Development and Applications of Parallel Robots

A special issue of Machines (ISSN 2075-1702). This special issue belongs to the section "Automation and Control Systems".

Deadline for manuscript submissions: closed (16 February 2023) | Viewed by 22964

Special Issue Editor

Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China
Interests: theory and design on the issues of mechanisms; parallel kinematics machines; parallel robots; advanced manufacturing equipment

Special Issue Information

Dear Colleagues,

As the counterpart of serial robots, parallel robots have attracted attention from both academia and industry, due to their high potentials in the aspects of compact structure, low moving inertia, and quick dynamic response. In this context, the development and application of parallel robots have become increasingly attractive topics in recent years. However, great challenges have been encountered in terms of optimal design, motion control, and accuracy assurance, due to their multi-closed-loop architecture.

The main objective of this Special Issue is to create a platform for scientists, engineers and practitioners to share their latest theoretical and technological results, as well as to discuss several issues for the research directions in the field of parallel robots. The papers to be published in this Special Issue are expected to provide recent results pertaining to the design, control and accuracy assurance of parallel robots, especially for cross-fertilizations between the fields of parallel robots and machining/manipulation/motion simulator applications. Papers containing experimental results regarding robotic machining and learning-based accuracy assurance are especially welcome.

Dr. Fugui Xie
Guest Editor

Manuscript Submission Information

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Keywords

  • type synthesis
  • performance evaluation
  • optimal design of parallel robots
  • kinematic calibration
  • learning-based accuracy assurance
  • dynamic optimization
  • dynamic control
  • high-speed pick-and-¬place manipulation
  • parallel/hybrid robotic machining
  • parallel kinematic motion simulator

Published Papers (13 papers)

