Force Estimation Error Research Articles

Accurate Drift-Invariant Single-Molecule Force Calibration Using the Hadamard Variance

Single-molecule force spectroscopy (SMFS) techniques play a pivotal role in unraveling the mechanics and conformational transitions of biological macromolecules under external forces. Among these techniques, multiplexed magnetic tweezers (MT) are particularly well suited to probe very small forces, ≤1 pN, critical for studying non-covalent interactions and regulatory conformational changes at the single-molecule level. However, to apply and measure such small forces, a reliable and accurate force calibration procedure is crucial.Here, we introduce a new approach to calibrate MT based on thermal motion using the Hadamard variance (HV). To test our method, we perform bead-tether Brownian dynamics simulations that mimic our experimental system and compare the performance of the HV method against two established techniques: power spectral density (PSD) and Allan variance (AV) analyses. Our analysis includes an assessment of each method’s ability to mitigate common sources of additive noise, such as white and pink noise, as well as drift, which often complicate experimental data analysis. We find that the HV method exhibits overall similar or higher precision and accuracy, yielding lower force estimation errors across a wide range of signal-to-noise ratios (SNR) and drift speeds compared to the PSD and AV methods. Notably, the HV method remains robust against drift, maintaining consistent uncertainty levels across the entire studied SNR and drift speed spectrum. We also explore the HV method using experimental MT data, where we find overall smaller force estimation errors compared to PSD and AV approaches.Overall, the HV method offers a robust method for achieving sub-pN resolution and precision in multiplexed MT measurements. Its potential extends to other SMFS techniques, presenting exciting opportunities for advancing our understanding of mechano-sensitivity and force generation in biological systems. To make our methods widely accessible to the research community, we provide a well-documented Python implementation of the HV method as an extension to the Tweezepy package.

Force estimation for human–robot interaction using electromyogram signals from varied arm postures

In this paper, a system for force estimation based on surface electromyography signals measured from the eight channels of the Myo armband is presented. We evaluated nineteen regression models to continuously estimate force in three scenario cases to cover the natural movement in two degrees of freedom planer rehabilitation mobile robots. The best estimation model that could overcome the challenge in a variety of different scenarios was determined. Based on the experimental results, the Gaussian process regression model performed best, giving a root mean square error in the overall range of 1.18–1.77 N. Additionally, the results showed that the exponential algorithm outperformed other solutions, significantly reducing the force estimation error.

Wrench Estimation and Friction Compensation Using Multiple Shooting Method for Tether Units Augmented to Remote Tendon-Driven Continuum Robots

Abstract Remote-actuated mechanisms that employ tendon sheaths or tether units can transmit mechanical force without directly connecting the actuators to the mechanism, but suffer from undesirable side effects like mechanical friction and induced external wrench disturbances on the distal side of the mechanism. In this work, a multiple shooting method is proposed as a superior method to the single shooting method to solve the Cosserat rod boundary value problems, to obtain the states of the system. With that, numerical experiments are provided to demonstrate the difficulty of solving these boundary value problems, simultaneously showing the validity of the proposed approach. 2D reconstruction experiments were conducted to show shape reconstruction capabilities. In addition, friction loss and 6-degree-of-freedom wrench estimations were also experimentally validated with the proposed mathematical model with 0.1679N and 0.0401Nm for root-mean-squared error (RMSE) force estimation and torque estimation error, respectively, while achieving a 3% mean absolute percentage steady-state friction estimation error. Finally, a modified resolved rate controller was applied to steer a remote tendon-driven continuum robot to compensate for friction loss for 3.1-m long tether units.

Acceleration-Based Estimation of Vertical Ground Reaction Forces during Running: A Comparison of Methods across Running Speeds, Surfaces, and Foot Strike Patterns.

