therefore, aiming at this problem, in this paper, we propose a method to carry out oscillating saw calibration by employing an optical stereo vision tracking system. At first, hand–eye calibration is conducted to ascertain the spatial pose of the vision frame within the manipulator’s base frame. Subsequently, employing a probe, the positions of the sawtooth points on the oscillating saw plane are captured within the vision frame. These positions are then translated to the manipulator’s end-effector frame using the positional elimination algorithm proposed in this paper. Finally, the pose of the oscillating saw plane within the manipulator’s end-effector frame is extrapolated from the positions of the three sawtooth points. The result shows that the position errors of the points on the oscillating saw plane are within 0.25 mm and the variance of the plane normal direction is 1.93∘ in the five experiments. This approach enables accurate calibration of the oscillating saw plane’s position and orientation within the manipulator’s end-effector frame. Furthermore, it mitigates the necessity of continual adjustments to the joint angles of the manipulator as required by the “six-point method”. However, this approach is hinged upon the availability of precision-oriented 3D positioning equipment.

Kinematics-Based Motion-Force Control for Redundant Manipulators With Quaternion Control

Motion-force control of redundant manipulators is universally regarded as a pivotal issue in industrial manufacturing, especially for the processing of precision instruments. This paper proposes a kinematics-based motion-force control (KBMFC) scheme for redundant manipulators, which is driven by joint velocity commands and different from the dynamics-based methods. Specifically, the force and motion are modeled and decoupled in the end-effector frame with the help of a stiffness coefficient. To control the orientation of the force, a quaternion control equation is designed by combining the rotation matrix and neural dynamics method. Different from traditional motion-force control methods, the proposed scheme is constructed as quadratic programming with the corresponding recurrent neural network (RNN) solver derived, which considers the kinematic optimization index and joint constraints. According to the generated control signals, a redundant manipulator is able to accurately fulfill the hybrid control of motion and force with the desired quaternion, which is intuitively confirmed by simulations and experiments. <i>Note to Practitioners</i>&#x2014;This paper is motivated by the deficiencies that restrict the real-world applications of the motion-force control of redundant manipulators. On the one hand, most existing motion-force control schemes are implemented under the framework of dynamics, which inevitably leads to some kinematics-related defects. On the other hand, the latest kinematics-based techniques introduce an admittance control to achieve motion-force control. However, they model the force in the Z-axis of the base coordinate while the motion planning is limited in the X-Y plane, which dramatically reduces real-world applications. In this paper, the deformation force is designed in the end-effector frame, and a quaternion control technology of the end-effector is developed. Such a scheme can realize the real-time control of the orientation and magnitude of the force while ensuring trajectory tracking. In addition, the introduction of optimization indexes and joint constraints dramatically improves the functionality of the proposed scheme. Finally, the contributions of this paper are verified through simulations, experiments and comparisons. This work proposes a feasible framework for the motion-force control and orientation control of redundant manipulators.

Mix Frame Visual Servo Control Framework for Autonomous Assistive Robotic Arms.

Assistive robotic arms (ARAs) that provide care to the elderly and people with disabilities, are a significant part of Human-Robot Interaction (HRI). Presently available ARAs provide non-intuitive interfaces such as joysticks for control and thus, lacks the autonomy to perform daily activities. This study proposes that, for inducing autonomous behavior in ARAs, visual sensors integration is vital, and visual servoing in the direct Cartesian control mode is the preferred method. Generally, ARAs are designed in a configuration where its end-effector’s position is defined in the fixed base frame while orientation is expressed in the end-effector frame. We denoted this configuration as ‘mixed frame robotic arms’. Consequently, conventional visual servo controllers which operate in a single frame of reference are incompatible with mixed frame ARAs. Therefore, we propose a mixed-frame visual servo control framework for ARAs. Moreover, we enlightened the task space kinematics of a mixed frame ARAs, which led us to the development of a novel “mixed frame Jacobian matrix”. The proposed framework was validated on a mixed frame JACO-2 7 DoF ARA using an adaptive proportional derivative controller for achieving image-based visual servoing (IBVS), which showed a significant increase of 31% in the convergence rate, outperforming conventional IBVS joint controllers, especially in the outstretched arm positions and near the base frame. Our Results determine the need for the mixed frame controller for deploying visual servo control on modern ARAs, that can inherently cater to the robotic arm’s joint limits, singularities, and self-collision problems.

Estimation and Control of Cooperative Aerial Manipulators for a Payload with an Arbitrary Center-of-Mass.

