Parallel Robot System Research Articles

Precision Sensitivity Optimization for Parallel Robotic System Based on Multi-Source Preventive Maintenance

This paper presents a multi-source preventive maintenance (MPM) based precision sensitivity optimization method for parallel robotic systems. Taking a parallel mechanism as an example, the input error can be divided into finite mutually independent uncertain error sources, and the probabilistic error model is established by the Monte Carlo stochastic method. Considering that several times of maintenance can lead to an increase of the accuracy degradation factor, a generalized hierarchy maintenance yield model is established, where the cost of preventive maintenance and failure replacement maintenance are distinguished between the independent error source and the overall error source. The nonlinear relationship between the maintenance yield per unit cost and influencing factors, including the error threshold and the maintenance times is obtained, which allows to develop an optimal maintenance strategy. Preventive maintenance is introduced to avoid unintended failure of the mechanism while extending the lifetime. The high-precision parallel mechanism has demonstrated promising applications in medical, industrial and other fields, and its economic benefits can be effectively improved by incorporating the MPM method. The experiment of manufacturing human lung models using a parallel 3D printing device demonstrates that the MPM method can improve the long-term precision and reliability of the parallel device, and the optimized human lung contour tracking precision can be improved by up to 55.56%.

Modeling and analysis of a parallel robotic system for lower limb rehabilitation with predefined operational workspace

The paper presents the mathematical modeling and analysis of LegUp, a novel parallel robotic system for lower limb rehabilitation of bedridden patients. The operational workspace of the robotic system is defined based on a set of parameters that describe the motion of the lower limb joints, which is natural in the rehabilitation task. To comply with this representation of the operational workspace, the parallel robot kinematic models describe the dependency between the robotic system actuators and the lower limb joints. Furthermore, the singularity analysis is achieved in the joint space, which shows whether the operational workspace is singularity-free. To achieve a feasible mechanical design for the prescribed operational workspace and to ensure safe operation, the design parameters of the parallel robotic system are determined based on a multi-objective optimization problem. Numerical simulations show that the operational workspace is singularity-free for the selected design parameters, which are then used to construct the experimental model of LegUp.

ROMI: Design and Experimental Evaluation of a Linear Delta Robotic System for High-Precision Applications

In this paper, the design and experimental evaluation of a parallel robotic system based on a linear delta geometry is presented. The design considers the requirements for high-precision applications including workspace, motion resolution, and payload. The entire design process includes robot kinematics, control, and optimization, resulting in the demonstration of a working device. The robot structure offers a versatile and simplified design when compared with state-of-the-art devices being able to be adapted to perform different tasks while keeping the advantages of high precision with reduced complexity. The presented robot prototype was constructed and evaluated experimentally through three proof-of-concept experiments mimicking tasks requiring high motion precision such as microsurgery, semiconductor testing, and optical device alignment. The obtained results in the three experimental scenarios validate that the here-proposed design can achieve an average motion precision of ~3.3 ± 0.3 μm with varying load conditions, thus confirming its potential to be used for high-precision tasks in industrial and medical settings.

On the Problem of Tension Forces Distribution in Cable System of Cable-Driven Parallel Robot

The paper proposes a method for controlling tension forces in statically indeterminable cable-driven systems based on the non-negative least squares method with control of singular or near-singular solutions and a complete search of all possible cable configurations. For cable-driven parallel robots the problem of controlling the cable tension forces is critical, because in the absence of control the cable tension forces are distributed unevenly, which leads to reduced robustness of the system, increased energy consumption and increased deterioration. And in special cases of cable system configuration the tension forces become so great that they lead to cable breaks. At the same time, correction of cable tension force distribution should not lead to significant deviations from the specified position of the mobile platform or, formulating the problem in terms of forces, to violation of kinetostatic equations. Thus, the problem of controlling the tension forces in the cable parallel robot system is solved as a problem of optimizing the tension forces of the cables according to the criteria of minimizing the norm of their vector in the configuration space and minimizing the norm of incoherence of the vector of forces and moments in the operational space of the robot. The developed algorithm is based on the solution of underdetermined systems of linear algebraic equations with finding the minimum least squares norms and subsequent zeroing of negative components of the solution vector. The paper considers examples of the solution of the set problem for the lower cable group of a construction 3D printer based on a cable-driven robot and for a 12-cable system

