The tension distribution problem of cable-driven parallel robots is inevitable in real-time control. Currently, iterative algorithms or geometric algorithms are commonly used to solve this problem. Iterative algorithms are difficult to improve in real-time performance, and the tension obtained by geometric algorithms may not be continuous. In this paper, a novel tension distribution method for four-cable, 3-DOF cable-driven parallel robots is proposed based on the wave equation. The tension calculated by this method is continuous and differentiable, without the need for iterative computation or geometric centroid calculations, thus exhibiting good real-time performance. Furthermore, the feasibility and rationality of this algorithm are theoretically proven. Finally, the real-time performance and continuity of cable tension are analyzed through a specific numerical example.

This paper presents a robust adaptive controller based on the backstepping technique using an extended state observer (ESO), implemented on a 2PUS+RR parallel robot, to minimize the trajectory tracking error. The proposed backstepping-ESO controller scheme is designed to compensate for the robot’s structured (parametric) and unstructured (nonlinear friction, external disturbances, and dynamics) uncertainties. The overall stability of the controller is guaranteed by the Lyapunov theory. Cosimulation in MATLAB-Simulink and ADAMS View is presented to validate the results of the ESO and backstepping controller implemented in the virtual and physical prototype. For the virtual prototype, it was determined that the system is stable in 2 s and presents a maximum absolute error of 3.5 × $10^{-6}$ m for the actuator position and 2.8 × $10^{-5}$ rad for mobile platform orientation. Regarding the physical robot, a maximum absolute error of 5 × $10^{-4}$ m for the actuator position and 0.0575 rad for the orientation of the robot mobile platform values do not represent a problem for ankle rehabilitation movements. Experimental results were also presented and compared with ankle motion to demonstrate that the applied control system meets the motion requirements of the ankle rehabilitator.

In this paper, a new hybrid fault-tolerant control (FTC) strategy based on nonsingular fast integral-type terminal sliding mode (NFITSM) and time delay estimation (TDE) is proposed for a Schönflies parallel manipulator. In order to detect, isolate, and accommodate actuator faults, TDE is used as an online fault estimation algorithm. Stability analysis of the closed-loop system is performed using Lyapunov theory. The proposed controller performance is compared with conventional sliding mode and feedback linearization control methods. The obtained results reveal the superiority of the proposed FTC based on TDE and NFITSM.

The docking simulators are significant ground test equipment for aerospace projects. The fidelity of docking simulation highly depends on the accuracy performance. This paper investigates the kinematic accuracy for the developed docking simulator. A novel kinematic calibration method which can reduce the number of parameters for error modeling is presented. The principle of parameters separation is studied. A simplified error model is derived based on Taylor series. This method can contribute to the simplification of the error model, fewer measurements, and easier convergence during the parameters identification. The calibration experiment validates this method for further accuracy enhancement.

This paper investigates a comparative kinematic analysis between nonredundant and redundant 2-Degree Of Freedom parallel manipulators. The nonredundant manipulator is based on the Five-Bar mechanism, and the redundant one is a 3-RRR planar parallel manipulator. This study is aimed to select the best structure for a haptic application. This latter requires a mechanism with a desired workspace of 10 cm × 10 cm and an admissible force of 5 N in all directions. The analysis criteria are the accuracy of the forward kinematic model and the required actuator torques. Thereby, the geometric parameters of the two structures are optimized in order to satisfy the required workspace such that parallel singularities are overcome. The analysis showed that the nonredundant optimally designed manipulator is more suitable for the haptic application.

This paper aims to provide an optimal design of geometric parameters of a special architecture of the delta parallel mechanism, in order to improve positioning accuracy, workspace size, and kinematic and dynamic performance characteristics. In the studied 3[P2(US)] robot, the radius of both fixed and moving platforms, length of the connecting rods, and installation angle of the actuators of the manipulator are chosen as the decision variables. These parameters are optimized to maximize the weighted objective function, comprising workspace volume, global dexterity, global mass, global error, and global error sensitivity indices. Optimizations are performed employing two distinct algorithms, Genetic and Harmony Search whose results confirm each other. The optimal design of the robot leads to maximum workspace size, high dexterity, and dynamic performance, with a minimum error of the end-effector position in its reachable workspace.

In this paper, a type of parallel robot with three translational degrees of freedom is studied. Inverse and forward kinematic equations are extracted for position and velocity analyses. The dynamic model is derived by Lagrange’s approach and the principle of virtual work and related computational algorithms implementing inverse and forward dynamics are presented. Furthermore, some numerical simulations are performed using the kinematic and dynamic models in which the results show good agreement with expected qualitative behavior of the mechanism. Comparisons with the results of work-energy and impulse-momentum methods quantitatively verify the validity of the derived equations of motion. Also, a relative computational effectiveness is observed in implementation of virtual work model via the simulations.