This paper presents an integrated framework that integrates the kinematic and dynamic parameter estimation of an irregular object with non-uniform mass distribution for cooperative aerial manipulators. Unlike existing approaches, including impedance-based control which requires expensive force/torque sensors or the first-order-momentum-based estimator which is weak to noise, this paper suggests a method without such sensor and strong to noise by exploiting the decentralized dynamics and sliding-mode-momentum observer. First, the kinematic estimator estimates the relative distances of multiple aerial manipulators by using translational and angular velocities between aerial robots. By exploiting the distance estimation, the desired trajectories for each aerial manipulator are set. Second, the dynamic parameter estimation is performed for the mass of the common object and the vector between the end-effector frame and the center of mass of the object. Finally, the proposed framework is validated with simulations using aerial manipulators combined with two degrees-of-freedom robotic arms using a noisy measurement. Throughout the simulation, we can decrease the mass estimation error by 60% compared to the existing first-order momentum-based method. In addition, a comparison study shows that the proposed method satisfactorily estimates an arbitrary center-of-mass of an unknown payload in noisy environments.

A Modern Solution for an Old Calibration Problem

Cameras endow a robot with a sense of vision to see the world. The data acquired from a camera is originally expressed in the camera coordinate system. However, a robot manipulator only accepts the data represented in the robot coordinate system. Under such circumstances, robotic applications that employ cameras necessitate the requirement of converting the camera-acquired data into the robot coordinate system. Since the robot coordinate system is often attached to the base of the robot, the relationship between the camera's and the robot's frames (commonly described by a homogeneous transformation matrix) is composed of two parts: the transformation matrix between the base frame and the end-effector frame of the robot manipulator; and the transformation matrix between the end-effector frame and the camera frame. As the first transformation matrix can be attained from robot kinematics, the problem of representing the camera-acquired data in the robot coordinate system boils down to the estimation of the transformation matrix between the robot's end-effector frame and the camera frame. This estimation problem is widely known as the hand-eye calibration problem since the end-effector and the camera are commonly regarded as the hand and the eye of a robot, respectively. The hand-eye calibration problem plays an important role in robotic applications as it enables the use of cameras in such applications. This problem also emerges in other applications such as visual servoing, 3D scanning systems, and other sensor calibrations.

Impedance Control Architecture for Robotic-Assisted Mold Polishing Based on Human Demonstration

This article presents a computed-torque impedance control architecture for robotic-assisted mold polishing based on human skills.The mold polishing process for plastic injection is critical since tiny surface imperfections are easily visible in the plastic product, having strong implications in the overall quality. A Cartesian impedance control referred to the end-effector frame with posture optimization is proposed to tackle this problem. A collaborative robot manipulator from Franka Emika and a steel mold are used in the experiments to validate our approach. Human skills are captured both in comanipulation and free-hand modes, where position and force patterns are analyzed. Those patterns are then autonomously replicated by the robotic system, validating the proposed methodology.

Combination of geometric and parametric approaches for kinematic identification of an industrial robot

Combination of geometric and parametric approaches of kinematic identification is proposed in this article. The experimental strategy is similar to that used in geometric approach wherein each axis of the robot is actuated one after the other. This adds clarity to experimental strategy, which becomes ambiguous while solely using a conventional parametric approach. Therefore it is easier to conduct experiments even if there are restrictions in workspace. The estimation was done using a parametric technique, but in a stage wise manner using a divide and conquer strategy. This allowed measurement of the robot accuracy after removing the errors arising due to the definition of base and end-effector frames. Additionally it is possible to visualize the reduction in errors during the estimation process. In addition to this, the Jacobian matrix that relates the pose errors to the correction in parameters is adapted during estimation using a damped least squares method depending upon the convergence of the parameters. Results were obtained after extensive experiments on industrial robots using three different measurement instruments namely laser tracker, monocular camera and multi-camera system. The proposed method performs better than the conventional approach which uses only geometric approach. Finally thanks to the new approach, it was possible to conduct experiments after dividing the workspace region into those with high and low levels of observability ; which is not easy while using conventional approaches. It was also possible to perform identification in regions closer and farther away from the robot where there is deterioration of observability. The results show that the proposed method could reduce the errors in pose in a consistent manner, even when different measurement instruments were used, or when there was a deterioration in observability due to the choice of poses during identification. • Combination of geometric and parametric approaches of identification makes it easy and less ambiguous to conduct the experiments even in the presence of restrictions in workspace. • Divide and conquer strategy combined with a damped least squares estimation process with checks on convergence of individual parameters to annul the effect of ill-conditioning of the identification Jacobian. • Possibility of measuring errors in pose at different stages, thus permitting assessment of the positioning accuracy of the robot, and its improvement during the estimation process. Estimation of nominal values defining pose of the base and end-effector coordinate system was used to measure the robot accuracy before identification and after refinement at first stage, such that the accuracy solely due to the robot kinematics could also be measured. • Experimental validation on Fanuc robot was through multiple experiments involving different measurement instruments like monocular camera, multi-camera and laser tracker and results show improvement over geometric approach proposed earlier, irrespective of the measurement region or instrument. Monocular camera could reduce the positioning errors though by a smaller scale compared to other expensive instruments suitable for off-line use. • Possibility of partitioning the robot workspace into different regions on the basis of observability. Experiments in these regions validate that improvement of the positioning accuracy of industrial robot is possible in a consistent manner in all the regions; and while using different measurement instruments.