Kinematic Modeling of a Trepanation Surgical Robot System

This paper presents the concept of a parallel medical robotic service system to assist in a surgical procedure involving precise exploratory trepanation holes in a patient’s skull. The target position and orientation of the trepanation tool in the cranial region is determined using a prior intracranial image analysis using an external medical imaging system. A trepanning actuation system is attached to the end-effector of the parallel robot. The end-effector will act as an accurate positioner for the trepanning drill in the medical intervention area. The conceptual design of the mechanical actuation subsystem of a trepanning robot was developed in the SolidWorks 2022 software environment. The virtual model of the kinematic chain of the robot and the assumed design parameters were used to analytically derive the equations describing the inverse kinematics task. An analysis of the forward kinematics task of the parallel manipulator was also carried out using analytical and numerical methods. A workspace analysis was performed using Matlab based on the kinematic model of the parallel robot. This paper significantly advances the field by presenting the conceptual design of the actuation subsystem, deriving the kinematics equations, conducting a thorough workspace analysis, and establishing a foundation for subsequent control-algorithm development.

An Application of Modified T2FHC Algorithm in Two-Link Robot Controller

Parallel robotic systems have shown their advantages over the traditional serial robots such as high payload capacity, high speed, and high precision. Their applications are widespread from transportation to manufacturing fields. Therefore, most of the recent studies in parallel robots focus on finding the best method to improve the system accuracy. Enhancing this metric, however, is still the biggest challenge in controlling a parallel robot owing to the complex mathematical model of the system. In this paper, we present a novel solution to this problem with a Type 2 Fuzzy Coherent Controller Network (T2FHC), which is composed of a Type 2 Cerebellar Model Coupling Controller (CMAC) with its fast convergence ability and a Brain Emotional Learning Controller (BELC) using the Lyaponov-based weight updating rule. In addition, the T2FHC is combined with a surface generator to increase the system flexibility. To evaluate its applicability in real life, the proposed controller was tested on a Quanser 2-DOF robot system in three case studies: no load, 180 g load and 360 g load, respectively. The results showed that the proposed structure achieved superior performance compared to those of available algorithms such as CMAC and Novel Self-Organizing Fuzzy CMAC (NSOF CMAC). The Root Mean Square Error (RMSE) index of the system that was 2.20E-06 for angle A and 2.26E-06 for angle B and the tracking error that was -6.42E-04 for angle A and 2.27E-04 for angle B demonstrate the good stability and high accuracy of the proposed T2FHC. With this outstanding achievement, the proposed method is promising to be applied to many applications using nonlinear systems.

Motion Planning for Variable Topology Trusses: Reconfiguration and Locomotion

Truss robots are highly redundant parallel robotic systems that can be applied in a variety of scenarios. The variable topology truss (VTT) is a class of modular truss robots. As self-reconfigurable modular robots, a VTT is composed of many edge modules that can be rearranged into various structures depending on the task. These robots change their shape by not only controlling joint positions as with fixed morphology robots but also reconfiguring the connectivity between truss members in order to change their topology. The motion planning problem for VTT robots is difficult due to their varying morphology, high dimensionality, the high likelihood for self-collision, and complex motion constraints. In this article, a new motion planning framework to dramatically alter the structure of a VTT is presented. It can also be used to solve locomotion tasks that are much more efficient compared with previous work. Several test scenarios are used to show its effectiveness.

The Efficacity of the NeuroAssist Robotic System for Motor Rehabilitation of the Upper Limb-Promising Results from a Pilot Study.