Twenty-seven methods of estimating vertical ground reaction force first peak, loading rate, second peak, average, and/or time series from a single wearable accelerometer worn on the shank or approximate center of mass during running were compared. Force estimation errors were quantified for 74 participants across different running surfaces, speeds, and foot strike angles and biases, repeatability coefficients, and limits of agreement were modeled with linear mixed effects to quantify the accuracy, reliability, and precision. Several methods accurately and reliably estimated the first peak and loading rate, however, none could do so precisely (the limits of agreement exceeded ±65% of target values). Thus, we do not recommend first peak or loading rate estimation from accelerometers with the methods currently available. In contrast, the second peak, average, and time series could all be estimated accurately, reliably, and precisely with several different methods. Of these, we recommend the 'Pogson' methods due to their accuracy, reliability, and precision as well as their stability across surfaces, speeds, and foot strike angles.

Sensorless Force Estimator for Bilateral Control Systems Using Adaptive Sliding-Mode-Assisted Disturbance Observer

Superior transparency, which includes precise force feedback and position tracking, is the main objective of bilateral operating systems. Therefore, force information estimation or measurement plays a critical role in improving the transparency of bilateral operating systems. This paper proposes a bilateral control scheme combined with an adaptive sliding-mode-assisted disturbance observer (ASMADO) for bilateral operating systems. First, ASMADO, comprising an adaptive disturbance observer and adaptive sliding mode-assisted control law, is used as a force detector to estimate the time-varying force in bilateral control systems. The adaptive disturbance observer with a fixed-time convergent auxiliary dynamic variable is designed without the prior knowledge of the upper bound of the force information derivative, which drives the force estimation error into a small bounded set. Then, the adaptive sliding mode-assisted control law is used to eliminate the estimated residuals of the adaptive disturbance observer in the inner loop of the force estimator. Stability analysis proves that the proposed ASMADO is practical finite-time stable. Subsequently, a bilateral control scheme based on the proposed ASMADO is developed to further improve the system transparency with force feedback and position tracking. Finally, comparative experimental studies are conducted to verify the superior performance of the proposed bilateral controller based on ASMADO.

A Transformer-based Multi-task Learning Framework for Myoelectric Pattern Recognition Supporting Muscle Force Estimation.

Simultaneous implementation of myoelectric pattern recognition and muscle force estimation is highly demanded in building natural gestural interfaces but a challenging task due to the gesture classification accuracy degradation under varying muscle strengths. To address this problem, a novel method using transformer-based multi-task learning (MTL-Transformer) for the prediction of both myoelectric patterns and corresponding muscle strengths was proposed to describe the inherent characteristics of an individual gesture pattern under different force conditions, thereby improving the accuracy of myoelectric pattern recognition. In addition, the transformer model enabled the characterization of long-term temporal correlations to ensure precise and smooth estimation of the muscle force. The performance of the proposed MTL-Transformer framework was evaluated via experiments of classifying eleven hand gestures and estimating the corresponding muscle force simultaneously, using high-density surface electromyogram (HD-sEMG) recordings from forearm flexor muscles of eleven intact-limbed subjects. The MTL-Transformer framework yielded high classification accuracy (98.70±1.21%) and low root mean square deviation (12.59±2.76%), and outperformed other two common temporally modelling methods significantly (p < 0.05) in terms of both improved gesture recognition accuracies and reduced muscle force estimation errors. The MTL-Transformer framework is demonstrated as an effective solution for simultaneous implementation of myoelectric pattern recognition and muscle force estimation. This study promotes the development of robust and smooth myoelectric control systems, with wide applications in gestural interfaces, prosthetic and orthotic control.

Novel Force Estimation Method for Magnetic Lead Screw-Based RotLin Actuator

This article proposes a method to precisely estimate the load force of magnetic lead screw (MLS)-based series elastic actuators (SEAs) in real time. The elastic transmissions of MLS-based SEAs generally comprise permanent magnets (PMs). Owing to the magnetic pole distortion and the characteristic nonlinear force of PMs, conventional force estimation methods are less accurate for MLS-based actuators than for SEAs with mechanical springs. In the proposed method, to precisely estimate force of MLSs, the nonlinear force characteristic of an MLS is modeled with a sinusoidal force model, and the magnetic force hysteresis phenomenon is predicted based on Bouc–Wen-type hysteresis equations. Moreover, a method called the relative displacement normalization method is proposed to detect the magnetic pole distortion and to compensate for the related force estimation error. In addition, the proposed method is applied to a rotary-linear (RotLin) actuator, which is a novel MLS-based linear SEA. The force estimation accuracy is experimentally evaluated by comparison with existing methods. The results demonstrate that the root-mean-square error of the proposed method is less than that of the existing polynomial model by up to 81.2%. Finally, a force controller and a static force control system is designed with the proposed model to prove its feasibility.

