Inverse Dynamics Research Articles

PID/FOPID Tuning Rule Based on a Second Order Inverse Response Process Model with Robustness Considerations

This paper deals with the design of a proportional-integral-derivative (PID) and fractional-order proportional-integral-derivative (FOPID) controller tuning rule for second-order controlled processes with inverse response. The design of the rules takes into account specific levels of robustness and performance for both load disturbance rejection and set-point tracking tasks. In the first step, the optimal parameters for both controllers are obtained from optimizations that seek to minimize the error in both control modes while maintaining the robustness constraint. Subsequently, fitting functions to the optimal parameters are sought to capture their behavior with the possibility of finding optimal parameters with the tuning rule designed between certain ranges of the model parameters. For FOPID and PID controllers, the rule IRM-RoT (Inverse Response Model Robust Tuning) have been developed. The performance of the controllers was compared using examples, and the results showed that fractional order controllers provide a novel solution for inverse response dynamics in process control.

Achieving kinematic identity across shape diversity in musculoskeletal modeling

Musculoskeletal modeling is emerging as a powerful approach to investigate the locomotor biomechanics of extinct taxa. These models rely on bony morphology to define joint locations and muscle geometry. Using different motion profiles to drive models of extinct and extant taxa complicates comparisons because results reflect both morphological and kinematic differences. Here we report on an approach that permits changes in shape while maintaining model kinematics. Using a human musculoskeletal model, we carried out walking simulations of ten humans. Next, we morphed the model pelvis and proximal femur to match a reconstructed australopithecine pelvis and proximal femur. Using the kinematic results from the human walking simulations, we created new motion files based on the positions of joint centers and tracked anatomical locations. These files were used to drive simulations of the same walking trials with the australopithecine model. Joint centers and axes of the human and australopithecine models were compared for each walking trial simulation. We found that joint centers in the australopithecine simulations were typically within ~1µm of their locations in human simulations, and joint axes differed by less than 0.005 degrees. Such small differences have negligible effects on external joint moments calculated during inverse dynamics analyses. This conservative comparison will serve as a baseline for more complex simulations. Although this work focuses on one taxon, the approach outlined is applicable to a wide variety of extinct animals.

Masked and Inverse Dynamics Modeling for Data-Efficient Reinforcement Learning.

In pixel-based deep reinforcement learning (DRL), learning representations of states that change because of an agent's action or interaction with the environment poses a critical challenge in improving data efficiency. Recent data-efficient DRL studies have integrated DRL with self-supervised learning (SSL) and data augmentation to learn state representations from given interactions. However, some methods have difficulties in explicitly capturing evolving state representations or in selecting data augmentations for appropriate reward signals. Our goal is to explicitly learn the inherent dynamics that change with an agent's intervention and interaction with the environment. We propose masked and inverse dynamics modeling (MIND), which uses masking augmentation and fewer hyperparameters to learn agent-controllable representations in changing states. Our method is comprised of a self-supervised multitask learning that leverages a transformer architecture, which captures the spatiotemporal information underlying in the highly correlated consecutive frames. MIND uses two tasks to perform self-supervised multitask learning: masked modeling and inverse dynamics modeling. Masked modeling learns the static visual representation required for control in the state, and inverse dynamics modeling learns the rapidly evolving state representation with agent intervention. By integrating inverse dynamics modeling as a complementary component to masked modeling, our method effectively learns evolving state representations. We evaluate our method by using discrete and continuous control environments with limited interactions. MIND outperforms previous methods across benchmarks and significantly improves data efficiency. The code is available at https://github.com/dudwojae/MIND.

Ferroelectricity of alkylamide-substituted triptycene derivatives

Ferroelectricity based on inversion dynamics of intermolecular amide hydrogen bonds in two-dimensional layers formed by three-fold symmetric triptycene molecules.

Prediction of Fusion Rod Curvature Angles in Posterior Scoliosis Correction Using Artificial Intelligence.

