Sparse Identification of Lagrangian for Nonlinear Dynamical Systems via Proximal Gradient Method

Distilling physical laws autonomously from data has been of great interest in many scientific areas. The sparse identification of nonlinear dynamics (SINDy) and its variations have been developed to extract the underlying governing equations from observation data. However, SINDy faces certain difficulties when the dynamics contain rational functions. The principle of the least action governs many mechanical systems, mathematically expressed in the Lagrangian formula. Compared to the actual equation of motions, the Lagrangian is much more concise, especially for complex systems, and does not usually contain rational functions for mechanical systems. Only a few methods have been proposed to extract the Lagrangian from measurement data so far. One of such methods, Lagrangian-SINDy, can extract the true form of Lagrangian of dynamical systems from data but suffers when noises are present. In this work, we develop an extended version of Lagrangian-SINDy (xL-SINDy) to obtain the Lagrangian of dynamical systems from noisy measurement data. We incorporate the concept of SINDy and utilize the proximal gradient method to obtain sparse expressions of the Lagrangian. We demonstrated the effectiveness of xL-SINDy against different noise levels with four nonlinear dynamics: a single pendulum, a cart-pendulum, a double pendulum, and a spherical pendulum. Furthermore, we also verified the performance of xL-SINDy against SINDy-PI (parallel, implicit), a recent robust variant of SINDy that can handle implicit dynamics and rational nonlinearities. Our experiment results show that xL-SINDy is 8-20 times more robust than SINDy-PI in the presence of noise

An Optimal Transport Based Transferable System for Detection of Erroneous Somato-Sensory Feedback from Neural Signals

This study is aimed at the detection of single-trial feedback, perceived as erroneous by the user, using a transferable classification system while conducting a motor imagery brain–computer interfacing (BCI) task. The feedback received by the users are relayed from a functional electrical stimulation (FES) device and hence are somato-sensory in nature. The BCI system designed for this study activates an electrical stimulator placed on the left hand, right hand, left foot, and right foot of the user. Trials containing erroneous feedback can be detected from the neural signals in form of the error related potential (ErrP). The inclusion of neuro-feedback during the experiments indicated the possibility that ErrP signals can be evoked when the participant perceives an error from the feedback. Hence, to detect such feedback using ErrP, a transferable (offline) decoder based on optimal transport theory is introduced herein. The offline system detects single-trial erroneous trials from the feedback period of an online neuro-feedback BCI system. The results of the FES-based feedback BCI system were compared to a similar visual-based (VIS) feedback system. Using our framework, the error detector systems for both the FES and VIS feedback paradigms achieved an F1-score of 92.66% and 83.10%, respectively, and are significantly superior to a comparative system where an optimal transport was not used. It is expected that this form of transferable and automated error detection system compounded with a motor imagery system will augment the performance of a BCI and provide a better BCI-based neuro-rehabilitation protocol that has an error control mechanism embedded into it

Augmenting Motor Imagery Learning for Brain–Computer Interfacing Using Electrical Stimulation as Feedback

International audienceBrain-computer Interfaces (BCI) and Functional electrical stimulation (FES) contribute significantly to induce cortical learning and to elicit peripheral neuronal activation processes and thus, are highly effective to promote motor recovery. This study aims at understanding the effect of FES as a neural feedback and its influence on the learning process for motor imagery tasks while comparing its performance with a classical visual feedback protocol. The participants were randomly separated into two groups: one group was provided with visual feedback (VIS) while the other received electrical stimulation (FES) as feedback. Both groups performed various motor imagery tasks while feedback was provided in form of a bi-directional bar for VIS group and targeted electrical stimulation on the upper and lower limbs for FES group. The results shown in this paper suggest that the FES based feedback is more intuitive to the participants, hence, the superior results as compared to the visual feedback. The results suggest that the convergence of BCI with FES modality could improve the learning of the patients both in terms of accuracy and speed and provide a practical solution to the BCI learning process in rehabilitation

A study on the effect of Electrical Stimulation during motor imagery learning in Brain-computer interfacing

International audienceFunctional Electrical Stimulation (FES) stimulates the affected region of the human body thus providing a neu-roprosthetic interface to non-recovered muscle groups. FES in combination with Brain-computer interfacing (BCI) has a wide scope in rehabilitation because this system can directly link the cerebral motor intention of the users with its corresponding peripheral mucle activations. Such a rehabilitative system would contribute to improve the cortical and peripheral learning and thus, improve the recovery time of the patients. In this paper, we examine the effect of electrical stimulation by FES on the electroencephalography (EEG) during learning of a motor imagery task. The subjects are asked to perform four motor imagery tasks over six sessions and the features from the EEG are extracted using common spatial algorithm and decoded using linear discriminant analysis classifier. Feedback is provided in form of a visual medium and electrical stimulation representing the distance of the features from the hyperplane. Results suggest a significant improvement in the classification accuracy when the subject was induced with electrical stimulation along with visual feedback as compared to the standard visual one

Multibranch convolutional neural network with contrastive representation learning for decoding same limb motor imagery tasks

