Kinematic Performance Measures and Optimization of Parallel Kinematics Manipulators: A Brief Review

This chapter covers a number of kinematic performance indices that are instrumental in designing parallel kinematics manipulators. These indices can be used selectively based on manipulator requirements and functionality. This would provide the very practical tool for designers to approach their needs in a very comprehensive fashion. Nevertheless, most applications require a more composite set of requirements that makes optimizing performance more challenging. The later part of this chapter will discuss single-objective and multi-objectives optimization that could handle certain performance indices or a combination of them. A brief description of most common techniques in the literature will be provided

Optimal Reconfiguration of a Parallel Robot for Forward Singularities Avoidance in Rehabilitation Therapies. A Comparison via Different Optimization Methods

[EN] This paper presents an efficient algorithm for the reconfiguration of a parallel kinematic manipulator with four degrees of freedom. The reconfiguration of the parallel manipulator is posed as a nonlinear optimization problem where the design variables correspond to the anchoring points of the limbs of the robot on the fixed platform. The penalty function minimizes the forces applied by the actuators during a specific trajectory. Some constraints are imposed to avoid forward singularities and guarantee the feasibility of the active generalized coordinates for a certain trajectory. The results are compared with different optimization approaches with the aim of avoiding getting trapped into a local minimum and undergoing forward singularities. The comparison covers evolutionary algorithms, heuristics optimizers, multistrategy algorithms, and gradient-based optimizers. The proposed methodology has been successfully tested on an actual parallel robot for different trajectories.This research was funded by the Spanish Ministry of Education, Culture and Sports, grant number DPI2017-84201-R.Llopis-Albert, C.; Valero Chuliá, FJ.; Mata Amela, V.; Pulloquinga-Zapata, J.; Zamora-Ortiz, P.; Escarabajal-Sánchez, RJ. (2020). Optimal Reconfiguration of a Parallel Robot for Forward Singularities Avoidance in Rehabilitation Therapies. A Comparison via Different Optimization Methods. Sustainability. 12(14):1-18. https://doi.org/10.3390/su12145803S1181214Rubio, 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. doi:10.1177/1729881419839596Jamwal, P. K., Xie, S. Q., Hussain, S., & Parsons, J. G. (2014). An Adaptive Wearable Parallel Robot for the Treatment of Ankle Injuries. IEEE/ASME Transactions on Mechatronics, 19(1), 64-75. doi:10.1109/tmech.2012.2219065Niu, X., Yang, C., Tian, B., Li, X., & Han, J. (2019). Modal Decoupled Dynamics Feed-Forward Active Force Control of Spatial Multi-DOF Parallel Robotic Manipulator. Mathematical Problems in Engineering, 2019, 1-13. doi:10.1155/2019/1835308Chablat, D., Kong, X., & Zhang, C. (2018). Kinematics, Workspace, and Singularity Analysis of a Parallel Robot With Five Operation Modes. Journal of Mechanisms and Robotics, 10(3). doi:10.1115/1.4039400Gao, Z., & Zhang, D. (2011). Workspace Representation and Optimization of a Novel Parallel Mechanism with Three-Degrees-of-Freedom. Sustainability, 3(11), 2217-2228. doi:10.3390/su3112217Hu, B., Shi, D., Xie, T., Hu, B., & Ye, N. (2020). Kinematically identical manipulators derivation for the 2-RPU+UPR parallel manipulator and their constraint performance comparison. Journal of Mechanisms and Robotics, 1-13. doi:10.1115/1.4047540Schappler, M., Tappe, S., & Ortmaier, T. (2019). Modeling Parallel Robot Kinematics for 3T2R and 3T3R Tasks Using Reciprocal Sets of Euler Angles. Robotics, 8(3), 68. doi:10.3390/robotics8030068Chen, Z., Xu, L., Zhang, W., & Li, Q. (2019). Closed-form dynamic modeling and performance analysis of an over-constrained 2PUR-PSR parallel manipulator with parasitic motions. Nonlinear Dynamics, 96(1), 517-534. doi:10.1007/s11071-019-04803-2Zhang, D., & Wei, B. (2017). Interactions and Optimizations Analysis between Stiffness and Workspace of 3-UPU Robotic Mechanism. Measurement Science Review, 17(2), 83-92. doi:10.1515/msr-2017-0011Wu, G., & Zou, P. (2016). Comparison of 3-DOF asymmetrical spherical parallel manipulators with respect to motion/force