Optimal Reconfiguration of a Limited Parallel Robot for Forward Singularities Avoidance

Carlos Llopis-Albert, Francisco Valero, Vicente Mata, Rafael J. Escarabajal, Pau Zamora-Ortiz, José L. Pulloquinga


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.


Parallel robot; non-linear optimization; rehabilitation; trajectory; singularity

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Arakelian, 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.2007.09.005

Araujo-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/s40430-019-1934-1

Araujo-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/10.1115/1.4037800

Beiranvand, V., Hare, W., & Lucet, Y. (2017). Best practices for comparing optimization algorithms. Optimization and Engineering, 18(4), 815–848. https://doi.org/10.1007/s11081-017-9366-1

Dash, 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.2005.01.001

Gosselin, C., & Angeles, J. (1990). Singularity Analysis of Closed-Loop Kinematic Chains. IEEE Transactions on Robotics and Automation, 6(3), 281–290. https://doi.org/10.1109/70.56660

Llopis-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.2018.9867

Patel, Y. D., & George, P. M. (2012). Parallel Manipulators Applications—A Survey. Modern Mechanical Engineering, 02(03), 57–64. https://doi.org/10.4236/mme.2012.23008

Rubio, 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.2016.09.008

Rubio, 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/10.1177/1729881419839596

Tsai, 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/S0263574719000407

Vallés, 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/10.1080/15397734.2017.1355249

Wehage, 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.2015.06.006

www.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/10.1177/02783649020210090501

Yang, X. (2017). Optimization Algorithms Optimization and Metaheuristic Algorithms in Engineering. (March). https://doi.org/10.1007/978-3-642-20859-1

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1. Modelling an Industrial Robot and Its Impact on Productivity
Carlos Llopis-Albert, Francisco Rubio, Francisco Valero
Mathematics  vol: 9  issue: 7  first page: 769  year: 2021  
doi: 10.3390/math9070769

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Universitat Politècnica de València

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