This study aimed to estimate post-operative rod angles in both concave and convex sides of scoliosis curvature in patients who had undergone posterior surgery, using neural networks and support vector machine (SVM) algorithms. Radiographs of 72 scoliotic individuals were obtained to predict post-operative rod angles at all fusion levels (all spinal joints fused by rods). Pre-operative radiographical indices and pre-operatively resolved net joint moments of the apical vertebrae were employed as inputs for neural networks and SVM with biomechanical modeling using inverse dynamics analysis. Various group combinations were considered as inputs, based on the number of pre-operative angles and moments. Rod angles on both the concave and convex sides of the Cobb angle were considered as outputs. To assess the outcomes, root mean square errors (RMSEs) were evaluated between actual and predicted rod angles. Among eight groups with various combinations of radiographical and biomechanical parameters (such as Cobb, kyphosis, and lordosis, as well as joint moments), RMSEs of groups 4 (with seven radiographical angles in each case, which is greater in quantity) and 5 (with four radiographical angles and one biomechanical moment in each case, which is the least possible number of inputs with both radiographical and biomechanical parameters) were minimum, particularly in prediction of the concave rod kyphosis angle (errors were 5.5° and 6.3° for groups 4 and 5, respectively). Rod lordosis angles had larger estimation errors than rod kyphosis ones. Neural networks and SVM can be effective techniques for the post-operative estimation of rod angles at all fusion levels to assist surgeons with rod bending procedures before actual surgery. However, since rod lordosis fusion levels vary widely across scoliosis cases, it is simpler to predict rod kyphosis angles, which is more essential for surgeons.

Posture-induced modulation of lower-limb joint powers in perturbed running.

Despite evidence on trunk flexion's impact on locomotion mechanics, its role in modulating lower-limb energetics during perturbed running remains underexplored. Therefore, we investigated posture-induced power redistribution in the lower-limb joints (hip, knee, and ankle), along with the relative contribution from each joint to total lower-limb average positive and negative mechanical powers (i.e., over time) during perturbed running. Twelve runners (50% female) ran at self-selected (~15°) and three more sagittal trunk inclinations (backward, ~0°; low forward, ~20°; high forward, ~25°) on a custom-built runway, incorporating both a level surface and a 10 cm visible drop-step positioned midway, while simultaneously recording three-dimensional kinematics and kinetics. We used inverse dynamics analysis to determine moments and powers in lower-limb joints. Increasing the trunk forward inclination yielded the following changes in lower-limb mechanics: a) an elevation in total positive power with a distoproximal shift and a reduction in total negative power; b) systematic increases in hip positive power, coupled with decreased and increased contribution to total negative (during level-step) and positive (during drop-step) powers, respectively; c) reductions in both negative and positive knee powers, along with a decrease in its contribution to total positive power. Regardless of the trunk posture, accommodating drop-steps while running demands elevated total limb negative and positive powers with the ankle as a primary source of energy absorption and generation. Leaning the trunk more forward induces a distoproximal shift in positive power, whereas leaning backward exerts an opposing influence on negative power within the lower-limb joints.

Inverse Dynamics Modeling as a State Estimation Aid for Underwater Robots Navigation

Inverse Dynamics Modeling as a State Estimation Aid for Underwater Robots Navigation

Transfer of Safety Controllers Through Learning Deep Inverse Dynamics Model

Control barrier certificates have proven effective in formally guaranteeing the safety of the control systems. However, designing a control barrier certificate is a time-consuming and computationally expensive endeavor that requires expert input in the form of domain knowledge and mathematical maturity. Additionally, when a system undergoes slight changes, the new controller and its correctness certificate need to be recomputed, incurring similar computational challenges as those faced during the design of the original controller. Prior approaches have utilized transfer learning to transfer safety guarantees in the form of a barrier certificate while maintaining the control invariant. Unfortunately, in practical settings, the source and the target environments often deviate substantially in their control inputs, rendering the aforementioned approach impractical. To address this challenge, we propose integrating inverse dynamics—a neural network that suggests required action given a desired successor state—of the target system with the barrier certificate of the source system to provide formal proof of safety. In addition, we propose a validity condition that, when met, guarantees correctness of the controller. We demonstrate the efficacy of our method with an inverted pendulum case study.

Global Event-Triggered Funnel Control of Switched Nonlinear Systems via Switching Multiple Lyapunov Functions.