This paper presents a concept of sequentially actuated multi-degree-of-freedom (DOF) robot with only one motor. A switching mechanism allowing to actuate sequentially the different joints–or combinations of the joints–of the robot is also proposed. Potential actuation schemes (joint combinations) are presented and their properties are discussed. Cartesian pick-and-place trajectories are then considered using different actuation schemes. An optimisation algorithm is presented in order to provide the best possible sequence by minimising the amplitude of the joint rotations for a given actuation combination. A simple planar two-DOF and the SCARA architectures are used to illustrate the concept. Finally, a prototype is developed with the aim of demonstrating the sequentially actuated manipulator concept.

The DELTA parallel robot, designed by an EPFL (Ecole Polytechnique Fédérale de Lausanne) research team, is a mechanical structure which has the advantage of parallel robots and ease of serial robots modeling. This paper presents solutions for a complete modeling of the DELTA parallel robot (direct and inverse kinematics, inverse statics, inverse dynamics), with few arithmetic and trigonometric operations. Our method is based on a satisfactory choice of kinematic parameters and on a few restricting hypotheses for the static and dynamic models. We give some details of each model, we present some computation results and we put the emphasis on some particular points, showing the capabilities of this mechanical structure.

This paper presents a novel deformable mobile robot with five degrees of freedom (DOFs). The robot contains two equivalent expandable triangular platforms connected by three equivalent chains. Each platform is a regular triangle with a single DOF. Each chain consists of two links and three joints (one spherical joint at the middle of a chain, and one revolute joint at each end of the chain). Through kinematic and locomotion mode analysis, the robot exhibits three motion modes: worm-like, self-crossing, and rolling modes. The worm-like and self-crossing modes can be used for narrow passages (e.g., pipelines, holes, and caves). The rolling mode has three different directions at the initial state. By switching between these, the robot can operate on rough ground. To verify the locomotion modes and functionality of the robot, the results of a series of experiments performed on a manufactured prototype are reported.

In this paper, a fast and efficient evolutional algorithm, called the G3-PCX has been implemented to solve the forward kinematics problem (FKP) of the general parallel manipulators being modeled by the 6-6 hexapod, constituted by a fixed and mobile platforms being non planar and non-symmetrical. The two platforms are connected by six linear actuators, each of which is located between one ball joint and one universal joint. Forward kinematics are formulated using Inverse Kinematics applying one position based equation system which is converted into an objective function by expressing the sum of squared error on kinematics chain lengths and mobile platform distances. In less than one second, the 16 unique real solutions are computed with improved accuracy when compared to previous methods.

In this research work, the maximum Cartesian workspace of a Tricept parallel robot with two rotational and one translational degrees of freedom was investigated. Generally, the Cartesian workspace identifies the maximum size of a work-piece, specifying its cubic x, y and z dimensions, on which the milling machine could perform operations. However, the workspace of a robot can be considered in its task space, such as ψ × θ × z for the Tricept Parallel Kinematic Mechanism (PKM). A novel homogeneous Jacobian matrix which transforms joint space velocity vector into end-effector Cartesian velocity vector has been generated named as a Cartesian Jacobian matrix. Using the indices derived from the homogeneous Cartesian Jacobian matrix, i.e. the maximum singular values and local conditioning indices, the manipulator is designed to reach the Cartesian workspace with rapid positioning rates as well as with singularity avoidance.

Performance evaluation of a parallel robot is a multicriteria problem. By taking Delta robot as an object of study, this paper presents the kinematic performance evaluation of a three translational degrees-of-freedom parallel robot from the viewpoint of singularity, isotropy, and velocity transmission. It is shown that the determinant of a Jacobian matrix cannot measure the distance from the singular configuration due to the existing inverse kinematic singularity of a Delta robot. The determinants of inverse and direct kinematic Jacobian matrices are adopted for the measurement of distance from the singular configuration based on the theory of numerical linear dependence. The denominator of the Jacobian matrix will be lost in the computation of the condition number when the end-effector is on the centerline of the workspace, so the Delta robot may also be nearly at a singular configuration when the condition number of the Jacobian matrix is equal to 1. The velocity transmission index whose physical meaning is the maximum input angular velocity when the end-effector translates in the unit velocity is presented. The evaluation of singularity, isotropy, and velocity transmission of a Delta robot is investigated by simulation. The velocity transmission index can also be used for the velocity transmission evaluation of a parallel robot with pure rotational degrees-of-freedom based on the principle of similarity. The physical meaning is modified to be the maximum input velocity when the end-effector rotates in the unit angular velocity.

