Optimal Reconfiguration of a Limited Parallel Robot for Forward Singularities Avoidance

[EN] The positioning of the anchoring points of a Parallel Kinematic Manipulator has an important impact on its later performance. This paper presents an optimization problem to deal with the reconfiguration of a Parallel Kinematic manipulator with four degrees of freedom and the corresponding algorithms to address such problem, with the subsequent test on an actual robot. The cost function minimizes the forces applied by the actuators along the trajectory and considers singular positions and the feasibility of the active generalized coordinates. Results are compared among different algorithms, including evolutionary, heuristics, multi-strategy and gradient-based optimizers.This work was supported by the Spanish Ministry of Education, Culture and Sports through the Project for Research and Technological Development with Ref. DPI2017-84201-RLlopis-Albert, C.; Valero, F.; Mata, V.; Escarabajal, RJ.; Zamora-Ortiz, P.; Pulloquinga, JL. (2020). Optimal Reconfiguration of a Limited Parallel Robot for Forward Singularities Avoidance. Multidisciplinary Journal for Education, Social and Technological Sciences. 7(1):113-127. https://doi.org/10.4995/muse.2020.13352OJS11312771Arakelian, V., Briot, S., & Glazunov, V. (2008). Increase of singularity-free zones in the workspace of parallel manipulators using mechanisms of variable structure. Mechanism and Machine Theory, 43(9), 1129-1140. https://doi.org/10.1016/J.MECHMACHTHEORY.2007.09.005Araujo-Gómez, P., Díaz-Rodríguez, M., Mata, V., & González-Estrada, O. A. (2019). Kinematic analysis and dimensional optimization of a 2R2T parallel manipulator. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 41(10), 425. https://doi.org/10.1007/s40430-019-1934-1Araujo-Gómez, P., Mata, V., Díaz-Rodríguez, M., Valera, A., & Page, A. (2017). Design and kinematic analysis of a novel 3UPS/RPU parallel kinematic mechanism with 2T2R motion for knee diagnosis and rehabilitation tasks. Journal of Mechanisms and Robotics, 9(6), 061004. https://doi.org/10.1115/1.4037800Beiranvand, V., Hare, W., & Lucet, Y. (2017). Best practices for comparing optimization algorithms. Optimization and Engineering, 18(4), 815-848. https://doi.org/10.1007/s11081-017-9366-1Dash, A. K., Chen, I. M., Yeo, S. H., & Yang, G. (2005). Workspace generation and planning singularity-free path for parallel manipulators. Mechanism and Machine Theory, 40(7), 776-805. https://doi.org/10.1016/j.mechmachtheory.2005.01.001Gosselin, C., & Angeles, J. (1990). Singularity Analysis of Closed-Loop Kinematic Chains. IEEE Transactions on Robotics and Automation, 6(3), 281-290. https://doi.org/10.1109/70.56660Llopis-Albert, C., Rubio, F., & Valero, F. (2018). Optimization approaches for robot trajectory planning. Multidisciplinary Journal for Education, Social and Technological Sciences, 5(1), 1. https://doi.org/10.4995/muse.2018.9867Patel, Y. D., & George, P. M. (2012). Parallel Manipulators Applications-A Survey. Modern Mechanical Engineering, 02(03), 57-64. https://doi.org/10.4236/mme.2012.23008Rubio, F., Llopis-Albert, C., Valero, F., & Suñer, J. L. (2016). Industrial robot efficient trajectory generation without collision through the evolution of the optimal trajectory. Robotics and Autonomous Systems, 86, 106-112. https://doi.org/10.1016/j.robot.2016.09.008Rubio, F., Valero, F., & Llopis-Albert, C. (2019). A review of mobile robots: Concepts, methods, theoretical framework, and applications. International Journal of Advanced Robotic Systems, 16(2), 172988141983959. https://doi.org/10.1177/1729881419839596Tsai, L.-W. (1999). Robot Analysis and Design. John Wiley & Sons, Inc. New York, NY, USA ©1999.Valero, F., Rubio, F., & Llopis-Albert, C. (2019). Assessment of the Effect of Energy Consumption on Trajectory Improvement for a Car-like Robot. Robotica, 37(11), 1998-2009. https://doi.org/10.1017/S0263574719000407Vallés, M., Araujo-Gómez, P., Mata, V., Valera, A., Díaz-Rodríguez, M., Page, Á., & Farhat, N. M. (2018). Mechatronic design, experimental setup, and control architecture design of a novel 4 DoF parallel manipulator. Mechanics Based Design of Structures and Machines, 46(4), 425-439. https://doi.org/10.1080/15397734.2017.1355249Wehage, K. T., Wehage, R. A., & Ravani, B. (2015). Generalized coordinate partitioning for complex mechanisms based on kinematic substructuring. Mechanism and Machine Theory, 92, 464-483. https://doi.org/10.1016/j.mechmachtheory.2015.06.006www.esteco.com. (n.d.). Retrieved June 10, 2019, from https://www.esteco.com/Xianwen Kong, B., & Gosselin, C. M. (2002). Kinematics and singularity analysis of a novel type of 3-CRR 3-DOF translational parallel manipulator. International Journal of Robotics Research, 21(9), 791-798. https://doi.org/10.1177/02783649020210090501Yang, X. (2017). Optimization Algorithms Optimization and Metaheuristic Algorithms in Engineering. (March). https://doi.org/10.1007/978-3-642-20859-

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

Gravitational Base Parameters Identification for a Knee Rehabilitation Parallel Robot

New robotic technology is emerging nowadays to tackle lower limb rehabilitation issues. However, the commercial robots available for lower limb rehabilitation are usually oversize and expensive. Knee rehabilitation is generally aided by a professional therapist, making this clinical procedure an interesting scope for robotics. Parallel robots are suitable candidates for knee rehabilitation due to their high load capacity, stiffness, and accuracy compared to serial ones. In contrast, this robot has singular configurations inside its workspace, and its dynamic model is generally complex. For these reasons, a parallel robot for knee rehabilitation needs an advanced control unit to solve complex mathematical problems that ensure patient security. This study proposes the base parameters identification of a compact gravitational linear model of a 3UPS+RPU parallel robot using singular value decomposition. This paper recommends adding a statistical method focused on condition number minimization to the singular value decomposition process. This statistical method reduces the computational resources taken searching for the best inertial parameters combination at the beginning of the base parameter identification. The gravitational base parameters identified have a physical meaning and low complexity. This fact makes the results of this research the basis of an adaptative control applied to 3UPS+RPU parallel robot. This study shows that the gravitational term is the most influential for knee rehabilitation tasks, compared with the inertial, Coriolis, and centrifugal components, regarding the dynamic behavior of the parallel robot