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Research

18 pages, 8121 KiB  
Article
Comprehensive Compensation Method for Motion Trajectory Error of End-Effector of Cable-Driven Parallel Mechanism
by Yanglong Li, Yujun Xue, Fang Yang, Haichao Cai and Hang Li
Machines 2023, 11(5), 520; https://doi.org/10.3390/machines11050520 - 01 May 2023
Viewed by 1053
Abstract
The accuracy of the end-effector motion trajectory is a critical performance indicator for cable-driven parallel mechanisms. This study aims to address the problem of trajectory error during the end-effector motion in a cable-driven parallel mechanism. It proposes a comprehensive compensation method based on [...] Read more.
The accuracy of the end-effector motion trajectory is a critical performance indicator for cable-driven parallel mechanisms. This study aims to address the problem of trajectory error during the end-effector motion in a cable-driven parallel mechanism. It proposes a comprehensive compensation method based on the simultaneous application of the improved sparrow search algorithm and the cable length space error compensation algorithm, leveraging kinematic analysis. To compensate for the motion trajectory error of the end-effector caused by the geometric parameter error, the study establishes the kinematic model of the cable-driven parallel mechanism using the vector method. It creates the end-effector position error model and motion trajectory error model using the differential kinematic theory, analyzes the impact of the geometric parameter error on the motion trajectory error, constructs the kinematic parameter identification matrix, and uses an improved sparrow search algorithm to compensate for the position error of the motion trajectory interpolation point. For the motion trajectory error of the end-effector caused by non-geometric parameter error, the study analyzes the intrinsic correlation between the adjacent position error of the end-effector and the variation of the cable length using the error similarity theory. It then compensates for the position error of the interpolation point of the trajectory using a cable length space interpolation compensation method to enhance the motion trajectory accuracy of the end-effector. The study experimentally verifies the proposed comprehensive compensation method for end-effector motion trajectory error on a 4-cable-driven 2-DOF parallel mechanism, which reduces the motion trajectory error of the end-effector by 75%. Full article
(This article belongs to the Special Issue Development and Applications of Parallel Robots)
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17 pages, 10325 KiB  
Article
Controller Design for Parallel Mechanism Solar Tracker
by Mustafa Engin
Machines 2023, 11(3), 372; https://doi.org/10.3390/machines11030372 - 09 Mar 2023
Cited by 3 | Viewed by 1428
Abstract
Solar energy is considered a sustainable solution that has proven its technological competence for electricity generation among renewable energy sources. While green resources provide high energy security, they also reduce environmental pollution and support the use of local resources. In this article, a [...] Read more.
Solar energy is considered a sustainable solution that has proven its technological competence for electricity generation among renewable energy sources. While green resources provide high energy security, they also reduce environmental pollution and support the use of local resources. In this article, a dual axis solar tracker that can operate with high accuracy in harsh operating conditions is proposed using the Stewart platform. The Stewart platform is designed using linear actuators using direct current (DC) motors. An embedded controller is designed to control the motors and to realize the sun tracking algorithm of the system. An STM32 board is adopted as a real-time controller to implement the decoupled control algorithm. Therefore, the proposed solar tracker panel control system monitors the daily trajectory of the sun by the photovoltaic panel, ensuring that the system’s energy production remains at its maximum throughout the day. First, the Simulink model of the system was created and the proportional derivative integral (PID) control algorithms were simulated. Experimental studies were carried out by producing the system; the experimental results exhibited a better performance, with an increase in the collected energy of about 32% compared with the fixed one. Full article
(This article belongs to the Special Issue Development and Applications of Parallel Robots)
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19 pages, 856 KiB  
Article
Unified Singularity Crossing of a 3-(rR)PS Metamorphic Parallel Mechanism through Dynamic Modeling
by Latifah Nurahmi, Dongming Gan and Wega Tama Adi Setya
Machines 2023, 11(3), 361; https://doi.org/10.3390/machines11030361 - 07 Mar 2023
Cited by 1 | Viewed by 1036
Abstract
Metamorphic parallel mechanisms can change into multiple configurations with different motion types and mobility, which consequently yield different solutions of inverse dynamics when crossing singularity. Thus, a unified solution of inverse dynamics to cross singularity becomes important. This solution relies on the consistency [...] Read more.