In this article, the global event-triggered (ET) funnel tracking control problem is studied for a class of switched nonlinear systems with structural uncertainties, where the solvability of the control problem for each subsystem is not needed. A switching multiple Lyapunov functions (MLFs) method is established, where MLFs are designed to handle switched inverse dynamics, and a switching barrier Lyapunov function is constructed to address switched sampled errors that may compromise system stability. This is achieved alongside a new switching dynamic event-triggering mechanism (DETM). By combining this method with backstepping, a dwell-time state-dependent switching law and an ET funnel controller of each subsystem are constructed, effectively eliminating the issue of the "explosion of complexity" encountered in traditional backstepping without using dynamic surface control or command filters. Additionally, the designed switching DETM ensures that the tracking error always evolves within a performance funnel in any consecutive triggering interval, excluding Zeno behavior, and guaranteeing positive constant lower bounds for two consecutive triggering intervals and any switching interval, respectively. Finally, an example is provided to show the validity of the theoretical results.

Robust trajectory tracking of quadrotors using adaptive radial basis function network compensation control

Radial Basis Function Neural Networks (RBFNN) methods have gained incredible efficiency and applicability in control. This paper presents a nested control strategy for robust trajectory tracking of a quadrotor using adaptive RBF compensation and NN-supervised control embedded with Integrator BackStepping (IBS). The approach addresses the robustness in the presence of modeling uncertainties, sensing noise, and bounded disturbances. The control design is derived from the decentralized inverse dynamics, using adaptive RBFNN for outer-loop disturbance approximation and compensation. In conjunction with an Inner-loop supervised control that stabilizes the quadrotor attitude, preventing initial instability during NN convergence. In addition, an adaptive Extended Kalman Filter (EKF) attenuates noisy signals. Simulation results demonstrate strong adaptability to changes in model parameters, and superior performance when compared to Proportional Integral Derivative (PID), Integrator BackStepping (IBS), and offline decentralized Multi-Layer Perceptron (MLP) algorithms, in terms of parameter convergence, disturbance compensation control, and noise attenuation.

Performance Comparison Between Centralized and Hierarchical Predictive Functional Control for Adaptive Cruise Control Application

This paper presents a performance comparison between two different control structures of Predictive Functional Control (PFC), namely centralized and hierarchical architectures for an Adaptive Cruise Control (ACC) system. Centralized PFC utilizes a linearized model of the vehicle longitudinal dynamics to compute the control law, while hierarchical PFC uses a simple kinematic model with inverse vehicle longitudinal dynamics. Based on the simulation results, both control structures produced a satisfactory performance. However, in the presence of disturbances such as road slopes and wind gusts, the centralized PFC becomes more sensitive and conservative than the hierarchical PFC. The main reason is that the linearization model used in centralized PFC is only effective around the selected nominal operating points. Since the decision-making process depends on the internal model performance, centralized PFC cannot compensate for this effect. Besides, it also takes a longer computation time than hierarchical PFC since more mathematical operations must be solved than the kinematic model, especially when physical and operational constraints are considered. The standard performance parameters such as Root Mean Squared Error (RMSE), settling time, and rise time are also used for the analysis. These findings can become a solid justification for using the hierarchical PFC structure in designing an ACC system for future work.

The gait1415+2 OpenSim musculoskeletal model of transfemoral amputees with a generic bone-anchored prosthesis

This short communication presents the gait1415+2 musculoskeletal model, that has been developed in OpenSim to describe the lower-extremity of a human subject with transfemoral amputation wearing a generic lower-limb bone-anchored prosthesis. The model has fourteen degrees of freedom, governed by fifteen musculotendon units (placed at the contralateral and residual limbs) and two generic actuators (one placed at the knee joint and one at the ankle joint of the prosthetic leg). Even though the model is a simplified abstraction, it is capable of generating a human-like walking gait and, specifically, it is capable of reproducing both the kinematics and the dynamics of a person with transfemoral amputation wearing a bone-anchored prosthesis during normal level-ground walking. The model is released as support material to this short communication with the final goal of providing the scientific community with a tool for performing forward and inverse dynamics simulations, and for developing computationally-demanding control schemes based on artificial intelligence methods for lower-limb prostheses.

