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. 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Computational neurorehabilitation: modeling plasticity and learning to predict recovery

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Although scheduling multiple tasks in motor learning to maximize long-term retention of performance is of great practical importance in sports training and motor rehabilitation after brain injury, it is unclear how to do so. We propose here a novel theoretical approach that uses optimal control theory and computational models of motor adaptation to determine schedules that maximize long-term retention predictively. Using Pontryagin’s maximum principle, we derived a control law that determines the trial-by-trial task choice that maximizes overall delayed retention for all tasks, as predicted by the state-space model. Simulations of a single session of adaptation with two tasks show that when task interference is high, there exists a threshold in relative task difficulty below which the alternating schedule is optimal. Only for large differences in task difficulties do optimal schedules assign more trials to the harder task. However, over the parameter range tested, alternating schedules yield long-term retention performance that is only slightly inferior to performance given by the true optimal schedules. Our results thus predict that in a large number of learning situations wherein tasks interfere, intermixing tasks with an equal number of trials is an effective strategy in enhancing long-term retention