Joint Torque Estimation Research Articles

Joint Angle and Torque Estimation Using Multifrequency Electrical Impedance Myography and Surface Electromyography

Joint Angle and Torque Estimation Using Multifrequency Electrical Impedance Myography and Surface Electromyography

Joint torque estimation method of industrial robot by combining error compensation model based on LSTM and iterative weighted parameter identification

It is essential for human-robot interaction to accurate joint torque value estimation of industrial robots without force/torque (F/T) sensors. The most common method to estimate the value of robot joint torque is based on dynamic model parameter identification. However, no matter how elaborate the modeling methods are used, there are always uncertainty errors when robot’s joint rotation direction changes. In this paper, an identification framework is proposed to estimate optimal model parameters, and a deep learning network is proposed to compensate for the uncertainty errors caused by the unmodeled dynamics part. At first, the dynamic parameters are estimated during the Least Squares (LS) identification process considering the noise influence and data outliers, and the nonlinear friction model is unified into the identification framework. Secondly, based on Long-Short Term Memory (LSTM) network, an error compensation model (ECM) is proposed to establish the mapping relationship between the joint motion and the identification errors. Finally, a 6-DOF robot is used for parameter identification and ECM validation. Experimental results show that the proposed identification method is better than the LS method. Compared with the torque value estimated by the identification method, the proposed ECM can compensate for the uncertainty errors and improve the torque estimation accuracy.

Adaptive fast terminal sliding mode control of robotic manipulators based on joint torque estimation and friction compensation

AbstractIn this work, an adaptive fast terminal sliding mode control (AFSMC) approach based on joint torque estimation and friction compensation is proposed to enhance the trajectory tracking accuracy of robotic manipulators under variable load conditions. The joint torque estimation utilizes an improved harmonic drive compliance model and adaptive low‐pass filtering, and friction compensation employs a hybrid model accounting for velocity and load torque effects. These compensations reduce the upper bound of the uncertainty, while AFSMC further reduces dependency on upper uncertainty bounds and minimizes the chattering. The stability analysis using the Lyapunov method confirms the effectiveness of this approach. Experimental results demonstrate that the proposed controller achieves smaller root mean square and maximum error of trajectory tracking, thus significantly improving trajectory tracking accuracy under variable load conditions.

MOB-Net: Limb-modularized uncertainty torque learning of humanoids for sensorless external torque estimation

Momentum observer (MOB) can estimate external joint torque without requiring additional sensors, such as force/torque or joint torque sensors. However, the estimation performance of MOB deteriorates due to the model uncertainty which encompasses the modeling errors and the joint friction. Moreover, the estimation error is significant when MOB is applied to high-dimensional floating-base humanoids, which prevents the estimated external joint torque from being used for force control or collision detection in the real humanoid robot. In this paper, the pure external joint torque estimation method named MOB-Net, is proposed for humanoids. MOB-Net learns the model uncertainty torque and calibrates the estimated signal of MOB, substantially reducing the estimation errors of MOB. The external joint torque can be estimated in the generalized coordinate including whole-body and virtual joints of the floating-base robot with only internal sensors (an IMU on the pelvis and encoders in the joints). Furthermore, MOB-Net shows more robust performance for the unseen data compared to the end-to-end learning method, and the robustness of MOB-Net is validated through extensive simulations, real robot experiments, and ablation studies. Finally, various collision handling scenarios are presented to show the versatility of MOB-Net: contact wrench feedback control for locomotion, collision detection, and collision reaction for safety.

Estimation of joint torque in dynamic activities using wearable A-mode ultrasound

The human body constantly experiences mechanical loading. However, quantifying internal loads within the musculoskeletal system remains challenging, especially during unconstrained dynamic activities. Conventional measures are constrained to laboratory settings, and existing wearable approaches lack muscle specificity or validation during dynamic movement. Here, we present a strategy for estimating corresponding joint torque from muscles with different architectures during various dynamic activities using wearable A-mode ultrasound. We first introduce a method to track changes in muscle thickness using single-element ultrasonic transducers. We then estimate elbow and knee torque with errors less than 7.6% and coefficients of determination (R2) greater than 0.92 during controlled isokinetic contractions. Finally, we demonstrate wearable joint torque estimation during dynamic real-world tasks, including weightlifting, cycling, and both treadmill and outdoor locomotion. The capability to assess joint torque during unconstrained real-world activities can provide new insights into muscle function and movement biomechanics, with potential applications in injury prevention and rehabilitation.