Bagged tree ensemble modelling with feature selection for isometric EMG-based force estimation

EMG-based force estimation is crucial in applications, such as control of powered prosthetic and rehabilitation devices. Most previous studies focus on intra-subject force modelling. However, a generalized EMG-force estimation model, which is capable of estimating force across users, is needed for surgical and rehabilitation robotics. In this study, EMG signals are recorded from the long head and short head of the biceps brachii, and brachioradialis using 3 linear surface electrode arrays, during isometric elbow flexions, at different joint angles and forearm postures, while recording the induced force at the wrist. The recorded EMGs are pre-processed and segmented, and 336 time and frequency domain features are extracted from 21 EMG channels. We explore developing a model that can perform well across subjects, where Bagged Tree Ensemble (BTE) models are used to learn the non-linear, complex relationships between the EMG and force data. The BTE models are compared with several machine learning approaches. The BTE model performs best, giving an average normalized mean squared error (%NMSE) of 5.65±16.24%. To reduce the dimensionality of the feature space and improve force estimation performance, a novel feature selection technique, called modified sequential feature selection (MSFS) is implemented and compared to other commonly used feature selection methods. Results show that the MSFS algorithm outperformed other methods tested, significantly reducing the force estimation error. We also found that there was no effect of forearm posture and joint angle on force modelling accuracy, permitting the development of an isometric force estimation model generalized across participants and arm positions.

A Novel Interaction Controller Design for Robotic Manipulators With Arbitrary Convergence Time

In this brief, robot-environment interaction control problem of n-link robotic manipulator system without force sensors is investigated. At first, a novel sliding mode (SM) based two-layer adaptive force observer is proposed to estimate the robot-environment interaction force. In comparison with the most existing force observers, the proposed force observer ensures arbitrary-time convergence of the observer errors and relaxes assumptions on the external force. Moreover, an admittance controller is developed to ensure exact trajectory tracking within arbitrary time. It is mathematically proved that both trajectory tracking errors and force estimation errors will converge to zero at any setting time. Finally, numerical simulations and comparisons show that the proposed force observer-based control scheme can provide superior interaction performance.

How Many Muscles? Optimal Muscles Set Search for Optimizing Myocontrol Performance.

In myo-control, for computational and setup constraints, the measurement of a high number of muscles is not always possible: the choice of the muscle set to use in a myo-control strategy depends on the desired application scope and a search for a reduced muscle set, tailored to the application, has never been performed. The identification of such set would involve finding the minimum set of muscles whose difference in terms of intention detection performance is not statistically significant when compared to the original set. Also, given the intrinsic sensitivity of muscle synergies to variations of EMG signals matrix, the reduced set should not alter synergies that come from the initial input, since they provide physiological information on motor coordination. The advantages of such reduced set, in a rehabilitation context, would be the reduction of the inputs processing time, the reduction of the setup bulk and a higher sensitivity to synergy changes after training, which can eventually lead to modifications of the ongoing therapy. In this work, the existence of a minimum muscle set, called optimal set, for an upper-limb myoelectric application, that preserves performance of motor activity prediction and the physiological meaning of synergies, has been investigated. Analyzing isometric contractions during planar reaching tasks, two types of optimal muscle sets were examined: a subject-specific one and a global one. The former relies on the subject-specific movement strategy, the latter is composed by the most recurrent muscles among subjects specific optimal sets and shared by all the subjects. Results confirmed that the muscle set can be reduced to achieve comparable hand force estimation performances. Moreover, two types of muscle synergies namely “Pose-Shared” (extracted from a single multi-arm-poses dataset) and “Pose-Related” (clustering pose-specific synergies), extracted from the global optimal muscle set, have shown a significant similarity with full-set related ones meaning a high consistency of the motor primitives. Pearson correlation coefficients assessed the similarity of each synergy. The discovering of dominant muscles by means of the optimization of both muscle set size and force estimation error may reveal a clue on the link between synergistic patterns and the force task.