A Comparative Analysis of Optimal and Biomechanical Torque Control Strategies for Powered Knee Exoskeletons in Squat Lifting

Abstract Exoskeletons have the ability to aid humans in physically demanding and injury-prone activities, such as lifting loads while squatting. However, despite their immense potential, the control of powered exoskeletons remains a persistent challenge. In this study, we first predict the human lifting motion and knee joint torque using an inverse dynamics optimization formulation with a two-dimensional (2D) human skeletal model. The design variables are human joint angle profiles. The normalized human joint torque squared is minimized subject to physical and lifting task constraints. After that, the biomechanical assistive knee exoskeleton torque is obtained by scaling the predicted human knee joint torque. Second, we also present a 2D human skeletal model with a powered knee exoskeleton for predicting the optimal assistive torque and lifting motion. The design variables are human joint angle profiles and exoskeleton motor current profiles. Then, the biomechanical and optimal exoskeleton torques are implemented in a powered knee exoskeleton in real-time to provide external assistance in human lifting motion. Finally, the biomechanical and optimal assistive exoskeleton torque controls for lifting are compared. It is observed that both control methods have a significant impact on reducing muscle activations for the specific muscle groups compared to the cases without the exoskeleton. Especially, peak activations of erector spinae and rectus femoris muscles are reduced by 57.79% and 47.26% with biomechanical assistive torque. Likewise, vastus medialis and vastus lateralis activations drop by 46.82% and 52.24% with optimal assistive torque.

Hip joint and muscle loading for persons with bilateral transfemoral/through-knee amputations: biomechanical differences between full-length articulated and foreshortened non-articulated prostheses

BackgroundCurrently, there is little available in-depth analysis of the biomechanical effect of different prostheses on the musculoskeletal system function and residual limb internal loading for persons with bilateral transfemoral/through-knee amputations (BTF). Commercially available prostheses for BTF include full-length articulated prostheses (microprocessor-controlled prosthetic knees with dynamic response prosthetic feet) and foreshortened non-articulated stubby prostheses. This study aims to assess and compare the BTF musculoskeletal function and loading during gait with these two types of prostheses.MethodsGait data were collected from four male traumatic military BTF and four able-bodied (AB) matched controls using a 10-camera motion capture system with two force plates. BTF completed level-ground walking trials with full-length articulated and foreshortened non-articulated stubby prostheses. Inverse kinematics, inverse dynamics and musculoskeletal modelling simulations were conducted.ResultsFull-length articulated prostheses introduced larger stride length (by 0.5 m) and walking speed (by 0.3 m/s) than stubbies. BTF with articulated prostheses showed larger peak hip extension angles (by 10.1°), flexion moment (by 1.0 Nm/kg) and second peak hip contact force (by 3.8 bodyweight) than stubbies. There was no difference in the hip joint loading profile between BTF with stubbies and AB for one gait cycle. Full-length articulated prostheses introduced higher hip flexor muscle force impulse than stubbies.ConclusionsCompared to stubbies, BTF with full-length articulated prostheses can achieve similar activity levels to persons without limb loss, but this may introduce detrimental muscle and hip joint loading, which may lead to reduced muscular endurance and joint degeneration. This study provides beneficial guidance in making informed decisions for prosthesis choice.

A Deep Learning Approach for Biped Robot Locomotion Interface Using a Single Inertial Sensor.

In this study, we introduce a novel framework that combines human motion parameterization from a single inertial sensor, motion synthesis from these parameters, and biped robot motion control using the synthesized motion. This framework applies advanced deep learning methods to data obtained from an IMU attached to a human subject's pelvis. This minimalistic sensor setup simplifies the data collection process, overcoming price and complexity challenges related to multi-sensor systems. We employed a Bi-LSTM encoder to estimate key human motion parameters: walking velocity and gait phase from the IMU sensor. This step is followed by a feedforward motion generator-decoder network that accurately produces lower limb joint angles and displacement corresponding to these parameters. Additionally, our method also introduces a Fourier series-based approach to generate these key motion parameters solely from user commands, specifically walking speed and gait period. Hence, the decoder can receive inputs either from the encoder or directly from the Fourier series parameter generator. The output of the decoder network is then utilized as a reference motion for the walking control of a biped robot, employing a constraint-consistent inverse dynamics control algorithm. This framework facilitates biped robot motion planning based on data from either a single inertial sensor or two user commands. The proposed method was validated through robot simulations in the MuJoco physics engine environment. The motion controller achieved an error of ≤5° in tracking the joint angles demonstrating the effectiveness of the proposed framework. This was accomplished using minimal sensor data or few user commands, marking a promising foundation for robotic control and human-robot interaction.

Artificial physics engine for real-time inverse dynamics of arm and hand movement.