Surface‐Level Muscle Deformation as a Correlate for Joint Torque

AbstractWearable technology excels in estimating kinematic and physiological data, but estimating biological torques remains an open challenge. Deformation of the skin above contracting muscles—surface‐level muscle deformation—has emerged as a promising signal for joint torque estimation. However, a lack of ground‐truth measures of surface‐level muscle deformation has complicated the evaluation of wearable sensors designed to measure surface‐level muscle deformation. A non‐contact methodology is proposed for ground‐truth measurement of surface‐level muscle deformation using a 2D laser profilometer. It shows how three metrics of surface‐level muscle deformation—peak radial displacement: r = 0.94 ± 0.05, surface curvature: r = 0.78 ± 0.10, surface strain: r = 0.83 ± 0.12—correlate strongly to changes in volitional elbow torque, further exploring the impact of measurement location or joint angle on these relationships. A nonlinear, lead‐lag relationship between surface‐level muscle deformation and torque is also found. The findings suggest that surface‐level muscle deformation is a promising signal for non‐invasive, real‐time estimates of torque. By standardizing measurement, the methodology can help inform the design of future wearable sensors.

Hybrid Adaptive Impedance and Admittance Control Based on the Sensorless Estimation of Interaction Joint Torque for Exoskeletons: A Case Study of an Upper Limb Rehabilitation Robot

Physiotherapy is the treatment to recover a patient’s mobility and limb function after an injury, illness, or disability. Rehabilitation robots can be used to replace human physiotherapists. To ensure safety during robot physical therapy, the patient’s limb needs to be controlled to track a desired joint trajectory, and the torque due to interaction force/torque needs to be measured and regulated. Therefore, hybrid impedance and admittance with position control (HIPC) is required to track the trajectory and simultaneously regulate the contact torque. The literature describes two structures of HIPC: (1) a switched framework between admittance and impedance control operating in parallel (HIPCSW); and (2) a series connection between admittance and impedance control without switching. In this study, a hybrid adaptive impedance and position-based admittance control (HAIPC) in series is developed, which consists of a proportional derivative-based admittance position controller with gravitational torque compensation and an adaptive impedance controller. An extended state observer is used to estimate the interaction joint torque due to human stiff contact with the exoskeleton without the use of force/torque sensor, which is then used in the adaptive algorithm to update the stiffness and damping gains of the adaptive impedance controller. Simulation results obtained using MATLAB show that the proposed HAIPC significantly reduces the mean absolute values of the actuation torques (control inputs) required for the shoulder and elbow joints in comparison with HIPC and HIPCSW.

A Fast Calibration Method for an sEMG-Based Lower Limb Joint Torque Estimation Model

The joint torque estimation model based on surface electromyography (sEMG) signals needs to recalibrate the model parameters when used for joint torque estimation at different volunteers. However, the feature transferability drops significantly in higher task-specific layers, which reduce the performance of the model. The generalization of joint torque estimation models among different volunteers has become a challenge. In this paper, a fast calibration method based on a deep adaptive regression network is proposed to reduce the frequency and time of model recalibration when volunteers change. The proposed method associates source domain (SD) data with target domain (TD) data through migration learning. The maximum mean difference (MMD) adaptive method is used to migrate the model trained in the SD dataset to the TD dataset, which avoids the recalibration required in the joint torque estimation model. The experimental results show that the proposed method can improve the migration ability of the model used for estimating joint torque and achieve the generalization application of the model on different volunteer datasets. Moreover, the proposed method can reduce the calibration operations and iterations of the model caused by volunteer changes and improve the speed of joint torque estimation. The optimal normalized root mean square error (NRMSE) and Pearson correlation coefficient (ρ) of knee extension/flexion joint torque estimation reached 0.02198/0.02565 and 0.9892/0.9839, respectively.