FBG-Based Estimation of External Forces Along Flexible Instrument Bodies.

A variety of medical treatment and diagnostic procedures rely on flexible instruments such as catheters and endoscopes to navigate through tortuous and soft anatomies like the vasculature. Knowledge of the interaction forces between these flexible instruments and patient anatomy is extremely valuable. This can aid interventionalists in having improved awareness and decision-making abilities, efficient navigation, and increased procedural safety. In many applications, force interactions are inherently distributed. While knowledge of their locations and magnitudes is highly important, retrieving this information from instruments with conventional dimensions is far from trivial. Robust and reliable methods have not yet been found for this purpose. In this work, we present two new approaches to estimate the location, magnitude, and number of external point and distributed forces applied to flexible and elastic instrument bodies. Both methods employ the knowledge of the instrument’s curvature profile. The former is based on piecewise polynomial-based curvature segmentation, whereas the latter on model-based parameter estimation. The proposed methods make use of Cosserat rod theory to model the instrument and provide force estimates at rates over 30 Hz. Experiments on a Nitinol rod embedded with a multi-core fiber, inscribed with fiber Bragg gratings, illustrate the feasibility of the proposed methods with mean force error reaching 7.3% of the maximum applied force, for the point load case. Furthermore, simulations of a rod subjected to two distributed loads with varying magnitudes and locations show a mean force estimation error of 1.6% of the maximum applied force.

Validation of Real-Time Nonlinear Model Predictive Control on Point Absorber Type Wave Energy Converter by Tank Test

Real-time implementation of a nonlinear model predictive control (NMPC) for a point absorber type wave energy converter (PAWEC) with a tubular air cored permanent magnet generator is experimentally validated through tank model tests. The control inputs of the NMPC were updated by the differential equation to trace the solution of an associated two-point boundary-value problem. Two conventional control strategies, the resistive load control and the approximate complex-conjugate control with considering the copper loss (ACL), and the NMPC were implemented to the PAWEC model. The floater heave motion, control force of the generator, and power generation characteristics were compared in these control strategies. The power generation performance of the NNPC was the same level of that of the ACL in regular and irregular waves. The sensitivities to the linear viscous damping estimation error and to the wave excitation force estimation error in the NMPC were experimentally evaluated by the tank model tests.

Sliding Mode Contact Force Control of n-Dof Robotics by Force Estimation

Control of the force exerted on an object is important for boosting system performance in robotics manipulators. Any undesired applied force may leave remarkable effects on the system, with the potential to damage the object. In addition, measuring external force is another challenge associated with such cases. Proposing an appropriate force estimation algorithm is a solution to overcome this deficiency. In this research, a control strategy is proposed to control the external force applied on the n-dof robotics. To eliminate force measurement in the controller, a force estimation strategy based on a disturbance observer is employed. Subsequently, a sliding-mode based control is implemented to cope with the force estimation error. The closed-loop stability of the system in the presence of estimated force is analytically considered. The proposed algorithm was implemented on piezoelectric actuators as the experimental setup. The experimental results confirm that by employing the proposed control scheme, precise force control is achievable. The force estimation algorithm can also suitably estimate external force.