transmission and stiffness. Mechanism and Machine Theory, 105, 369-387. doi:10.1016/j.mechmachtheory.2016.07.017Meng, W., Xie, S. Q., Liu, Q., Lu, C. Z., & Ai, Q. (2017). Robust Iterative Feedback Tuning Control of a Compliant Rehabilitation Robot for Repetitive Ankle Training. IEEE/ASME Transactions on Mechatronics, 22(1), 173-184. doi:10.1109/tmech.2016.2618771Yang, Z., & Zhang, D. (2019). ENERGY OPTIMAL ADAPTION AND MOTION PLANNING OF A 3-RRS BALANCED MANIPULATOR. International Journal of Robotics and Automation, 34(5). doi:10.2316/j.2019.206-0171Zhang, D., & Gao, Z. (2012). Optimal Kinematic Calibration of Parallel Manipulators With Pseudoerror Theory and Cooperative Coevolutionary Network. IEEE Transactions on Industrial Electronics, 59(8), 3221-3231. doi:10.1109/tie.2011.2166229Lou, Y., Zhang, Y., Huang, R., Chen, X., & Li, Z. (2014). Optimization Algorithms for Kinematically Optimal Design of Parallel Manipulators. IEEE Transactions on Automation Science and Engineering, 11(2), 574-584. doi:10.1109/tase.2013.2259817Dumlu, A., & Erenturk, K. (2014). Trajectory Tracking Control for a 3-DOF Parallel Manipulator Using Fractional-Order $\hbox{PI}^{\lambda}\hbox{D}^{\mu}$ Control. IEEE Transactions on Industrial Electronics, 61(7), 3417-3426. doi:10.1109/tie.2013.2278964Llopis-Albert, C., Rubio, F., & Valero, F. (2018). Optimization approaches for robot trajectory planning. Multidisciplinary Journal for Education, Social and Technological Sciences, 5(1), 1. doi:10.4995/muse.2018.9867Gosselin, C., & Angeles, J. (1990). Singularity analysis of closed-loop kinematic chains. IEEE Transactions on Robotics and Automation, 6(3), 281-290. doi:10.1109/70.56660Briot, S., Arakelian, V., Bonev, I. A., Chablat, D., & Wenger, P. (2008). Self-Motions of General 3-RPR Planar Parallel Robots. The International Journal of Robotics Research, 27(7), 855-866. doi:10.1177/0278364908092466Karimi, A., Masouleh, M. T., & Cardou, P. (2016). Avoiding the singularities of 3-RPR parallel mechanisms via dimensional synthesis and self-reconfigurability. Mechanism and Machine Theory, 99, 189-206. doi:10.1016/j.mechmachtheory.2016.01.006Patel, Y. D., & George, P. M. (2012). Parallel Manipulators Applications—A Survey. Modern Mechanical Engineering, 02(03), 57-64. doi:10.4236/mme.2012.23008Araujo-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). doi: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). doi:10.1115/1.4037800Vallés, M., Araujo-Gómez, P., Mata, V., Valera, A., Díaz-Rodríguez, M., Page, Á., & Farhat, N. M. (2017). 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. doi:10.1080/15397734.2017.1355249Koziel, S., & Yang, X.-S. (Eds.). (2011). Computational Optimization, Methods and Algorithms. Studies in Computational Intelligence. doi:10.1007/978-3-642-20859-1Beiranvand, V., Hare, W., & Lucet, Y. (2017). Best practices for comparing optimization algorithms. Optimization and Engineering, 18(4), 815-848. doi:10.1007/s11081-017-9366-1Page, A., De Rosario, H., Mata, V., Hoyos, J. V., & Porcar, R. (2006). Effect of marker cluster design on the accuracy of human movement analysis using stereophotogrammetry. Medical and Biological Engineering and Computing, 44(12), 1113-1119. doi:10.1007/s11517-006-0124-3Arora, J. S., Chahande, A. I., & Paeng, J. K. (1991). Multiplier methods for engineering optimization. International Journal for Numerical Methods in Engineering, 32(7), 1485-1525. doi:10.1002/nme.1620320706Modefrontier Toolhttps://www.esteco.com.202

Optimal dimensional synthesis of force feedback lower arm exoskeletons

This paper presents multi-criteria design optimization of parallel mechanism based force feedback exoskeletons for human forearm and wrist. The optimized devices are aimed to be employed as a high fidelity haptic interfaces. Multiple design objectives are discussed and classified for the devices and the optimization problem to study the trade-offs between these criteria is formulated. Dimensional syntheses are performed for optimal global kinematic and dynamic performance, utilizing a Pareto front based framework, for two spherical parallel mechanisms that satisfy the ergonomic necessities of a human forearm and wrist. Two optimized mechanisms are compared and discussed in the light of multiple design criteria. Finally, kinematic structure and dimensions of an optimal exoskeleton are decided

