6-DOF Parallel Robot Research Articles

A novel real-time tension distribution method for cable-driven parallel robots

Abstract 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.

A Numerical Approximation Approach for Deriving Computational Efficient Inverse Dynamics of 6-DOF Parallel Robots Based on Principle of Virtual Work

A Numerical Approximation Approach for Deriving Computational Efficient Inverse Dynamics of 6-DOF Parallel Robots Based on Principle of Virtual Work

Dynamic modelling and energy-efficiency optimization in a 3-DOF parallel robot

AbstractEnergy efficiency is a challenging and relevant research field in modern manufacturing industries, where robotic systems play an essential role in the automation of several industrial operations. In this paper, we present an approach for the energy-efficiency optimization of a 3-DOF parallel robot. The proposed strategy leverages the task placement, the execution time, and the length of the robot lower arms to minimize the energy consumption for the execution of a predefined high-speed pick-and-place operation. To evaluate the actuators energy consumption, the kinematic, dynamic and electro-mechanic mathematical models, as well as an equivalent multibody model, of the parallel robot are implemented. The results of extensive numerical simulations show that the proposed strategy provides notable improvements in the energy efficiency of the parallel robot, with respect to alternative approaches. Starting from a pick-and-place task with optimal task placement with a consumption of 38.2 J (with a cycle time of 0.4 s), the energy expenditure can be reduced to 3.75 J (with a cycle time of 1.86 s), with a reduction percentage of 90.2%, by additionally optimizing the execution time, and the length of the robot lower arms. These results lead to a reduction from 5733 J/min (for 150 cycles/min) to 121 J/min (for 32 cycles/min), allowing to choose the best trade-off between robot productivity and consumed energy.

Sensorless admittance control of 6-DoF parallel robot in human-robot collaborative assembly

This paper presents an adaptive admittance control to achieve human-robot collaborative (HRC) assembling of large, heavy components without using external sensors. This sensorless adaptive admittance control is constructed by the dynamic model of a six degree-of-freedom (DoF) parallel robot based on finite and instantaneous screw (FIS) theory. The dynamic model is intuitive and easy to be programmed. After getting stable actuation force by Kalman filter and identifying friction by LuGre model, accurate force estimator is built. Admittance controller is adopted to convert the change of estimated force to the change in position, velocity and acceleration. As a result, the 6-DoF parallel robot is capable of following the guidance of operator. Particularly, adaptive admittance control is design by using robot velocity as reference. A fast motion before contacting and a fine motion during contacting are allowed. Experiments are conducted to verify force estimator, admittance control and adaptive admittance control for HRC assembly. Results show that external force is accurately estimated. Robot complaint control in response to operator's force is achieved. The adaptive admittance control enhances execution time, accuracy of the HRC assembly.

Kinematically redundant (6＋2)-dof HEXA robot for singularity avoidance and workspace augmentation

This paper introduces a novel (6＋2)-degree-of-freedom (dof) kinematically redundant parallel robot. The proposed architecture is based on the 6-dof HEXA parallel robot. The paper applies methodologies for avoiding type II singularities using kinematic redundancy that were originally proposed for robots with prismatic actuators to a new architecture with revolute actuators. The singularities of the HEXA robot are first examined based on previous work, and new instances of singularities are discovered. The singularity locus in the orientational workspace is identified using the Power Inspired Measure. Then, a novel kinematically redundant leg architecture is proposed to allow for the avoidance of these type II singularities. It is shown that the singularities present within the orientational workspace can successfully be avoided if two kinematically redundant legs are included in the robot architecture. The performance of the new architecture is then examined in various trajectories within the orientational workspace. Results show that the attainable orientational workspace is significantly increased with the proposed architecture.