Force compensation for precise positioning in machine tools via state observer design

In machining, cutting force generated is identified as input disturbance to the servo drive systems of the positioning table. In frequency domain, the cutting force magnitudes can be synthesized according to various harmonic components depending on the cutting tool spindle speed rotation. This paper focuses on compensation of high-frequency harmonic components of the cutting force using a state estimator named disturbance force observer (DFO) which explicitly estimates the input disturbance force. The force estimation error and tracking performances of the state estimator and the cascade P/PI positioning controller were analyzed experimentally on a single axis ball screw driven positioning table resembling a milling machine. The cascade P/PI controller was designed using traditional loop shaping frequency domain method while the force observer simultaneously estimated the input disturbance force based on the fundamental frequency dictated by the spindle rotational speeds. In experimental validations, a single, double, and triple harmonic-based force observers were designed at fundamental frequencies of 0.2 Hz, 0.5 Hz, and 0.8 Hz, and at amplitudes of 0.5 mm, 0.3 mm, and 0.2 mm, respectively. In time domain, the tracking performances of the system were analyzed and evaluated using root mean square of the position errors (RMSE) while in frequency domain, fast Fourier transform (FFT) analyses were performed on the tracking error signals. Results of the spectral analyses showed a 99.82% (single harmonic), 99.87% and 98.79% (two harmonics), and 99.83%, 97.13%, and 99.18% (three harmonics) reduction in respective force component magnitudes indicating close to successful estimation of the disturbance force observer. Meanwhile in time domain, numerical results of RMSE values showed reductions of 94.82%, 96.83%, and 94.01% for the three different input disturbance configurations while the experimental result showed reduction of 96.10%, 92.76%, and 92.44%, respectively. The work is to be expanded to include actual measured cutting forces as the input disturbance.

A Sensorless Hand Guiding Scheme Based on Model Identification and Control for Industrial Robot

Most industrial robots are not capable of teaching by hand and require path points to be specified by teaching pendants. To enable the teaching of industrial robots by hand without any force sensors, this paper proposes a scheme to minimize the external force estimation error and reduce disturbance in the guiding task by using the virtual mass and virtual friction model. In this case, the maximum velocity and acceleration of the robot end effector shall be limited to ensure safety. Thus, the operator is allowed to guide the robot by hand. The joint torque is obtained from the motor current. The inertial force and friction of the links and driving systems are analyzed. The nonlinear dynamic model of the industrial robot is built and its parameters are calibrated by a nonlinear method. The force estimation is referenced to set the virtual friction and to design the force-following controller. Hence the end effector can follow the direction of external force compliantly and suppress jitters. Finally, several experiments on a six degrees of freedom industrial robot demonstrate the validity of the proposed control scheme.

Fuzzy-Observer-Based Hybrid Force/Position Control Design for a Multiple-Sampling-Rate Bimanual Teleoperation System

In this paper, a novel fuzzy-observer-based hybrid force/position control method is investigated for a bimanual teleoperation system in the presence of dynamics uncertainties, random network-induced time delays, and multiple sampling rates of remote control signals and local measured data. The system structure consists of two pairs of position observers and contact force/torque estimators. The position observers are designed based on Takagi–Sugeno fuzzy inference rules to estimate the delayed remote state with low sampling rates. The force/torque estimators are designed for estimating the coupled item of uncertain dynamics and contact forces without acceleration information. By adding a compensatory item based on an auxiliary model, the force estimation and motion-tracking errors caused by varying dynamics uncertainties decrease, which is certified by two comparative force estimation techniques. The stability condition for the closed-loop system is also proved by the linear matrix inequality method based on the Lyapunov function. Finally, two simulations verify the effectiveness of the proposed method. The results indicate that the proposed method enables a better motion synchronization effect in soft-handling environment.

Heterogeneity Counts More than Power for HD-sEMG-Based Joint Force Estimation.

The aim of the proposed work is to utilize the heterogeneity information, in input signal extraction, to improve the joint force estimation from high-density surface electromyography (HD-sEMG). For this purpose, joint force and HD-sEMG signals from biceps brachii and brachialis were collected synchronously during isometric elbow flexion. The input signal of the force model was obtained after the following procedures: first, HD-sEMG signals were decomposed by principal component analysis into principal components and weight vectors; second, the first several weight maps were segmented to obtain heterogeneity information by the Otsu and Moore-Neighbor tracing methods, and the principal component covering the most activated areas (maximum heterogeneity) was selected; and last, the selected principal component was low-pass filtered to obtain the input signal. The force model was built using a polynomial fitting technique. The conventional power-based input signal was compared with our obtained input signal. According to the obtained results, the proposed heterogeneity-based input signal can reduce the force estimation error significantly than the power-based input signal. The proposed heterogeneity-based input signal extraction methods had more neuromuscular control information and will be tested in more muscles and force tasks in future works.