Metamorphic parallel mechanisms can change into multiple configurations with different motion types and mobility, which consequently yield different solutions of inverse dynamics when crossing singularity. Thus, a unified solution of inverse dynamics to cross singularity becomes important. This solution relies on the consistency condition, the first indeterminate form, and this paper proposes an additional condition by extending into the second indeterminate form. This paper presents unified dynamic models of a 3-(rR)PS metamorphic parallel mechanism to pass through singularities. The analysis is carried out on all three configurations of the 3-(rR)PS metamorphic parallel mechanism. The dynamic models are established using Lagrange formulation, and three conditions to cross singularities are employed. The first condition is based on the consistency condition where the uncontrollable motion should be reciprocal to the wrench matrix. The denominator of inverse Jacobian is its determinant whose value is zero at singularities. This singularity can be discarded by compensating the numerator to be zero. Both the numerator and denominator are null, and this indeterminate form becomes the second condition. Both conditions are sufficient for inverse dynamics of one configuration to pass through singularity, but not for other configurations. Therefore, the second indeterminate form is proposed to be the third condition to be fulfilled. Consequently, the 11th-degree polynomial is required for path planning. The results are presented and confirmed by ADAMS simulation. Full article
(This article belongs to the Special Issue Development and Applications of Parallel Robots)
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19 pages, 2211 KiB  
Article
Minimum Dynamic Cable Tension Workspace Generation Techniques and Cable Tension Sensitivity Analysis Methods for Cable-Suspended Gangue-Sorting Robots
by Peng Liu, Hongwei Ma, Xiangang Cao, Xuhui Zhang, Xuechao Duan and Zhen Nie
Machines 2023, 11(3), 338; https://doi.org/10.3390/machines11030338 - 01 Mar 2023
Cited by 2 | Viewed by 964
Abstract
The separation of gangues from coals with robots is an effective and practicable means. Therefore, a cable-suspended gangue-sorting robot (CSGSR) with an end-grab was developed in our early work. Due to the unidirectional characteristic, the flexibility of cables, and the dynamic impact of [...] Read more.
The separation of gangues from coals with robots is an effective and practicable means. Therefore, a cable-suspended gangue-sorting robot (CSGSR) with an end-grab was developed in our early work. Due to the unidirectional characteristic, the flexibility of cables, and the dynamic impact of pick-and-place gangues, one of the significant issues with the robots is robustness under internal and external disturbances. Cable tensions, being the end-grab’s constraints, have a crucial effect on the robustness of the CSGSR while disturbances are on. Two main issues related to the CSGSR, as a result, are addressed in the present paper: minimum dynamic cable tension workspace generation and a sensitivity analysis method for the dynamic cable tensions. Firstly, the four cable tensions and minimum dynamic cable tension while the end-grab was located at an arbitrary position of the task space were obtained with the dynamics of the CSGSR. In addition, with the dynamics of the CSGSR, a minimum dynamic cable tension workspace (MDCTW) generating approach is presented, where the minimum dynamic cable tensions are greater than a preset value, therefore ensuring the robustness of the end-grab under the disturbances. Secondly, a method for dynamic cable tension sensitivity (DCTS) of the robots is proposed with grey relational analysis, by which the influence degree of the end-grab’s positions on the four dynamic cable tensions and the minimum dynamic cable tensions was considered. Finally, the effectiveness of the proposed MDCTW generation algorithm and the DCTS analysis method were examined through simulation on the CSGSR, and it was indicated that the proposed MDCTW generation algorithm and the DCTS analysis method were able to provide theoretical guidance for pick-and-place trajectory planning and generation of the end-grab in practice. Full article
(This article belongs to the Special Issue Development and Applications of Parallel Robots)
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21 pages, 19716 KiB  
Article
Dynamic Modeling and Model-Based Control with Neural Network-Based Compensation of a Five Degrees-of-Freedom Parallel Mechanism
by Dingxu Guo, Zenghui Xie, Xiuting Sun and Shu Zhang
Machines 2023, 11(2), 195; https://doi.org/10.3390/machines11020195 - 01 Feb 2023
Cited by 3 | Viewed by 1487
Abstract
In this paper, a spatial parallel mechanism with five degrees of freedom is studied in order to provide a promising dynamic model for the control design. According to the inverse kinematics of the mechanism, the dynamic model is derived by using the Lagrangian [...] Read more.
In this paper, a spatial parallel mechanism with five degrees of freedom is studied in order to provide a promising dynamic model for the control design. According to the inverse kinematics of the mechanism, the dynamic model is derived by using the Lagrangian method, and the co-simulation using MSC ADAMS and MATLAB/Simulink is adopted to verify the established dynamic model. Then the pre-trained deep neural network (DNN) is introduced to predict the real-time state of the end-effector of the mechanism. Compared to the traditional Newton’s method, the DNN method reduces the cost of the forward kinematics calculation while ensuring prediction accuracy, which enables the dynamic compensation based on feedback signals. Furthermore, the computed torque control with DNN-based feedback compensation is implemented for the trajectory tracking of the mechanism. The simulations show that, in the most complicated case that involves friction and external disturbance, the proposed controller has better tracking performance. The results indicate the necessity of dynamic modeling in the design of control with high precision. Full article
(This article belongs to the Special Issue Development and Applications of Parallel Robots)
