Unlike parallel robots, for which hundreds of different architectures have been proposed, the vast majority of six-degree-of-freedom (DOF) serial robots have one of two simple architectures. In both architectures, the inverse kinematics can be solved in closed form and the singularities described by trivial geometric and algebraic conditions. These conditions can be readily obtained by analyzing the determinant of the robot’s Jacobian matrix, and provide an in-depth understanding of the robot’s singularities, which is essential for its optimal use. However, for various reasons, robot arms with unorthodox architectures are occasionally designed. Such arms do not have closed-form inverse kinematics and little insight into their singularities can be gained by analyzing the determinant of their Jacobian. One such robot arm for which the conventional singularity analysis approach fails is the new Link 6 collaborative robot by Kinova. In this paper, we study the complex singularities of Link 6 by investigating all possibilities for screw dependencies, deriving a simple equation for each case, and then describing each singularity type using Grassmann line geometry. Twelve different singularity configurations are identified and described with seven relatively simple geometric conditions. Our approach is general and can be applied to other robot arms.

Given that the success of an interaction task depends on the capability of the robot system to handle physical contact with its environment, pure motion control is often insufficient. This is especially true in the context of medical freehand ultrasound where the human body is a deformable surface and an unstructured environment, representing both a safety concern and a challenge for trajectory planning and control. The systematic tuning of practical high degree-of-freedom physical human-robot interaction (pHRI) tasks is not trivial and there are many parameters to be tuned. While traditional tuning is generally performed ad hoc and requires knowledge of the robot and environment dynamics, we propose a simple and effective online tuning framework using differential evolution (DE) to optimize the motion parameters for parallel force/impedance control in a pHRI and medical ultrasound motion application. Through real-world experiments with a KUKA LBR iiwa 7 R800 collaborative robot, the DE framework tuned motion control for optimal and safe trajectories along a human leg phantom. The optimization process was able to successfully reduce the mean absolute error of the motion contact force to 0.537 N through the evolution of eight motion control parameters.

We propose an automated, closed-loop, and local calibration method for serial robots that uses a new, low-cost, 3D measuring device. The device consists of three Mitutoyo digital indicators, arranged in an orthogonal manner, and a mastering fixture based on kinematic coupling. The indicators communicate, via wireless connection, with a PC that controls the movements of the robot. To measure absolute Cartesian coordinates, the device is positioned incrementally over each of several 0.5-inch precision balls until all indicators are at zero, at which time the robot joint encoders are read. The balls are fixed with respect to the robot's base. The precise relative positions of the centers of these balls must be known in advance. In this study, the measuring device is mounted on the flange of an ABB IRB 120 robot. Only three precision balls are used, spaced 300 mm apart, and the distances between these balls are measured with a Renishaw telescoping ballbar. The absolute accuracy of the robot was enhanced by minimizing its position errors, using the least squares method. The feasibility of the calibration approach was demonstrated through a simulation study. Finally, an experimental validation showed that our calibration method caused the maximum position error of the robot, inside a sphere of 400 mm in diameter, to be reduced to 0.491 mm.

This paper presents an elasto-geometrical calibration method for improving the position accuracy of an industrial robot (ABB IRB 1600). Geometric parameter errors and joint stiffness parameters are identified through measuring the position of the robot's end-effector in several robot configurations using a laser tracker. Contrary to previous works, robot's position errors are measured under a wide range of external forces and torques for each robot configuration. A 6-DOF cable-driven parallel robot is employed to automatically apply the desired load on the end-effector of the ABB robot. Before the experiment, an observability analysis is performed in order to improve the robustness of the calibration process with respect to measurement noise and unmodeled errors. Accordingly, an optimal set of robot configurations and external loads is selected for the calibration process. The measured position errors of the ABB robot for this selected set are used to identify the real robot's elasto-geometrical parameters. Finally, the calibration efficiency is evaluated for a number of random combinations of robot configurations and external loads. The experimental results revealed that the proposed elasto-geometrical calibration approach is able to reduce the maximum position error to 0.960 mm, while a customary kinematic calibration can reduce the maximum position error only to 2.571 mm.

This work presents a comparison of the five observability indices used for robot calibration. The comparison is realized in order to determine the most appropriate observability index, which allows for the best parameter identification of a calibrated robot, and therefore leading to the best improvement of the robot accuracy. In this study, the accuracy analysis is based on the robot end-effector errors, which are expressed in term of Euclidean errors. The parameter identification process is based on minimizing the residual of the position errors. The actual values of these positions are usually measured by an external measurement device and have measurement noise. The position residuals are calculated in all the calibration configurations, which are selected by using observability indices. An optimal set of configurations is the one reducing the impact of the measurement noise on the parameter identification efficacy. Our study is carried out for the calibration of four robots: two degrees of freedom (DOF) and 6-DOF serial robots, and 2-DOF and 3-DOF planar parallel robots. The comparison of the observability indices was achieved through a Monte Carlo simulation, using 100 different cases for each of the four robots considered. The position measurement noise was assumed to be within a range of ± 200 μm. Investigations led to conclude that there is a specific index that may be considered the best observability index for robot calibration. Finally, an experimental study has been applied to a LR Mate 200ic FANUC robot and confirms the simulated results.