Dynamic Model of Lower Limb Motion in the Sagittal Plane during the Gait Cycle

Context: This work presents the development of a dynamic model for human lower limb motion in the sagittal plane during the gait cycle. The primary objective of this model is to serve as a powerful tool for the design of rehabilitation and assistive devices, such as exoskeletons, prostheses, and orthoses. It achieves this by facilitating the estimation of joint torques, the detailed analysis of kinematic variables, optimal actuator selection, and the exploration of advanced control techniques. Method: The dynamic model consists of two primary components: (1) the plant model and (2) a closed-loop controller. The plant model represents the forward dynamics of human gait and is based on a multi-mass pendulum composed of three segments of the lower limb (thigh, lower leg, and foot) and three joints (hip, knee, and ankle). It is analyzed using the Euler-Lagrange formulation and the nonlinear second-order differential equations are implemented in MATLAB’s Simulink. To reproduce reference human gait trajectories and simulate the functioning of the neuromusculoskeletal system and the central nervous system, a closed-loop PID controller is incorporated into the plant model. It is noteworthy that the scope of this dynamic model is specifically confined to the sagittal plane. Results: The dynamic model is evaluated in terms of angular displacement tracking using the relative maximum error (RME) and the root mean square error (RMSE) for reference trajectories of healthy adult male human gait as reported in the literature. The model demonstrates tracking with errors below 2.2 [°] in magnitude and 3,5% for all three considered segments (thigh, lower leg, and foot). Conclusions: The quantitative results show that the dynamic model developed in this work is reliable and allows for a precise reproduction of human gait trajectories.

Optimized Impedance Control of a Lightweight Gait Rehabilitation Exoskeleton Based on Accurate Knee Joint Torque Estimation

Optimized Impedance Control of a Lightweight Gait Rehabilitation Exoskeleton Based on Accurate Knee Joint Torque Estimation

Myoelectric Model Reference Adaptive Control with Adaptive Kalman Filter for a soft elbow exoskeleton

Rehabilitation and assistance exoskeletons have been widely studied because they allow to provide more effective, intensive, and adaptive therapies; in addition, they can be used to augment the user’s capabilities in order to provide movement assistance. In particular, soft robotic exoskeletons have been researched during the past decade because they allow the device to adapt to the body contours, increasing the user’s comfort. One of the main challenges in the development of soft robotic exoskeletons is the design of controllers that allow intuitive and active control of the device. This work addresses the development of a myoelectric Model Reference Adaptive Controller (MRAC) with an Adaptive Kalman Filter for controlling a cable driven soft elbow exoskeleton. The proposed MRAC controller proved to be suitable for both passive and active control of the soft elbow exoskeleton. The controlled system achieved a Mean Absolute Error (MAE) of approximately 4.5° in passive mode and 10° during active mode. Additionally, the active control mode allowed an average reduction of 34% to 40% in the joint torque RMS when performing dynamic Flexion–Extension movements. The active control mode is based on a surface electromyography (sEMG) joint torque estimation algorithm that achieved an approximate MAE of 1Nm. The proposed MRAC controller proved to be robust enough to adapt to the exoskeleton uncertainties and external disturbances; additionally, the adaptive scheme allowed the system to operate with only two sEMG channels and the measurement of the joint angle, which is estimated by using two Inertial Measurement Units.

Development and Dynamic State Estimation for Robotic Knee–Ankle Orthosis With Shape Memory Alloy Actuators

Abstract The development of rehabilitation robots has long been an issue of increasing interest in a wide range of fields. An important aspect of the ongoing research field is applying flexible components to rehabilitation equipment to enhance human−machine interaction. Another major challenge is to accurately estimate the individual’s intention to achieve safe operation and efficient training. In this article, a robotic knee−ankle orthosis (KAO) with shape memory alloy (SMA) actuators is developed, and the estimation method is proposed to determine the joint torque. First, based on the analysis of human lower limb structure and walking patterns, the mechanical design of the KAO that can achieve various rehabilitation training modes is detailed. Next, the dynamic model of the hybrid-driven KAO is established using the thermodynamic constitutive equation and Lagrange formalism. In addition, the joint torque estimation is realized by the nonlinear Kalman filter method. Finally, the prototype and human subject experiments are conducted, and the experimental results demonstrate that the KAO can assist lower limb movements. In the three experimental scenarios, reductions of 59.1%, 16.5%, and 73% of the torque estimation error during the knee joint movement are observed, respectively.

Physical Human–Robot Interaction Control of Variable Stiffness Exoskeleton With sEMG-Based Torque Estimation

Robotic exoskeleton assistance is an effective method for the treatment of patients with movement disorders. Firstly, this paper presents a variable stiffness knee exoskeleton robot (VS-KExo), which can independently control stiffness and position and has a large stiffness range under low preload. Then, combined with the designed variable stiffness exoskeleton, a physical human-robot interaction (pHRI) control scheme based on joint torque estimation is proposed. Different from previous studies, this method uses the mechanical properties of the exoskeleton to achieve pHRI without complex control algorithms and force/torque sensors. Furthermore, the joint torque is estimated based on the surface electromyography signal (sEMG) and the Hill-based muscle model, and the exoskeleton can realize assist-as-needed (AAN) function: 1) when the subject trains with less effort, the exoskeleton maintains a high output physical impedance to provide high tracking accuracy; and 2) when the subject trains with greater effort, the exoskeleton maintains a low output impedance to provide high physical compliance. Finally, we conducted experiments on three healthy subjects and two subjects with lower limb motor dysfunction to verify the effectiveness of the torque estimation method and the pHRI control scheme.