Kinematic Optimization for the Design of a Collaborative Robot End-Effector for Tele-Echography

Tele-examination based on robotic technologies is a promising solution to solve the current worsening shortage of physicians. Echocardiography is among the examinations that would benefit more from robotic solutions. However, most of the state-of-the-art solutions are based on the development of specific robotic arms, instead of exploiting COTS (commercial-off-the-shelf) arms to reduce costs and make such systems affordable. In this paper, we address this problem by studying the design of an end-effector for tele-echography to be mounted on two popular and low-cost collaborative robots, i.e., the Universal Robot UR5, and the Franka Emika Panda. In the case of the UR5 robot, we investigate the possibility of adding a seventh rotational degree of freedom. The design is obtained by kinematic optimization, in which a manipulability measure is an objective function. The optimization domain includes the position of the patient with regards to the robot base and the pose of the end-effector frame. Constraints include the full coverage of the examination area, the possibility to orient the probe correctly, have the base of the robot far enough from the patient’s head, and a suitable distance from singularities. The results show that adding a degree of freedom improves manipulability by 65% and that adding a custom-designed actuated joint is better than adopting a native seven-degrees-freedom robot.

Camera-Based Method for Identification of the Layout of a Robotic Workcell

In this paper, a new method for the calibration of robotic cell components is presented and demonstrated by identification of an industrial robotic manipulator’s base and end-effector frames in a workplace. It is based on a mathematical approach using a Jacobian matrix. In addition, using the presented method, identification of other kinematic parameters of a robot is possible. The Universal Robot UR3 was later chosen to prove the working principle in both simulations and experiment, with a simple repeatable low-cost solution for such a task—image analysis to detect tag markers. The results showing the accuracy of the system are included and discussed.

Trilateral teleoperation control of kinematically redundant robotic manipulators

Teleoperation control of kinematically redundant robots requires a strategy for resolving their redundancy. A trilateral two-master/one-slave control approach is proposed for delay-free applications in which the first master controls a primary task control frame, e.g. the slave end-effector frame; meanwhile, another master device can manipulate a secondary task frame attached to the slave robot, e.g. to avoid collision with obstacles in the task environment. Any remaining degrees of motion are resolved autonomously. Teleoperation control is achieved in three steps employing joint-space Lyapunov-based adaptive motion/force controllers, a velocity-level redundancy resolution method, and task-space coordinating reference commands. Priority can be given to either the primary or secondary control frame so that the high-priority task can be transparently carried out without interference from the other task. Whenever applicable, the lower-priority task control frame would be restricted to the natural constraints imposed by prioritization or otherwise, decoupling between the tasks is achieved with the use of an arbitrarily weighted pseudo-inverse. Experiments with a planar teleoperation system consisting of two master devices controlling a closed-chain four degree-of-motion redundant slave robot show the feasibility of the approach.

Kinematic and dynamic model-based control of wheeled mobile manipulators: a unified framework for reactive approaches

SUMMARYThe work presented in this paper aims at providing a unified modelling framework for the reactive control of wheeled mobile manipulators (WMM). Where most work in the literature often provides models, sometimes simplified, of a given type of WMM, an extensive description of obtaining explicit kinematic and dynamic models of those systems is given. This modelling framework is particularly well suited for reactive control approaches, which, in the case of mobile manipulation missions, are often necessary to handle the complexity of the tasks to be fulfilled, the dynamic aspect of the extended workspace and the uncertainties on the knowledge of the environment. A flexible reactive framework is thus also provided, allowing the sequencing of operational tasks (in our case, tasks described in the end-effector frame) whose natures are different but also an on-line switching mechanism between constraints that are to be satisfied using the system redundancy. This framework has been successfully implemented in simulation and on a real robot. Some of the obtained results are presented.