The research aimed to evaluate the efficacy of the NeuroAssist, a parallel robotic system comprised of three robotic modules equipped with human-robot interaction capabilities, an internal sensor system for torque monitoring, and an external sensor system for real-time patient monitoring for the motor rehabilitation of the shoulder, elbow, and wrist. The study enrolled 10 consecutive patients with right upper limb paresis caused by stroke, traumatic spinal cord disease, or multiple sclerosis admitted to the Neurology I Department of Cluj-Napoca Emergency County Hospital. The patients were evaluated clinically and electrophysiologically before (T1) and after the intervention (T2). The intervention consisted of five consecutive daily sessions of 30-45 min each of 30 passive repetitive movements performed with the robot. There were significant differences (Wilcoxon signed-rank test) between baseline and end-point clinical parameters, specifically for the Barthel Index (53.00 ± 37.72 vs. 60.50 ± 36.39, p = 0.016) and Activities of Daily Living Index (4.70 ± 3.43 vs. 5.50 ± 3.80, p = 0.038). The goniometric parameters improved: shoulder flexion (70.00 ± 56.61 vs. 80.00 ± 63.59, p = 0.026); wrist flexion/extension (34.00 ± 28.75 vs. 42.50 ± 33.7, p = 0.042)/(30.00 ± 22.97 vs. 41.00 ± 30.62, p = 0.042); ulnar deviation (23.50 ± 19.44 vs. 33.50 ± 24.15, p = 0.027); and radial deviation (17.50 ± 18.14 vs. 27.00 ± 24.85, p = 0.027). There was a difference in muscle activation of the extensor digitorum communis muscle (1.00 ± 0.94 vs. 1.40 ± 1.17, p = 0.046). The optimized and dependable NeuroAssist Robotic System improved shoulder and wrist range of motion and functional scores, regardless of the cause of the motor deficit. However, further investigations are necessary to establish its definite role in motor recovery.

Robust Adaptive Finite-Time Synergetic Tracking Control of Delta Robot Based on Radial Basis Function Neural Networks

This paper presents a robust proportional derivative adaptive nonsingular finite-time synergetic tracking control (PDAFS) for a parallel Delta robot system. First, a finite-time synergetic controller combined with a proportional derivative (PD) control is constructed based on an object-oriented model to fulfill the robust tracking control of the robot. Then, an adaptive radial basis function approximation neural network (RBF) is designed to compensate for the effects of uncertainty parameters and external disturbances. Second, a second-order sliding mode (SOSM) differentiator is implemented to reduce the chattering noises due to the low-resolution encoders. Third, the stability theorems of the proposed control scheme are provided, where the Lyapunov stability theory is used to prove the theorems. Then, simulations of the helix trajectory tracking and the pick-and-place task are demonstrated on the Delta robot to validate the advantages of the proposed control scheme. Based on the advances, an implementing control system of the proposed controller is performed to improve the Delta robot’s performance in the experiments.

Singularity Analysis and Geometric Optimization of a 6-DOF Parallel Robot for SILS

The paper presents the singularity analysis and the geometric optimization of a 6-DOF (Degrees of Freedom) parallel robot for SILS (Single-Incision Laparoscopic Surgery). Based on a defined set of input/output constraint equations, the singularities of the parallel robotic system are determined and geometrically interpreted. Then, the geometric parameters (e.g., the lengths of the mechanism links) for the 6-DOF parallel robot for SILS are optimized such that the robotic system complies with an operational workspace defined in correlation with the SILS task. A numerical analysis of the singularities showed that the operational workspace is singularity free. Furthermore, numerical simulations validate the parallel robot for the next developing stages (e.g., designing and prototyping stages).

Parallel assistive robotic system for knee rehabilitation: kinematic and dynamic modeling validation

The knee joint is frequently exposed to injuries in people of all ages. In some cases, physical therapy is prescribed to recover the strength and mobility of a patient. The robotic assistance devices are gaining community attention and aim to improve the quality of life of people. In this work, we present the kinematic and dynamic modelling of a five-bar-linkage assistive device for knee rehabilitation according to anthropometric data from Latin-American population. We obtain a dynamic model of the proposed rehabilitation system and compare the knee trajectories with obtained using the assistive system to evaluate appropriate control strategies in the future. For this purpose, we present the kinematic formulation of the device, and then we derive the dynamics using two approaches to validate the model; we obtain the motion equation using the Lagrange approach and an algebraic method that simplifies modelling. Both approaches yield a unique model, which is validated either in simulation and by experimental trials, showing the functionality of the system and the validity of the models when performing rehabilitation routines.

Analysis of Position, Pose and Force Decoupling Characteristics of a 4-UPS/1-RPS Parallel Grinding Robot

For the application of parallel robots in the grinding industry, a parallel robot equipped with a constant force actuator that produces a constant force for grinding is designed. To study the characteristics of the parallel robot’s spatial positions and poses, the inverse solutions of the moving platform’s spatial positions and poses as well as the workspace where objects were ground were established by using DH parameters and geometric methods. The experimental results showed that the workspace where objects were ground was a cylinder with a cross section similar to a symmetric circular sector. To analyze the characteristics of the forces produced by the parallel robotic system, the dynamics equation was established via the Newton–Euler method to verify the rationality of the force decoupling design. Theoretical calculation combined with simulation and experimental analyses confirmed the viability of the theoretical analyses which lay a theoretical foundation for the design, manufacture and control of the parallel robotic system proposed in this paper.