Model-Based Estimation of Individual Muscle Force Based on Measurements of Muscle Activity in Forearm Muscles During Isometric Tasks.

Several forward dynamics estimation approaches have been proposed to estimate individual muscle force. However, characterization of the estimation error that arises when measurements are available only from a subset of the muscles involved in the movement under analysis, as is the case of the forearm muscles, has been limited. Our objectives were: first, to quantify the accuracy of forward-dynamics muscle force estimators for forearm muscles; and second, to develop a muscle force estimator that is accurate even when measurements are available only from a subset of muscles acting on a given joint or segment. We developed a neuromusculoskeletal (NMSK) estimator that integrates forward dynamics estimation with a neural model of muscle cocontraction to estimate individual muscle force during isometric contractions, suitable to operate when measurements are not available for all muscles. We developed a computational framework to assess the effect of physiological variability in muscle cocontraction, cross-talk, and measurement error on the estimator accuracy using a sensitivity analysis. We thus compared the performance of our estimator with that of a standard estimator that neglects the contribution of unmeasured muscles. The NMSK estimator reduces the estimation error by 25% in average noise conditions. Moreover, the NMSK estimator is robust against physiological variability in muscle cocontraction and outperforms the standard estimator even when the validity of the neural model is compromised. In isometric tasks, the NMSK estimator reduces muscle force estimation error compared to a standard estimator, and may enable future applications involving estimation of forearm muscle force during coordinated movements.

Experimental characterization, modeling and compensation of hysteresis in force sensing resistors

Los Sensores de Fuerza Resistivos (FSRs) despliegan cantidades considerables de histéresis y de error de repetitividad que inhiben su uso en aplicaciones que requieren lecturas de fuerza de alta precisión. En este trabajo se presenta la caracterización y modelado de histéresis del sensor de presión Tekscan A201-1 empleando la función Operador de Preisach (OP). Con el fin de compensar la histéresis durante el funcionamiento del sensor, el OP inverso se halló numéricamente sobre la base del algoritmo de coincidencia más cercana (CMA). Se construyó un banco de pruebas, capaz de manejar dieciséis sensores simultáneamente, lo que permitió la caracterización y posterior prueba del CMA. Los perfiles de fuerza de agarre se aplicaron a los sensores durante la prueba y los resultados experimentales mostraron una reducción considerable del error de estimación de la fuerza en comparación con el método de regresión lineal propuesto por el fabricante. Estos resultados abren el camino para un uso más amplio de los FSRs en aplicaciones con exigentes requisitos de precisión. Finalmente, un modelo de sensor generalizado para compensación de histéresis que simplifica la obtención de los parámetros PO, es presentado.

A Back-EMF Estimation Error Compensation Method for Accurate Rotor Position Estimation of Surface Mounted Permanent Magnet Synchronous Motors

This paper proposes a back electromotive force estimation error compensation method for accurate rotor position estimation of surface mounted permanent magnet synchronous motors. When estimating the rotor position of surface mounted permanent magnet synchronous motor sensorless drives, a direct current offset error component occurs in the voltage sensor. As a result, the rotor position is distorted and the sensorless control in surface mounted permanent magnet synchronous motor is degraded. In addition, the dq-axis voltages in the synchronous reference frame have the direct current offset error component, ripples compared with the motor frequency under the distorted rotor position. In this paper, the effects of the direct current offset errors are analyzed based on the synchronous reference frame phase locked loop. To remove this direct current offset error component, a d-axis voltage is converted into a synchronous reference frame again to compensate. In other words, it is a dual synchronous coordinate conversion compensation method. The compensator utilizes a proportional-integral controller that compensates by estimating the direct current offset error component. The proposed method is useful for the improvement of surface mounted permanent magnet synchronous motor sensorless control and operating performance. The effectiveness of the proposed algorithm is verified through PSIM simulation and experimental results.