This paper presents an adaptive force/position controller for a parallel robot executing constrained motions. This controller, based on an MLPNN (or Multi-Layer Perceptron Neural Network), does not require the inverse dynamic model of the robot to derive the control law. A neural identification of the dynamic model of the robot is proposed to determine the principal components of the MLPNN input vector. The latter is used to compensate the dynamic effects arising from the robot–environment interaction and its parameters are adjusted according to an adaptation law based on the Lyapunov-analysis methodology. The proposed controller is evaluated experimentally on the C5 parallel robot. This method is capable of tracking accurately the force/position trajectories and its stability robustness is proved.

This paper deals with dynamic dimensional synthesis of the Delta robot using the pressure/transmission angle constraints. Two types of pressure/transmission angles are defined, with which the direct and indirect singularities can be identified in a straightforward manner. Two novel global dynamic metrics are proposed for minimisation, which are associated respectively with the inertial and centrifuge/Coriolis components of the driving torque. Various geometrical and performance constraints are taken into account in terms of workspace/machine volume ratio, pressure/transmission angles, etc. The effects of pressure/transmission angle constraints on the feasible domain of design variables are investigated in depth via an example, and a set of optimised dimensional parameters is obtained for achieving a good kinematic and dynamic performance throughout the entire task workspace.

This paper presents the teleoperation of a parallel robot based on the Stewart–Gough platform. The robot is an experimental prototype capable of sliding along electrical lines in order to carry out different inspection and maintenance tasks. The paper also describes the kinematic equations of the parallel robot and their solution. The teleoperation of the prototype took place in a testing bank developed in the laboratory and containing the basic elements of electrical lines. The operator who performs the task uses a six degrees-of-freedom master-arm with force reflection, which also has an image-viewing system providing the operator with stereoscopic vision and allowing him/her to calibrate the information of the local station simulator with the real environment through the blending of images. The paper also presents the results of the laboratory experiments of the robot sliding along a line.

L’obtention de pièces structurales en fonderie sable aluminium de haute techniciténécessite un processus de parachèvement conséquent comprenant la découpe du système decoulée, suivie d’un ponçage quasi global des surfaces. Les exigences industrielles entermes de sécurité et de rentabilité remettent fortement en cause la réalisation manuellede ces opérations. Cet article présente le développement d’une nouvelle cellule robotiséepour ce parachèvement, mené en collaboration avec La Société des Fonderies d’Ussel (SFU)du groupe ALCAN. La première partie est consacrée à la caractérisation des contraintesliées aux spécifications fonctionnelles attendues sur la pièce et aux procédés d’usinageet de ponçage. Ceci a abouti à la définition d’une cellule redondante 8 axes pour répondreau critère d’espace de travail et intégrant un robot à structure hybride (Tricept) pourses capacités à réaliser les opérations d’usinage en conditions UGV et de ponçage. Ladeuxième partie porte sur la définition de critères pour une gestion optimisée desredondances en vue d’améliorer le comportement global de la cellule et répondre auxexigences de précision et de capacité cinématique. La dernière partie présentel’optimisation mise en œuvre et les résultats validés sur un ensemble de pièces.

This paper deals with the design, implementation, and performance evaluation of a new type of 4-DOF parallel mechanism providing three translations and one rotation for high-speed handling and machining. This parallel mechanism is named H4. A necessary condition and system configuration of the H4 are also described. Hardware and kinematics of the H4 is addressed and the manipulability ellipsoid which is one of the widely used methods to examine the design of parallel mechanisms is addressed. The performance evaluation is carried out to demonstrate the H4 robot. The simulation and experimental results show that three different controllers, the PD, PD + velocity feed-forward, and dynamic compensation controller, dramatically improve the trajectory tracking accuracy.

This paper presents a particular architecture of a parallel robot which is characterized by a diagonal stiffness matrix. This result suggests the use of a parallel robot in the final phase of insertion as a passive compliance device. The stiffness rate of this device is controlled by the gain of the feedback loop. As the correction of small angular misalignments due to contact forces do not generate lateral errors and vice versa, we have the equivalent of an isoelastic swivel.

This paper presents at first a static and kinematic analysis of closed chains mechanisms which permits to deduce different possible fully parallel architectures. Then we focus on a particular parallel architecture with C5 links designed to perform precise assembly tasks. A general modeling of this C5 parallel robot is presented. Two typical assembly tasks in the automotive industry are also proposed; the first one uses the C5 links parallel robot as a left-hand device, while the second one uses it as the terminal tool of a sequential manipulator.