Automated spatial localization of ankle muscle sites and model-based estimation of joint torque post-stroke via a wearable sensorised leg garment.

Assessing a patient's musculoskeletal function during over-ground walking is a primary objective in post-stroke rehabilitation, due to the importance of walking recovery for everyday life. However, the quantitative assessment of musculoskeletal function currently requires lab-constrained equipment, and labor-intensive analyses, which hampers assessment in standard clinical settings. The development of fully wearable systems for the online estimation of muscle-tendon forces and resulting joint torque would aid clinical assessment of motor recovery, it would enhance the detection of neuro-muscular anomalies and it would consequently enable highly personalized treatments. Here, we present a wearable technology that combines (1) a soft garment for the human leg sensorized with 64 flexible and dry electromyography (EMG) electrodes, (2) a generalized and automated algorithm for the localization of leg muscle sites, and (3) an EMG-driven musculoskeletal modeling framework for the estimation of ankle dorsi-plantar flexion torques. Our results showed that the automated clustering algorithm could detect muscle locations in both healthy and post-stroke individuals. The estimated muscle-specific EMG envelopes could be used to drive forward person-specific musculoskeletal models and estimate resulting joint torques accurately across all healthy and post-stroke individuals and across different walking speeds (R2 >0.82 and RMSD <0.16). The technology we proposed opens new avenues for automated muscle localization and quantitative musculoskeletal function assessment during gait in both healthy and neurologically impaired individuals.

Strain Gauge Neural Network-Based Estimation as an Alternative for Force and Torque Sensor Measurements in Robot Manipulators

When a robotic manipulator interacts with its environment, the end-effector forces need to be measured to assess if a task has been completed successfully and for safety reasons. Traditionally, these forces are either measured directly by a 6-dimensional (6D) force–torque sensor (mounted on a robot’s wrist) or by estimation methods based on observers, which require knowledge of the robot’s exact model. Contrary to this, the proposed approach is based on using an array of low-cost 1-dimensional (1D) strain gauge sensors mounted beneath the robot’s base in conjunction with time series neural networks, to estimate both the end-effector 3-dimensional (3D) interaction forces as well as robot joint torques. The method does not require knowledge of robot dynamics. For comparison reasons, the same approach was used but with 6D force sensor measurements mounted beneath the robot’s base. The trained networks showed reasonably good performance, using the long-short term memory (LSTM) architecture, with a root mean squared error (RMSE) of 1.945 N (vs. 2.004 N; 6D force–torque sensor-based) for end-effector force estimation and 3.006 Nm (vs. 3.043 Nm; 6D force–torque sensor-based) for robot joint torque estimation. The obtained results for an array of 1D strain gauges were comparable with those obtained with a robot’s built-in sensor, demonstrating the validity of the proposed approach.

Accurate Real-Time Joint Torque Dynamic Prediction of Human Estimation for Locomotion.

Inverse dynamics is a common tool for determining human joint torques during walking. The traditional approaches rely on ground reaction force and kinematics measurements prior to analysis. A novel real-time hybrid method is proposed in this work by integrating a neural network and dynamic model that only requires kinematic data. An end-to-end neural network for direct joint torque estimation is also developed based on kinematic data. The neural networks are trained on a variety of walking conditions, including starting and stopping, sudden speed changes, and asymmetrical walking. The hybrid model is first tested in a detailed dynamic gait simulation (OpenSim) which results in root mean square errors less than 5 N.m and a correlation coefficient of greater than 0.95 for all the joints. Experiments demonstrate that the end-to-end model on average outperforms the hybrid model across the whole test when compared to the gold standard approach which requires both kinetic and kinematic information. The two torque estimators are also tested on one participant wearing a lower limb exoskeleton. In this case, the hybrid model (R>0.84) has significantly better performance than the end-to-end neural network (R>0.59). This indicates that the hybrid model is better applicable to scenarios which differ from the training data.