Evaluation of different setting configurations with a new developed telemedical interface of a parallel kinematic robotic system - An experimental development study.

For development of a minimally invasive intracorporal micromanipulator, a master-slave telemanipulation system was required. Different input positions for a tablet-based input device with a heads-up centred screen were evaluated. Personal preference was assessed using a questionnaire. Then, the most ergonomic and intuitive position was compared to a surgical reference position based on laparoscopic sigmoid resection. After comparing a 45°, 75° (pitch) and 60°/20° (pitch/yaw) to a 60° reference position no significant differences in processing time and number of failures could be demonstrated. Study participants indicated the 60°/20° position as the most comfortable in the questionnaire. This was therefore compared with the laparoscopic reference position, both sitting and standing. Here, the laparoscopic sitting position was perceived to be the most ergonomic. The developed input device offers a maximum of flexibility and individualisation to reach ergonomic and intuitive conditions. General recommendations regarding an optimal setting cannot be given, based on our results.

Dynamics Modeling and Vibration Analysis of Planar 3-RRR Flexible Parallel Robot

To address the issue of complicated dynamics modeling and difficult solution of 3-RRR flexible parallel robot, we propose a method of building a flexible parallel robot dynamics model using screw bond graph. Firstly, the structure of the flexible parallel robot is analyzed; secondly, the multi-energy domain dynamics model of the robot is built using screw bond graph and vector bond graph considering the elastomeric transformation in the middle flexible linkage; finally, based on the model, the closed-loop control strategy for suppressing harmful vibration of the system, and the speed loop error compensation for different control parameters is also studied. Author establishes the vector bond and spin bond conversion junction type based on the power conservation transfer principle, which realizes the combination of rigid and flexible system in this paper. And we construct the dynamical model of multi-energy domain flexible parallel robot system.

Inverse modeling of the stewart foot

The Stewart's leg is used today in the majority of parallel robotic systems, such as the Stewart platform, but also in many other types of mechanisms and kinematic chains, in order to operate them or to transmit motion. A special character in the study of robots is the study of inverse kinematics, with the help of which the map of the motor kinematic parameters necessary to obtain the trajectories imposed on the effector can be made. For this reason, in the proposed mechanism, we will present reverse kinematic modeling in this paper. The kinematic output parameters, ie the parameters of the foot and practically of the end effector, ie those of the point marked with T, will be determined for initiating the working algorithm with the help of logical functions, "If log(ical)", with the observation that here they play the role of input parameters; it is positioned as already specified in the inverse kinematics when the output is considered as input and the input as output. The logical functions used, as well as the entire calculation program used, were written in Math Cad.

Dynamic Modeling and Control of a Parallel Mechanism Used in the Propulsion System of a Biomimetic Underwater Vehicle

Incorporation of parallel mechanisms inside propulsion systems in biomimetic autonomous underwater vehicles (BAUVs) is a novel approach for motion generation. The vehicle to which the studied propulsion system is implemented presents thunniform locomotion, and its thrust depends mainly on the oscillation from its caudal fin. This paper describes the kinematic and dynamic modeling of a 3-DOF spherical 3UCU-1S parallel robotic system to which the caudal fin of a BAUV is attached. Lagrange formalism was employed for inverse dynamic modeling, and its derivation is detailed throughout this paper. Additionally, the implementation of control strategies to compute forces required to actuate limbs to change platform’s flapping frequencies was developed. Four controllers: classic PD, a feedforward plus feedback PD, an adaptive Fuzzy-PD, and a feedforward plus Fuzzy-PD were compared in different simulations. Results showed that augmenting oscillating frequencies (from 0.5 to 5 Hz) increased the complexity of the path tracking task, where the classic control strategy (i.e., PD) was not sufficient, reaching percentage errors above 9%. Control strategies using feedforward terms combined with adaptive feedback techniques reduced tracking error below 2% even during the presence of external disturbances.