Novel and Robust Forward Kinematic Algorithm for Real-Time Control of General Six-Degree-of-Freedom Parallel Robot for Tele-Manipulation and Tele-Navigation

Abstract The forward kinematics (FK) of a 6-6 universal-prismatic-spherical (UPS) structure of a parallel robot is highly nonlinear, coupled, and has a one-to-many nature of mapping. There exists no close form solution to a forward kinematic problem (FKP), and real-time kinematic control is extremely difficult. This paper presents the implementation of time efficient and robust solution for FKP using a trajectory modifier algorithm along with a Newton Raphson (NR) method. One micrometer in translation and 0.001 deg in orientation accuracy with an average pose computation time of 2.3 ms are achieved. The novel algorithm is elaborated and the detailed performance parameters are tabulated. The paper presents trajectory following experiments to show robust, real-time FK solution and efficient kinematic control on both standalone and master–slave modes to be used for robot-assisted neurosurgery. The neuro-registration using the FK solutions in real time in a tele-manipulation mode is demonstrated.

Kinematic Calibration for the 3-UPS/S Shipborne Stabilized Platform Based on Transfer Learning

The three-degrees-of-freedom (3-DOF) parallel robot is commonly employed as a shipborne stabilized platform for real-time compensation of ship disturbances. Pose accuracy is one of its most critical performance indicators. Currently, neural networks have been applied to the kinematic calibration of stabilized platforms to compensate for pose errors and enhance motion accuracy. However, collecting a large amount of measured configuration data for robots entails high costs and time, which restricts the widespread use of neural networks. In this study, a “transfer network” is established by combining fine-tuning with a Back Propagation (BP) neural network. This network takes the motion transmission characteristics inherent in the ideal kinematic model as prior knowledge and transfers them to a network trained based on the actual poses. Compared with the conventional BP neural network trained by actual poses alone, the transfer network shows significant performance advantages, effectively solving the problems of low prediction accuracy and weak generalization ability in the case of small-sample measured data. Considering this, the impact pattern of the sample number of the actual pose on the effectiveness of transfer learning is revealed through the construction of multiple transfer network models under varying sample numbers of the actual pose, providing valuable marine engineering guidance. Finally, simulated sea-service experiments were conducted on the 3-UPS/S shipborne stabilized platform to validate the correctness and superiority of the proposed method.

Development of a 6-DOF Parallel Robot for Potential Single-Incision Laparoscopic Surgery Application

This paper presents the development of a 6-DOF (Degrees of Freedom) parallel robot for single-incision laparoscopic surgery (SILS). The concept of the robotic system is developed with respect to a medical protocol designed by the medical experts in the team targeting a SILS procedure in urology. The kinematic model of the robotic system was defined to determine the singularities that may occur during functioning. FEM analyses were performed to determine the components of the robotic structure that may compromise the rigidity of the robotic system, and these components were redesigned and integrated into the final design of the robot. To verify the kinematic model a series of numerical and graphical simulations were performed, while to test the functionality of the robotic system, a low-cost experimental model was developed. The accuracy of the experimental model was measured using an optical motion tracking system.

Research on Active Disturbance Rejection Algorithm for Loading Control of 3-DOF Parallel Robot

A three-dimensional (3D) loading device based on a pneumatic 3-universal-prismatic-universal (UPU) parallel manipulator (three chains with UPU joint each) is designed to apply time-varying multi-dimensional loads to a target. First, according to the principle of vector superposition and Newton–Raphson method, the inverse and forward kinematics of the loading device are analyzed. Second, based on the screw theory, the static mapping between the dynamic platform and actuations is derived. Third, a second-order mathematical model is established for pneumatic 3-UPU parallel mechanism based on proportional flow valve and a metal seal pneumatic cylinder. A referential inaccurate model is provided for the control algorithm during modeling. Fourth, based on active disturbance rejection control (ADRC) technique, a 3D loading control algorithm is proposed and dynamic loading control is realized. Experimental results show that the ADRC algorithm has good robustness against disturbances, the steady-state control accuracy is less than 2 N, and the mean square error in dynamic tracking (sinusoidal tracking at 0.2 Hz) is less than 10.5 N.