Muscle-Driven Joint-Torque Estimation Based on Voltage-Torque Mapping of Electrical Impedance Sensing

This paper offers an impedance sensing method taking advantage of the conductivity changes due to muscle contraction to estimate muscle-driven joint torques through a convolutional neural network (CNN) where the input images are derived from a finite set of boundary voltage measurements. Guided by a physical model combining the forearm biomechanics and the muscle electric field along with the CNN criteria considering the receptive fields, the effects of two image formats (for quasi-static and dynamic states) on the CNN performance are experimentally studied on eight human subjects’ forearms using a prototype impedance sensing system. By comparing the CNN-estimated torques with that measured on a haptic device, the findings verify that the impedance-based method can estimate the joint torques driven by both the deep and superficial muscles within 9% errors of the three degrees-of-freedom wrist torque and 10% error of the gripping torque, and that it is feasible to share data among a similar group to reduce data collection and time when training a CNN for uses on a new subject.

A nonlinear robot joint friction compensation method including stick and sliding characteristics

PurposeDue to dynamic model is the basis of realizing various robot control functions, and it determines the robot control performance to a large extent, this paper aims to improve the accuracy of dynamic model for n-Degree of Freedom (DOF) serial robot.Design/methodology/approachThis paper exploits a combination of the link dynamical system and the friction model to create robot dynamic behaviors. A practical approach to identify the nonlinear joint friction parameters including the slip properties in sliding phase and the stick characteristics in presliding phase is presented. Afterward, an adaptive variable-step moving average method is proposed to effectively reduce the noise impact on the collected data. Furthermore, a radial basis function neural network-based friction estimator for varying loads is trained to compensate the nonlinear effects of load on friction during robot joint moving.FindingsExperiment validations are carried out on all the joints of a 6-DOF industrial robot. The experimental results of joint torque estimation demonstrate that the proposed strategy significantly improves the accuracy of the robot dynamic model, and the prediction effect of the proposed method is better than that of existing methods.Originality/valueThe proposed method extends the robot dynamic model with friction compensation, which includes the nonlinear effects of joint stick motion, joint sliding motion and load attached to the end-effector.

Development of a hierarchical control strategy for a soft knee exoskeleton based on wearable multi-sensor system

Soft exoskeleton is a newly emerging approach for providing assistive forces to the movement of disabled individuals, which has aroused the interest of many researchers due to its promising prospects in rehabilitation training and motion assistance. In this article, a wearable wireless multi-sensor system and a hierarchical control architecture are developed for a soft knee exoskeleton. First, the major components of the soft knee exoskeleton are introduced, including the flexible Bowden-cable actuators, the soft wearable components, and the sensing modules and the control system. The wearable wireless multi-sensor system consists of an inertial measurement unit–based knee flexion–extension angle sensing module, a surface electromyogram–based joint torque estimation module, a miniature pulling force sensing module, and a central communication unit. And then, a three-level hierarchical control strategy—which fuses a high-level motion recognition and torque estimation algorithm, a mid-level knee trajectory generation strategy, and a low-level fuzzy impedance controller—is proposed to realize human motion assistance. Finally, experiments are carried out to verify the effectiveness of the proposed control strategy. The experimental setup is established with the soft knee exoskeleton, a treadmill, a wearable robotic rotary joint with an encoder, and an inelastic rope. The experimental result indicates that the root mean square errors of the joint angle estimation strategy and joint torque estimation strategy are less than 4.3° and 4.8 Nm, while the surface electromyogram–based assistance efficiency and torque-based assistance efficiency under different loading conditions are higher than 10.2% and 18.2%, respectively.

Adaptive Cooperative Control Strategy for a Wrist Exoskeleton Using Model-Based Joint Impedance Estimation

Wrist rehabilitation exoskeletons have gained much attention over the last decades, striving to restore motor functions for patients with neuromuscular disorders. Electromyography signal has been employed to estimate the motion intention to achieve interactive training schemes. However, it is a challenging task to estimate the joint impedance in real time, as it is a crucial parameter for control of exoskeletons. This article proposes an adaptive cooperative control strategy for a wrist exoskeleton based on a real-time joint impedance estimation approach. By explicitly interpreting the underlying transformation in the muscular and skeletal systems, the proposed approach estimates the motion intention and the joint impedance of a human subject simultaneously without additional calibration procedures and regulates the training trajectories and assistance accordingly. Results indicate the proposed method outperforms other training protocols, including the trajectory tracking control and the fixed cooperative control. The proposed control strategy provides an additional 66.25% motion deviation when estimated joint torque increases 12.36%, which enhances the training effectiveness and the interaction safety and promotes subjects' active engagement.