Adaptive Sliding Mode Neural Network Control and Flexible Vibration Suppression of a Flexible Spatial Parallel Robot

With the goal of creating a flexible spatial parallel robot system in which the elastic deformation of the flexible link causes a rigid moving platform to produce small vibrations, we proposed an adaptive sliding mode control algorithm based on a neural network. To improve the calculation efficiency, the finite element method was used to discretize the flexible spatial link, and then the displacement field of the flexible spatial link was described based on floating frame of reference coordinates, and the dynamic differential equation of the flexible spatial link considering high-frequency vibrations was established through the Lagrange equation. This was combined with the dynamic equation of the rigid link and the dynamic equation considering small displacements of the rigid movable platform due to elastic deformation, and a highly nonlinear and accurate dynamic model with a rigid–flexible coupling effect was obtained. Based on the established accurate multi-body dynamics model, the driving torque with coupling effects was calculated in advance for feedforward compensation, and the adaptive sliding mode controller was used to improve the tracking performance of the system. The nonlinear error was examined to determine the performance of the neural network’s approximation of the nonlinear system. The trajectory errors of the moving platform in the X-, Y-, and Z-directions were reduced by 12.1%, 38.8%, and 50.34%, respectively. The results showed that the designed adaptive sliding mode neural network control met the control accuracy requirements, and suppressed the vibrations generated by the deformation of the flexible spatial link.

Parallel robots modelling and optimization

Parallel robots are mechanical systems with numerous applications in manufacturing, medicine, space industry, etc. Such robots are characterized by closed kinematic chains ensuring robustness and maneuverability. The design of a fully functional parallel robot is a time-consuming task as an engineer needs to enumerate and compare many variants in order to find one with the best characteristics. Typical characteristics are the area of the workspace, the number of singularity-free regions, dexterity index. The design of a parallel robot is thus a multi-objective constraint optimization problem. We propose to use interval analysis to reliably compute characteristics and multiobjective optimization methods to find the Pareto-optimal set of robot parameters. The proposed approach is illustrated on a set of several realistic parallel robotic systems.

Real-time trajectory tracking control of a parallel robot with flexible links

Real-time end-effector trajectory tracking is applied to a newly developed parallel robotic system with two highly flexible links. In contrast to previous works, which are typically based on offline precalculations or rigid model inversion, a dynamic flexible multibody model is inverted online. As the underactuated system is non-minimum phase, the inverse model needs to be rendered stable for real-time integration. Therefore, three approaches are developed for the considered robot. Firstly, output redefinition is applied by directly weighting the elastic deformations and rotations of the links. Secondly, a small counter weight is attached at an advantageous location on the robot having only a minor influence on the eigenfrequencies. Lastly, the rotational degree of freedom of the end-effector is used to stabilize the internal dynamics of the inverse model with a small motion of a rotary motor. The concepts and real-time applicability are validated within experiments which extends the related literature being highly based on theoretical investigations. The experimental end-effector tracking performance based on the three minimum phase approaches is close to the desired trajectory and clearly outperforms classical rigid body inversion.

Mapping Stresses on the Tibial Plateau Cartilage in an Ovine Model Using In-Vivo Gait Kinematics.

Understanding stresses within the knee joint is central to understanding knee function, and the etiology and progression of degenerative joint diseases such as post-traumatic osteoarthritis. In this study, in vivo gait kinematics of four ovine subjects were recorded using a highly accurate Instrumented Spatial Linkage (ISL) as each subject walked on a standard treadmill. The subjects were then sacrificed, and the right hind limbs removed. Ten purpose-built Fibre Bragg Grating (FBG) sensors were positioned within each stifle joint and used to measured contact stresses on the articulating surface of the tibial plateau as the recorded gait was replicated using a 6-degrees-of-freedom parallel robotic system. This study provides the first accurate, direct measurement of stress in a joint during in vivo gait replication. It was hypothesized that the results would indicate a direct link between gait kinematics and measured stress values. Contrary to this expectation no direct link was found between individualistic differences in kinematics and differences in stress magnitudes. This finding highlights the complex multifactorial nature of stress magnitudes and distribution patterns across articular joints. The results also indicate that stress magnitudes within the knee joint are highly position dependent with magnitudes varying substantially between points only a few mm apart.