A backdrivable 6-dof parallel robot for sensorless dynamically interactive tasks

In order to combine low mechanical impedance and sufficient interaction forces, a six-degree-of-freedom robot featuring a mechanically backdrivable transmission with a low reduction ratio is proposed in this paper. Also, a parallel architecture is used in order to allow the use of relatively large and high-torque actuators. The architecture of the robot is first presented. Then, the geometry of the robot and the ratio of the transmissions are analysed in order to ensure that the selected design parameters yield the desired properties. Shock absorbers are also included in the legs of the robot so that impacts can be applied, e.g., for the assembly of some components. Then, algorithms are presented for Cartesian stiffness control and gravity compensation of the robot. Finally, a prototype is presented and validated experimentally for position control, impedance control and impact generation. The parallel robot presented in this paper is of particular interest for industrial assembly tasks.

Synchronous Sliding Mode Control for a 4-DOF Parallel Manipulator in Practice

This paper proposes a synchronous sliding mode control (SSMC) method for a 4-DOF parallel robot model in practice with the influence of uncertain dynamics such as friction, external noise, and model error. A closed kinematic chain structure characterizes the parallel robot. The moving platform is controlled by four kinematic chains working together to follow a predetermined trajectory. However, traditional control methods only control each joint individually; if one of the actuators fails or has an external force, it can lead to system breakdown. Therefore, synchronous control to coordinate the operation of the arms is necessary. The synchronization algorithm is characterized by the cross-coupling error, which is the combination of tracking and synchronization errors for the system to achieve the synchronization goal. Cross-coupling error is used to design the sliding surface of the SSMC. The advantages of sliding mode control (SMC) are that it resists the influence of uncertain dynamics and it is combined with the synchronization algorithm. A control law is developed based on the sliding surface to ensure simultaneous convergence of both tracking and synchronization errors towards zero. The stability of the system is proven using the Lyapunov theory. In order to verify the effectiveness of the proposed approach, a 4-DOF parallel robot testbench is constructed. The SSMC controller results are compared with the testbench’s proportional-integral-derivative (PID), synchronous proportional-integral-derivative (SPID), and SMC controllers.

Synchronous PD Control Using a Time Delay Estimator for a Four-Degree-of-Freedom Parallel Robot in Practice

This paper presents a synchronous proportional derivative (PD) control method using a time delay estimator (SPD-TDE) for a four-degree-of-freedom (DOF) parallel robot in practice. The proposed control is a method that is developed from a synchronous PD control method combined with a time delay estimator to guarantee the tracking objectives and synchronous requirements of the robot. Firstly, the synchronous PD control method is designed by defining cross-coupling errors. A cross-coupling error is determined by incorporating the tracking error and deviation of tracking error among two adjacent joints or synchronous errors. Then, the asynchronous problem between the kinematic chains is solved and guarantees that the goal of synchronicity is achieved. Consequently, to improve the tracking performance of the robot, a time delay estimator is used to estimate and eliminate the uncertainty components of the system, such as modeling errors and actuator faults. In addition, the Lyapunov theory is also used to demonstrate the stability and robustness of the proposed control method. Finally, a testbench 4-DOF parallel robot is built, and the controllers are embedded in the control board from MATLAB Simulink using the Waijung block set library to operate the robot preset trajectory tracking. The experimental results of the proposed control method for the 4-DOF parallel robot are compared with those obtained using other controllers to prove its effectiveness.