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16 pages, 4306 KiB  
Article
An Improved Data-Driven Calibration Method with High Efficiency for a 6-DOF Hybrid Robot
by Zhibiao Yan, Youyu Wang, Haitao Liu, Juliang Xiao and Tian Huang
Machines 2023, 11(1), 31; https://doi.org/10.3390/machines11010031 - 27 Dec 2022
Cited by 1 | Viewed by 1263
Abstract
This paper proposes an improved data-driven calibration method for a six degrees of freedom (DOF) hybrid robot. It focuses mainly on improving the measurement efficiency and practicability of existing data-driven calibration methods through the following approaches. (1) The arbitrary motion of the hybrid [...] Read more.
This paper proposes an improved data-driven calibration method for a six degrees of freedom (DOF) hybrid robot. It focuses mainly on improving the measurement efficiency and practicability of existing data-driven calibration methods through the following approaches. (1) The arbitrary motion of the hybrid robot is equivalently decomposed into three independent sub-motions by motion decomposition. Sequentially, the sub-motions are combined according to specific motion rules. Then, a large number of robot poses can be acquired in the whole workspace via a limited number of measurements, effectively solving the curse of dimensionality in measurement. (2) A mapping between the nominal joint variables and joint compensation values is established using a back propagation neural network (BPNN), which is trained directly using the measurement data through a unique algorithm involving inverse kinematics. Thus, the practicability of data-driven calibration is significantly improved. The validation experiments are carried out on a TriMule-200 robot. The results show that the robot’s maximal position/orientation errors are reduced by 91.16%/88.17% to 0.085 mm/0.022 deg, respectively, after calibration. Full article
(This article belongs to the Special Issue Development and Applications of Parallel Robots)
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17 pages, 3476 KiB  
Article
A General Pose Recognition Method and Its Accuracy Analysis for 6-Axis External Fixation Mechanism Using Image Markers
by Sida Liu, Yimin Song, Binbin Lian and Tao Sun
Machines 2022, 10(12), 1234; https://doi.org/10.3390/machines10121234 - 16 Dec 2022
Viewed by 1197
Abstract
The 6-axis external fixation mechanism with Gough-Stewart configuration has been widely applied to the correction of long bone deformities in orthopedics. Pose recognition of the mechanism is essential for trajectory planning of bone correction, but is usually implemented by the surgeons’ experience, resulting [...] Read more.
The 6-axis external fixation mechanism with Gough-Stewart configuration has been widely applied to the correction of long bone deformities in orthopedics. Pose recognition of the mechanism is essential for trajectory planning of bone correction, but is usually implemented by the surgeons’ experience, resulting in a relatively low level of correction accuracy. This paper proposes a pose recognition method based on novel image markers, and implements accuracy analysis. Firstly, a pose description of the mechanism is established with several freely installed markers, and the layout of the markers is also parametrically described. Then, a pose recognition method is presented by identifying the orientation and position parameters using the markers. The recognition method is general in that it encompasses all possible marker layouts, and the recognition accuracy is investigated by analyzing variations in the marker layout. On this basis, layout principles for markers that achieve a desired recognition accuracy are established, and an error compensation strategy for precision improvement is provided. Finally, experiments were conducted. The results show that volume errors of pose recognition were 0.368 ± 0.130 mm and 0.151 ± 0.045°, and the correction accuracy of the fracture model after taking compensation was 0.214 ± 0.573 mm and −0.031 ± 0.161°, validating the feasibility and accuracy of the proposed methods. Full article
(This article belongs to the Special Issue Development and Applications of Parallel Robots)
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19 pages, 4566 KiB  
Article
Elastostatic Stiffness Modeling and Performance Evaluation of a 2UPR–2PRU Redundantly Actuated Parallel Manipulator
by Xinxue Chai, Wei Ye, Qinchuan Li and Lingmin Xu
Machines 2022, 10(12), 1219; https://doi.org/10.3390/machines10121219 - 15 Dec 2022
Cited by 1 | Viewed by 966
Abstract
Redundantly actuated parallel manipulators (PMs) have attracted a great deal of attention since they generally have better stiffness than non-redundantly actuated ones. This paper presents an analytical elastostatic stiffness modeling and performance study of a 2UPR–2PRU PM with actuation redundancy, which has two [...] Read more.
Redundantly actuated parallel manipulators (PMs) have attracted a great deal of attention since they generally have better stiffness than non-redundantly actuated ones. This paper presents an analytical elastostatic stiffness modeling and performance study of a 2UPR–2PRU PM with actuation redundancy, which has two rotational and one translational degrees of freedom (U: universal joint; P: prismatic joint; R: revolute joint). First, the inverse displacement is reviewed and verified briefly. Second, the stiffness matrices of UPR and PRU limbs are deduced by using the principle of strain energy, followed by the overall stiffness matrix of the 2UPR–2PRU PM. Combined with the ANSYS software, the finite element analysis method is then used to verify the correctness and universality of the stiffness models by calculating the deformations of four selected configurations. Finally, the stiffness index based on the virtual work is used to evaluate the performance of the 2UPR–2PRU PM, and the influence of different external loads and operational heights on the stiffness performance is discussed. The relationship between singular configurations and the stiffness index is also presented. The stiffness models and performance distributions of the 2UPR–2PRU PM with actuation redundancy can provide references for the actual applications. Full article