A fast workspace-density-driven inverse kinematics method for hyper-redundant manipulators

Hyper-redundant manipulators have a very large number of redundant degrees of freedom. They have been recognized as a means to improve manipulator performance in complex and unstructured environments. However, the high degree of redundancy also poses new challenges when performing inverse kinematics calculations. Prior works have shown that the workspace density (generated by sampling the joint space and evaluating the frequency of occurrence of the resulting end-effector reference frames) is a valuable quantity for use in ${\cal O}(P)$ inverse kinematics algorithms. Here $P$ is the number of modules in a manipulator constructed of a serial cascade of modules. This paper develops a new “divide-and-conquer” method for inverse kinematics using the workspace density. This method does not involve a high-dimensional Jacobian matrix and offers high accuracy. And its computational complexity is only ${\cal O}({\rm log}_2\,P)$, which makes it ideal for very high degree-of-freedom systems. Numerical simulations are performed to demonstrate this new method on a planar example, and a detailed comparison with a breadth-first search method is conducted.

An analysis of the inverse kinematics for a 5-DOF manipulator

This paper proposes an analytical solution for a 5-DOF manipulator to follow a given trajectory while keeping the orientation of one axis in the end-effector frame. The forward kinematics and inverse kinematics for a 5-DOF manipulator are analyzed systematically. The singular problem is discussed after the forward kinematics is provided. For any given reachable position and orientation of the end-effector, the derived inverse kinematics will provide an accurate solution. In other words, there exists no singular problem for the 5-DOF manipulator, which has wide application areas such as welding, spraying, and painting. Experiment results verify the effectiveness of the methods developed in this paper.

Hybrid Motion Control and Planning Strategies for Visual Servoing

This paper presents two hybrid strategies for robot visual servoing. Two specific image constraints, the image singularities and image local minima, are considered in both strategies. The hybrid motion control strategy consists of a local switching control between the image-based and position-based visual servoing for direct avoidance of image singularities and image local minima. The hybrid motion planning strategy consists of an artificial potential field-based global hybrid trajectory planner, where a complete set of Cartesian, image, and robot joint constraints under a complex visual servoing scenario are considered. In this strategy, the image singularities are resolved using the damped-least-square-based joint trajectory planning, while the image local minima are evaluated only along the planned image trajectories and automatically avoided in the image-based trajectory tracking. Two global planning methods are considered. In the first method, the end-effector trajectory is directly planned with respect to the stationary target object frame, which provides a much shorter translational path compared with the local planning method. In the second method, the target trajectory is planned with respect to the current end-effector frame, which minimizes the chances of image trajectories leaving the camera field of view. Simulation and experimental results are given to demonstrate the efficiency of the two hybrid strategies.

User-controlled kinematic modeling

Kinematic modeling of robotic arms is essential for robot control and calibration. The models used usually encompass matrix representation of the geometric behavior of the robot joints. The parameters of kinematic models should be designed such that the spatial relations between the successive joint axes are adequately described. However, most of the models currently available for users either suffer from numerical singularities (both apparent and hidden) or do not possess certain properties required for robot calibration. In the present work, a new kinematic model is proposed, to overcome the drawbacks of the models currently available. The proposed model, which is referred to as the Φ-model. possesses a zero-initial position characteristic in the sense that the various joint displacements can be assigned the value of zero at any desired initial configuration. The Φ-model is also equipped with a parameter-control tool which is presented as a new concept in the field of robot kinematic modeling and is designed such that all possible poses of the end-effector frame can be adequately described to ensure the model completeness.

Relative end-effector control using Cartesian position based visual servoing

This paper presents a complete design methodology for Cartesian position based visual servo control for robots with a single camera mounted at the end-effector. Position based visual servo control requires the explicit calculation of the relative position and orientation (POSE) of the workpiece object with respect to the camera. This is accomplished using image plane measurements of a number of known feature points on the object, and then applying an extended Kalman filter to obtain a recursive solution of the photogrammetric equations, and to properly combine redundant measurements. The control is then designed by specifying the desired trajectories with respect to the object and forming the control error in the end-effector frame. The implementation using a distributed computer architecture is described. An experimental system has been built and used to evaluate the performance of the POSE estimation and the position based visual servo control. Several results for relative trajectory control and target tracking are presented. Results of the experiments showing the effect of loss of some of the redundant features are also presented.

A Fast Algorithm for Inverse Kinematic Analysis of Robot Manipulators

To solve the inverse kinematics problem, we obtain with little effort a reduced and complete set of equations by a conve nient choice of end-effector frame and application of rotation orthogonality. This approach does not require computation of the forward kinematics and can be used with manipulators of any geometry, although it is most efficient when applied to orthogonal manipulators, a class of robot arms defined in this paper. For manipulators requiring numerical techniques, but for which knowledge of one joint variable allows closed- form solutions of the remaining joint variables, an iterative inverse kinematic method, simple and fast enough to be suitable for real-time manipulator control, has been devel oped. The concepts and techniques presented in this paper are illustrated with two examples. The iterative method devel oped here performs a kinematic inversion of a 6-degree-of- freedom manipulator with no closed-form solutions in less than 30 ms using a desktop computer, an order of magnitude faster than times found in the literature.