Imitation Learning-Based System for the Execution of Self-Paced Robotic-Assisted Passive Rehabilitation Exercises

The development of robotic-assisted rehabilitation exercises involving physical human-robot interaction requires extreme care since an injured limb may be in physical contact with the robot, so compliant behavior is imperative for these tasks. Typical approaches involve force control schemes like admittance controllers that allow humans to adapt the motion. However, when the patient's limb has limited mobility or is potentially injured, unintentional forces may occur during the robot's trajectory that could be incompatible with these controllers. This paper addresses a new way of generating compliant trajectories for passive rehabilitation exercises, considering that previous positions of the trajectory are attainable for the patient, so reversing the trajectory is a safe operation. Since there is no clear way to optimize such a goal due to the physiological variability among patients, the condition of reversal is based on imitation learning by taking the analogous healthy limb of the patient as a reference and encoding the forces using Gaussian Mixture Regression, and reversibility is accomplished by means of Reversible Dynamic Movement Primitives. The system allows for self-paced rehabilitation exercises by back-and-forth movements along the trajectory according to the patient's reaction, and it has been successfully applied to a 4-DOF parallel robot for lower-limb rehabilitation.

Model-Based Control of a 4-DOF Rehabilitation Parallel Robot with Online Identification of the Gravitational Term.

Parallel robots are being increasingly used as a fundamental component of lower-limb rehabilitation systems. During rehabilitation therapies, the parallel robot must interact with the patient, which raises several challenges to the control system: (1) The weight supported by the robot can vary from patient to patient, and even for the same patient, making standard model-based controllers unsuitable for those tasks since they rely on constant dynamic models and parameters. (2) The identification techniques usually consider the estimation of all dynamic parameters, bringing about challenges concerning robustness and complexity. This paper proposes the design and experimental validation of a model-based controller comprising a proportional-derivative controller with gravity compensation applied to a 4-DOF parallel robot for knee rehabilitation, where the gravitational forces are expressed in terms of relevant dynamic parameters. The identification of such parameters is possible by means of least squares methods. The proposed controller has been experimentally validated, holding the error stable following significant payload changes in terms of the weight of the patient's leg. This novel controller allows us to perform both identification and control simultaneously and is easy to tune. Moreover, its parameters have an intuitive interpretation, contrary to a conventional adaptive controller. The performance of a conventional adaptive controller and the proposed one are compared experimentally.

A Pose Resolution Analysis Method for a Stewart Parallel Robot

In order to develop a high-resolution 6-DOF parallel robot, a method for analysing parallel robot’s position and orientation resolution is proposed, which is based on the same scale scaling and quantifying of struts increment. Firstly, calculating struts increment of the target position and orientation. Secondly, reducing struts increment in the same proportion. Thirdly, quantifying them with the resolution of the strut, and the minimum struts increment and struts length are obtained. Lastly, six single DOF minimum motion increments, namely pose resolution, are obtained after forward kinematic solution. The analysis software is compiled with VC++, and the 6-DOF Stewart parallel robot for the secondary mirror of a high-resolution space camera is designed. The measured results show that the analysis results of pose resolution are basically consistent with the measured values, and the analysis method has strong engineering guiding value.

Experimental Evaluation of a 3-Armed 6-DOF Parallel Robot for Femur Fracture Surgery

This paper presents the experimental position and force testing of a 3-armed 6-DOF Parallel Robot, Robossis, that is specifically designed for the application of long-bone femur fracture surgery. Current surgical techniques require a significant amount of time and effort to restore the fractured femur fragments’ length, alignment and rotation. To address these issues, the Robossis system will facilitate the femur fracture surgical procedure and oppose the large traction forces/torques of the muscle groups surrounding the femur. As such, Robossis would subsequently improve patient outcomes by eliminating intraoperative injuries, reducing radiation exposure from X-rays during surgery and decreasing the likelihood of follow-up operations. Specifically, in this paper, we study the accuracy of the Robossis system while moving in the operational workspace under free and simulated traction loads of ([Formula: see text]–1100[Formula: see text]N). Experimental testing in this study demonstrates that Robossis can reach the most extreme points in the workspace, as defined by the theoretical workspace, while maintaining minimal deviation from those points with an average deviation of 0.324[Formula: see text]mm. Furthermore, the force testing experiment shows that Robossis can counteract loads that are clinically relevant to restoring the fractured femur fragments’ length, alignment and rotation. In addition, we study the accuracy of Robossis motion while coupled with the master controller Sigma 7. The results show that Robossis can follow the desired trajectory in real-time with an average error of less than 1[Formula: see text]mm. To conclude, these results further establish the ability of the Robossis system to facilitate the femur fracture surgical procedure and eliminate limitations faced with the current surgical techniques.