(This article belongs to the Special Issue Development and Applications of Parallel Robots)
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14 pages, 3435 KiB  
Article
Kinematic Optimization Design and Performance Simulation of Novel 5-DOF Parallel Machining Robots with Spatial Layout
by Ruoyu Wang, Zhili Niu, Kaixuan Chen and Tao Sun
Machines 2022, 10(12), 1187; https://doi.org/10.3390/machines10121187 - 08 Dec 2022
Viewed by 1436
Abstract
High efficiency and precision machining of complex components with spatial free-form surface features is facing significant scientific challenges, which put forward higher requirements for the design of machining equipment. Considering the requirements of engineering practice on the rotation ability, motion ability, stiffness performance [...] Read more.
High efficiency and precision machining of complex components with spatial free-form surface features is facing significant scientific challenges, which put forward higher requirements for the design of machining equipment. Considering the requirements of engineering practice on the rotation ability, motion ability, stiffness performance and mass of equipment, two novel parallel five degree of freedom (5-DOF) machining robots with spatial layout are proposed. This kind of robot is approximately centrally symmetric, with reasonable constraint and driving wrench design, and greatly releases the flexibility of the spindle. A multi-objective optimization approach incorporating the NSGA-II algorithm is used to optimize the kinematic performance of the robots. According to the cooperative equilibrium criterion, the optimal virtual prototype parameters for the two types of robots are selected and contrasted. Then, the static performance of the more optimal virtual prototype is verified using finite element analysis. The numerical simulation demonstrates that the designed 5-DOF machining robot offers satisfactory static behavior and flexibility, which is of significant application value. Full article
(This article belongs to the Special Issue Development and Applications of Parallel Robots)
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24 pages, 12467 KiB  
Article
Stiffness-Performance-Based Redundant Motion Planning of a Hybrid Machining Robot
by Yuhao He, Fugui Xie, Xin-Jun Liu, Zenghui Xie, Huichan Zhao, Yi Yue and Mingwei Li
Machines 2022, 10(12), 1157; https://doi.org/10.3390/machines10121157 - 03 Dec 2022
Viewed by 1308
Abstract
Large-scale components usually have complex structures with high local stiffness, and the holes on them are required to be machined with high precision, which makes it important and challenging to study how to efficiently and precisely drill in the large-scale components. This article [...] Read more.
Large-scale components usually have complex structures with high local stiffness, and the holes on them are required to be machined with high precision, which makes it important and challenging to study how to efficiently and precisely drill in the large-scale components. This article presents mobile hybrid machining equipment that consists of a five-axis parallel module, a 2-degree-of-freedom (DoF) robotic, arm and an automated guide vehicle (AGV) connected in series. With the ability of wide-range positioning and precise local processing, it has potential advantages in the drilling processing of large-scale components. Stiffness is one of the most important performances for machining equipment, and it’s highly related to the its configuration. For the discussed equipment, the stiffness is determined by the two-stage-positioning hybrid machining robot, which comprises a five-axis parallel module and a two-DoF robotic arm. The redundant motion of the hybrid machining robot makes it possible to optimize its configuration by reasonably planning redundant motion. Therefore, a redundant motion-planning method based on stiffness performance is proposed. A kinematic analysis of the five-axis parallel module, the robotic arm, and the hybrid machining robot is carried out. A hybrid robot usually consists of several subsystems, and to take the compliance of each subsystem into consideration, the stiffness-modeling method for the hybrid robot with n subsystems connected in series is proposed. The stiffness model of the hybrid machining robot is established by using this method, and the variation of the stiffness magnitude has the same trend as that obtained by using FEA software. Stiffness magnitude and isotropy indices are proposed to evaluate the robot’s stiffness performance along the axis of the spindle and in the plane perpendicular to the axis of the spindle. The redundant motion of the hybrid machining robot is planned by maximizing the stiffness magnitude along the spindle axis, with priority to the stiffness isotropy index. Finally, the drilling experiment is carried out, and the results show that the relative error of the hole diameter obtained under the optimal configuration of the hybrid machining robot is 1.63%, which is smaller than those obtained under the other two configurations for comparison with relative errors of 3.75% and 3.50%, respectively. It proves the validity of the redundant motion-planning method. The proposed stiffness-modeling method and the stiffness-performance indices are also applicable to other hybrid machining robots. Full article