This paper presents a novel six-legged parallel robot, the kinematic model of which is simpler than that of the simplest six-axis serial robot. The new robot is the 6-DOF extension of the Cartesian parallel robot. It consists of three pairs of base-mounted prismatic actuators, the directions in each pair parallel to one of the axes of a Cartesian coordinate system. In each of the six legs, there are also two passive revolute joints, the axes of which are parallel to the direction of the prismatic joint. Finally, each leg is attached to the mobile platform via a spherical joint. The direct kinematics of the novel parallel robot can be solved easily by partitioning the orientation and the position of the mobile platform. There are eight distinct solutions, which can be found directly by solving a linear system and alternating the signs of three radicals. This parallel robot has a large workspace and is suitable for machining or rapid prototyping, as detailed in this paper.

Hexapods are widely used for precision positioning, but their workspace is too limited for some applications. Often, a rotary stage is added to enlarge the orientation workspace, but this increases the system cost. As an alternative, rotary hexapods have been proposed in which the legs are of fixed length and the base attachment points slide along a common circular path. However, these hexapods have a reduced range of motion in some degrees of freedom due to mechanical interferences. In contrast, we propose a design in which two concentric circular rails are used in addition to double spherical joints, three extra rotary sensors, and two high-accuracy rotary encoders. As a result, the workspace of our robot is significantly increased, its direct kinematics can be solved linearly, and its high accuracy is guaranteed. A prototype has been built and is described in detail.

This paper presents the closed-form solutions to the direct kinematics of three 3-DOF symmetric zero-torsion parallel mechanisms. These mechanisms are composed of three identical legs ending with a spherical joint that is constrained to move in one of three equally spaced planes intersecting at one line. The closed-form solutions are based on the use of a not-well-known intuitive orientation representation. The latter, previously introduced under the name of Tilt-and-Torsion angles, is briefly described. Then, the interdependence between the Cartesian coordinates of the general class of parallel mechanisms is derived. Finally, the direct kinematics of the mechanisms are derived and numerical examples are presented.

This paper presents the singularity analysis of four 3-DOF symmetric zero-torsion parallel mechanisms. These mechanisms are composed of three identical legs ending with a spherical joint that is constrained to move in one of three equally spaced planes intersecting at one line. The computation of the singularity loci is based on the degeneracy of the system of screws applied on the platform by the legs. The whole study is based on the use of a special orientation representation, previously introduced under the name of Tilt-and-Torsion angles. This representation is briefly introduced. Then the interdependence between the Cartesian coordinates of the general class of parallel mechanisms is derived. Finally, the singularity loci are derived and the size of the workspace taking into account all singular configurations is shown.

One of the main drawbacks of parallel robots is their relatively small workspace. Furthermore, this workspace is often segmented by singularities. The most direct approach to making better use of the robot's workspace is to devise control methods for crossing Type 2 singularities. However, near these singularities, the robot precision is very poor and thus the usable workspace remains segmented. In general, parallel robots with multiple working modes (inverse kinematic solutions) have different Type 2 singularity loci for each working mode. Thus, by crossing Type 1 singularities only, these robots can make optimal use of their workspace with simple control strategies. While this idea is not entirely new, this paper is the first to apply it to a 2-DOF planar parallel robot with revolute joints only, in the context of practical implementation.

This paper deals with the in-depth kinematic analysis of a special parallel wrist, called the agile eye. The agile eye is a three-legged spherical parallel robot with revolute joints, in which all pairs of adjacent joint axes are orthogonal. Its most peculiar feature, demonstrated in this paper for the first time, is that its workspace is unlimited and flawed only by six singularity curves (instead of surfaces). These curves correspond to self-motions of the mobile platform and of the legs, or to a lockup configuration. This paper also demonstrates that the four solutions to the direct kinematics of the agile eye (assembly modes) have a simple direct relationship with the eight solutions to the inverse kinematics (working modes)

This paper presents a methodology for the analytical determination and representation of the workspace boundaries of symmetrical spherical parallel mechanisms (SPMs). The methodology is based on an intuitive orientation representation which, while not well known, has proven to be very useful for the analysis of symmetrical parallel mechanisms. The latter, previously introduced as "tilt-and-torsion angles," are briefly described. Then, relatively simple analytical expressions are found for the workspace boundaries of general symmetrical SPMs. Next, using these expressions and a simple numerical procedure, a fast algorithm is proposed for representing the so-called constant-torsion workspace. Finally, several examples are provided

This paper presents the computation and representation of the Type 2 singularity loci of symmetric spherical parallel mechanisms based on a not-well-known intuitive orientation representation. The latter, previously introduced under the name of the Tilt-and-Torsion angles, is briefly described. Then, to illustrate the approach, the two most basic spherical parallel mechanisms are considered and their Type 2 singularities are fully analyzed for various designs.

The concept of constraint singularity is introduced. This is a phenomenon occurring in parallel mechanisms with reduced freedoms when the screw system, formed by the constraint wrenches in all legs, loses rank.