Three-Stage Design Analysis and Multicriteria Optimization of a Parallel Ankle Rehabilitation Robot Using Genetic Algorithm

This paper describes the design analysis and optimization of a novel 3-degrees of freedom (DOF) wearable parallel robot developed for ankle rehabilitation treatments. To address the challenges arising from the use of a parallel mechanism, flexible actuators, and the constraints imposed by the ankle rehabilitation treatment, a complete robot design analysis is performed. Three design stages of the robot, namely, kinematic design, actuation design, and structural design are identified and investigated, and, in the process, six important performance objectives are identified which are vital to achieve design goals. Initially, the optimization is performed by considering only a single objective. Further analysis revealed that some of these objectives are conflicting, and hence these are required to be simultaneously optimized. To investigate a further improvement in the optimal values of design objectives, a preference-based approach and evolutionary-algorithm-based nondominated sorting algorithm (NSGA II) are adapted to the present design optimization problem. Results from NSGA II are compared with the results obtained from the single objective optimization and preference-based optimization approaches. It is found that NSGA II is able to provide better design solutions and is adequate to optimize all of the objective functions concurrently. Finally, a fuzzy-based ranking method has been devised and implemented in order to select the final design solution from the set of nondominated solutions obtained through NSGA II. The proposed design analysis of parallel robots together with the multiobjective optimization and subsequent fuzzy-based ranking can be generalized with modest efforts for the development of all of the classes of parallel robots

Multi-objective particle swarm optimization for the structural design of concentric tube continuum robots for medical applications

Concentric tube robots belong to the class of continuum robotic systems whose morphology is described by continuous tangent curvature vectors. They are composed of multiple, interacting tubes nested inside one another and are characterized by their inherent flexibility. Concentric tube continuum robots equipped with tools at their distal end have high potential in minimally invasive surgery. Their morphology enables them to reach sites within the body that are inaccessible with commercial tools or that require large incisions. Further, they can be deployed through a tight lumen or follow a nonlinear path. Fundamental research has been the focus during the last years bringing them closer to the operating room. However, there remain challenges that require attention. The structural synthesis of concentric tube continuum robots is one of these challenges, as these types of robots are characterized by their large parameter space. On the one hand, this is advantageous, as they can be deployed in different patients, anatomies, or medical applications. On the other hand, the composition of the tubes and their design is not a straightforward task but one that requires intensive knowledge of anatomy and structural behavior. Prior to the utilization of such robots, the composition of tubes (i.e. the selection of design parameters and application-specific constraints) must be solved to determine a robotic design that is specifically targeted towards an application or patient. Kinematic models that describe the change in morphology and complex motion increase the complexity of this synthesis, as their mathematical description is highly nonlinear. Thus, the state of the art is concerned with the structural design of these types of robots and proposes optimization algorithms to solve for a composition of tubes for a specific patient case or application. However, existing approaches do not consider the overall parameter space, cannot handle the nonlinearity of the model, or multiple objectives that describe most medical applications and tasks. This work aims to solve these fundamental challenges by solving the parameter optimization problem by utilizing a multi-objective optimization algorithm. The main concern of this thesis is the general methodology to solve for patient- and application-specific design of concentric tube continuum robots and presents key parameters, objectives, and constraints. The proposed optimization method is based on evolutionary concepts that can handle multiple objectives, where the set of parameters is represented by a decision vector that can be of variable dimension in multidimensional space. Global optimization algorithms specifically target the constrained search space of concentric tube continuum robots and nonlinear optimization enables to handle the highly nonlinear elasticity modeling. The proposed methodology is then evaluated based on three examples that include cooperative task deployment of two robotic arms, structural stiffness optimization under the consideration of workspace constraints and external forces, and laser-induced thermal therapy in the brain using a concentric tube continuum robot. In summary, the main contributions are 1) the development of an optimization methodology that describes the key parameters, objectives, and constraints of the parameter optimization problem of concentric tube continuum robots, 2) the selection of an appropriate optimization algorithm that can handle the multidimensional search space and diversity of the optimization problem with multiple objectives, and 3) the evaluation of the proposed optimization methodology and structural synthesis based on three real applications