(This article belongs to the Special Issue Development and Applications of Parallel Robots)
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14 pages, 3300 KiB  
Article
Type Synthesis of 4-DOF Non-Overconstrained Parallel Mechanisms with Symmetrical Structures
by Wei Ye, Qinchuan Li and Xinxue Chai
Machines 2022, 10(12), 1123; https://doi.org/10.3390/machines10121123 - 27 Nov 2022
Cited by 2 | Viewed by 1115
Abstract
This paper presents the type synthesis of 4-DOF non-overconstrained parallel mechanisms (PMs) with symmetrical structures. A special topological structure that includes two intermediate platforms and one moving platform is employed. Constraint conditions for 3R1T, 2R2T, and 1R3T (R: rotation; T: translation) symmetrical PMs [...] Read more.
This paper presents the type synthesis of 4-DOF non-overconstrained parallel mechanisms (PMs) with symmetrical structures. A special topological structure that includes two intermediate platforms and one moving platform is employed. Constraint conditions for 3R1T, 2R2T, and 1R3T (R: rotation; T: translation) symmetrical PMs are analyzed. Several classes of hybrid limbs that exert a constraint force or a constraint couple are synthesized using screw theory. These limbs are then used to construct 4-DOF PMs, resulting in many novel non-overconstrained 3R1T, 2R2T, and 1R3T PMs with symmetrical structures. The non-overconstrained feature is verified based on the Grübler/Kutzbach criterion. Full article
(This article belongs to the Special Issue Development and Applications of Parallel Robots)
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25 pages, 6861 KiB  
Article
Morphing Wing Based on Trigonal Bipyramidal Tensegrity Structure and Parallel Mechanism
by Jian Sun, Xiangkun Li, Yundou Xu, Tianyue Pu, Jiantao Yao and Yongsheng Zhao
Machines 2022, 10(10), 930; https://doi.org/10.3390/machines10100930 - 13 Oct 2022
Cited by 1 | Viewed by 1623
Abstract
The development of morphing wings is in the pursuit of lighter weight, higher stiffness and strength, and better flexible morphing ability. A structure that can be used as both the bearing structure and the morphing mechanism is the optimal choice for the morphing [...] Read more.
The development of morphing wings is in the pursuit of lighter weight, higher stiffness and strength, and better flexible morphing ability. A structure that can be used as both the bearing structure and the morphing mechanism is the optimal choice for the morphing wing. A morphing wing composed of a tensegrity structure and a non-overconstrained parallel mechanism was designed. The self-balancing trigonal bipyramidal tensegrity structure was designed based on the shape-finding method and force-equilibrium equation of nodes. The 4SPS-RS parallel mechanism that can complete wing morphing was designed based on the configuration synthesis method. The degree of freedom and inverse solution of the parallel mechanism was obtained based on the screw theory, and the Jacobian matrix of the parallel mechanism was established. The stiffness model of the tensegrity structure and the 4SPS-RS parallel mechanism was established. The relationship between the deformation of the 4SPS-RS parallel mechanism and sweep angle, torsion angle, spanwise bending, and span was obtained. Through the modular assembly and distributed drive, the morphing wing could perform smooth and continuous morphing locally and globally. In the static state, it has the advantages of high stiffness and large bearing capacity. In the process of morphing, it can complete morphing motion with four degrees of freedom in changing sweep, twist, spanwise bending, and span of the wing. Full article
(This article belongs to the Special Issue Development and Applications of Parallel Robots)
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28 pages, 6202 KiB  
Article
Stewart Platform Motion Control Automation with Industrial Resources to Perform Cycloidal and Oceanic Wave Trajectories
by Diego Silva, Julio Garrido and Enrique Riveiro
Machines 2022, 10(8), 711; https://doi.org/10.3390/machines10080711 - 19 Aug 2022
Cited by 9 | Viewed by 6994
Abstract
Research on motion control automation of Stewart Platforms with industrial configurations (motion and controllers) is less present in the literature than other types of automation with low-cost devices such as Arduino, or via simulations in MATLAB or Simulink. Moreover, direct kinematics is less [...] Read more.
Research on motion control automation of Stewart Platforms with industrial configurations (motion and controllers) is less present in the literature than other types of automation with low-cost devices such as Arduino, or via simulations in MATLAB or Simulink. Moreover, direct kinematics is less widely applied because of heavy calculation in real-time device implementations. The paper first analyzes the design, kinematic modelling, and trajectory generation of a Stewart Platform robot and addresses direct kinematics and motion automation. Next, the automation architecture with industrial controllers is detailed. The paper presents the results of the inverse kinematic in two use scenarios: cycloidal trajectories that carry out point-to-point and oceanic wave movements. The efficient calculation of direct kinematics in real time was also studied. This opens the possibility of closing the positioning loop at the controller or implementing supervisors such as the “tracking error”. Further research might investigate the effects of the sequence planning to avoid collisions with objects inside the workspace while considering the feedback of the tracking error. Full article
(This article belongs to the Special Issue Development and Applications of Parallel Robots)
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