Quantitative analysis of decoupling and spatial isotropy of a generalised rotation-symmetric 6-DOF Stewart platform

The Stewart platform is one of the most frequently studied six-degree-of-freedom (6-DOF) parallel robots. Although it has an uncomplicated architecture, it still poses some remaining research challenges, especially regarding Cartesian stiffness, decoupling, and isotropy. Although it is well established that spatial isotropy is only dependent on the direction vectors of the six links, the diagonal values in the stiffness matrix, and in particular the relationship between the first three elements and the last three elements, are affected by other factors. The methodology proposed in this paper aims at designing decoupled and spatially isotropic Stewart platforms with user-selected values of these diagonal elements. A parametric model of a generalised rotation-symmetric Stewart platform is established and the expression of the corresponding Cartesian stiffness matrix is derived. The approach in this paper is first to find the different cases when the expressions of off-diagonal elements of the Cartesian stiffness matrix are zero and then, within each case, quantitatively derive conditions for decoupling and spatial isotropy. By applying this approach, several novel decoupled and spatially isotropic architectures with three horizontal links were derived.

Evaluation and prediction method of robot pose repeatability based on statistical distance

Pose repeatability is one of the most important performance specifications of robots, and its evaluation and prediction methods are of great significance to give full play to the precision characteristics of robot. In this paper, a pose repeatability evaluation method based on statistical distance and spatial probability ellipsoid is proposed, which can accurately and effectively describe the coupling effect between repeatability of various dimensionalities. On this basis, a prediction model of pose repeatability based on equivalent system is proposed. In this model, the pose repeatability of the end-effector is considered to be generated only by the equivalent repeatability of the actuated joint, and the latter is described as a function of the ideal actuated joint variables, which can accurately describe the variation of the pose repeatability caused by the uncertainties of the robot system in the whole workspace. Simulation and experimental study on a 6-DOF parallel robot are carried out to illustrate the effectiveness of the proposed approach.

Object-oriented modeling, simulation and control of a 6-DoF parallel kinematic manipulator for remote handling in DONES facility

This paper describes the modeling and simulation activities performed, within the EUROfusion framework, to support the engineering design and the development of the control system of the DONES Parallel Kinematic Manipulator (PKM), a 6-DoF parallel robot part of the Remote Handling System of the DONES facility. The main tasks of the PKM are the planned annual replacement of the Target Assembly and the High Flux Test Module, two of the crucial and most activated components of DONES. The PKM model, developed using the Modelica object-oriented language, is able to simulate the dynamics of the entire robots, including the main non-linear effects due to backlashes and static friction. The simulator is employed to support the preliminary design of the control system, based on an independent-joint approach with dual-loop cascade-PID logic. Simulations are then conducted to assess robot performances in terms of resolution, accuracy, repeatability and generated forces.

A 4-DoF Parallel Robot With a Built-in Gripper for Waste Sorting

This article presents a new robot concept dedicated to fast and energy-efficient waste sorting applications. This parallel robot can provide at the same time the three translations in space (3-DoF) and the opening/closing of a built-in gripper (1 additional DoF). The movement of the clamp is enabled thanks to a configurable platform at the end of the parallel structure. This platform is composed of a two-gear train gripper which is directly controlled by the 4 actuators attached to the base of the manipulator. The inverse kinematic as well as the differential models have been developed. A first prototype has been realized to validate this new parallel architecture for pick-and-toss tasks.