IntroductionEmerging deep learning approaches to decode motor imagery (MI) tasks have significantly boosted the performance of brain-computer interfaces. Although recent studies have produced satisfactory results in decoding MI tasks of different body parts, the classification of such tasks within the same limb remains challenging due to the activation of overlapping brain regions. A single deep learning model may be insufficient to effectively learn discriminative features among tasks.MethodsThe present study proposes a framework to enhance the decoding of multiple hand-MI tasks from the same limb using a multi-branch convolutional neural network. The CNN framework utilizes feature extractors from established deep learning models, as well as contrastive representation learning, to derive meaningful feature representations for classification.ResultsThe experimental results suggest that the proposed method outperforms several state-of-the-art methods by obtaining a classification accuracy of 62.98% with six MI classes and 76.15 % with four MI classes on the Tohoku University MI-BCI and BCI Competition IV datasets IIa, respectively.DiscussionDespite requiring heavy data augmentation and multiple optimization steps, resulting in a relatively long training time, this scheme is still suitable for online use. However, the trade-of between the number of base learners, training time, prediction time, and system performance should be carefully considered

Deep Reinforcement Learning for Tailorable Natural Quadruped Gait Generation

The 11th International Symposium on Adaptive Motion of Animals and Machines. Kobe University, Japan. 2023-06-06/09. Adaptive Motion of Animals and Machines Organizing Committee.Poster Session P2

Energy-Efficient Speed Control in a Reflex-based Bipedal Walking Model

The 11th International Symposium on Adaptive Motion of Animals and Machines. Kobe University, Japan. 2023-06-06/09. Adaptive Motion of Animals and Machines Organizing Committee.Poster Session P1

Voluntary EMG-to-force estimation with a multi-scale physiological muscle model

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.International audienceBackgroundEMG-to-force estimation based on muscle models, for voluntary contraction has many applications in human motion analysis. The so-called Hill model is recognized as a standard model for this practical use. However, it is a phenomenological model whereby muscle activation, force-length and force-velocity properties are considered independently. Perreault reported Hill modeling errors were large for different firing frequencies, level of activation and speed of contraction. It may be due to the lack of coupling between activation and force-velocity properties. In this paper, we discuss EMG-force estimation with a multi-scale physiology based model, which has a link to underlying crossbridge dynamics. Differently from the Hill model, the proposed method provides dual dynamics of recruitment and calcium activation.MethodsThe ankle torque was measured for the plantar flexion along with EMG measurements of the medial gastrocnemius (GAS) and soleus (SOL). In addition to Hill representation of the passive elements, three models of the contractile parts have been compared. Using common EMG signals during isometric contraction in four able-bodied subjects, torque was estimated by the linear Hill model, the nonlinear Hill model and the multi-scale physiological model that refers to Huxley theory. The comparison was made in normalized scale versus the case in maximum voluntary contraction.ResultsThe estimation results obtained with the multi-scale model showed the best performances both in fast-short and slow-long term contraction in randomized tests for all the four subjects. The RMS errors were improved with the nonlinear Hill model compared to linear Hill, however it showed limitations to account for the different speed of contractions. Average error was 16.9% with the linear Hill model, 9.3% with the modified Hill model. In contrast, the error in the multi-scale model was 6.1% while maintaining a uniform estimation performance in both fast and slow contractions schemes.ConclusionsWe introduced a novel approach that allows EMG-force estimation based on a multi-scale physiology model integrating Hill approach for the passive elements and microscopic cross-bridge representations for the contractile element. The experimental evaluation highlights estimation improvements especially a larger range of contraction conditions with integration of the neural activation frequency property and force-velocity relationship through cross-bridge dynamics consideration

Leg Morphologies Essential for Environmental Adaptive Hexapod Walking Driven by Reflex-based Intra-limb Coordination

The 11th International Symposium on Adaptive Motion of Animals and Machines. Kobe University, Japan. 2023-06-06/09. Adaptive Motion of Animals and Machines Organizing Committee.Poster Session P3

In Vivo

International audienceSkeletal muscle system has nonlinear dynamics and subject-specific characteristics. Thus, it is essential to identify unknown parameters from noisy biomedical signals to improve the modeling accuracy in neuroprosthetic control. The objective of this work is to develop an experimental identification method for subject-specific biomechanical parameters of a physiological muscle model which can be employed to predict the nonlinear force properties of stimulated muscle. Our previously proposed muscle model, which can describe multi-scale physiological system based on the Hill and Huxley models, was used for the identification. The identification protocols were performed on two rabbit experiments, where the medial gastrocnemius was attached to a motorized lever system to record the force by the nerve stimulation. The muscle model was identified using nonlinear Kalman filters: Sigma-Point and Extended Kalman Filter. The identified model was evaluated by comparison with experimental measurements in cross-validation manner. The feasibility could be demonstrated by comparison between the estimated parameter and the measured value. The estimates with SPKF showed 5.7% and 2.9% error in each experiment with 7 different initial conditions. It reveals that SPKF has great advantage especially for the identification of multi-scale muscle model which accounts for the high nonlinearity and discontinuous states between muscle contraction and relaxation process