Simulating human body dynamics requires detailed and accurate mathematical models. When solved inversely, these models provide a comprehensive description of force generation that considers subject morphology and can be applied to control real-time assistive technology, for example, orthosis or muscle/nerve stimulation. Yet, model complexity hinders the speed of its computations and may require approximations as a mitigation strategy. Here, we use machine learning algorithms to provide a method for accurate physics simulations and subject-specific parameterization. Several types of artificial neural networks (ANNs) with varied architecture were tasked to generate the inverse dynamic transformation of realistic arm and hand movement (23 degrees of freedom). Using a physical model, we generated representative limb movements with bell-shaped end-point velocity trajectories within the physiological workspace. This dataset was used to develop ANN transformations with low torque errors (less than 0.1 Nm). Multiple ANN implementations using kinematic sequences solved accurately and robustly the high-dimensional kinematic Jacobian and inverse dynamics of arm and hand. These results provide further support for the use of ANN architectures that use temporal trajectories of time-delayed values to make accurate predictions of limb dynamics.

INVERSE AND FORWARD KINEMATICS AND DYNAMICS OF A TWO LINK ROBOT ARM

This paper deals with the kinematic and dynamic analysis of a two-element robot model. We have solved the problem using inverse kinematics. The result is the plotted trajectory of the robot's end point along defined points of the robot's workspace. The angular quantities computed are the rotation angle, angular velocity and angular acceleration in each kinematic pair. Furthermore, an inverse dynamics problem is solved. The moments in the kinematic pairs are computed. Subsequently, using the direct dynamics problem, the correctness of the obtained solution is confirmed. The programs designed for the simulation of dynamical systems - Matlab/Simulink and SimMechanics - were used in the solution. The results are presented in the form of graphs and tables.

Determining the effects of AR/VR HMD design parameters (mass and inertia) on cervical spine joint torques

This study aimed to determine gravitational and dynamic torques and muscle activity of the neck across a series of design parameters of head mounted displays (mass, center of mass, and counterweights) associated with virtual and augmented reality (VR/AR). Twenty young adult participants completed five movement types (Slow and Fast Flexion/Extension and Rotation, and Search) while wearing a custom-designed prototype headset that varied the three design parameters: display mass (0, 200, 500, and 750 g), distance of the display's center of mass in front of the eyes (approximately 1, 3, and 5 cm anteriorly), and counterweights of 0, 166, 332, and 500 g to balance the display mass of 500 g at 7 cm. Inverse dynamics of a link segment model of the head and headset provided estimates of the torques about the joint between the skull and the occiput-first cervical vertebrae (OC1) and joint between the C7 and T1 vertebrae (C7). Surface electromyography (EMG) measured bilateral muscle activity of the splenius and upper trapezius muscles. Adding 750 g of display mass nearly doubled root mean square joint torques across all movement types. Increasing the distance of the display mass in front of the eyes by 4 cm increased torques about OC1 for the Slow and Fast Rotation and Search movements by approximately 20%. Adding a counterweight decreased torques about OC1 during the rotation and search tasks but did not decrease the torques experienced in the lower cervical spine (C7). For the flexion/extension axis, the magnitude of the dynamic torque component was 20% or less of the total torque experienced whereas for the rotation axis the magnitude of the dynamic torque component was greater than 50% of the total torque. Surface EMG root mean square values significantly varied across movement types with the fast rotation having the largest values; however, they did not vary significantly across the headset configurations.

Performance Improvement of Human Centrifuge Systems through Multi-Objective Configurational Design Optimisation

Human Centrifuge Systems (HCSs) are an effective training tool to improve the G-acceleration and Spatial Disorientation (SD) tolerance of aircrew. Though highly capable HCSs are available, their structure and performance are yet to be fully optimised to efficiently recreate the G-vectors produced using Aircraft Combat Manoeuvres (ACMs). To achieve this improvement, the relationship between configurational design and HCS performance should be profoundly investigated. This work proposes a framework for identifying the optimal configurational design of an active four Degree-of-Freedom (DoF) HCS. The relationship between configurational design parameters and objective criteria is established using inverse kinematics and dynamics. Then, a multi-objective evolutionary optimiser is used to identify the optimum arm length and seat position, minimising the Coriolis effect, relative acceleration ratio, and cost. The results of the work show that the applied optimisation step can significantly contribute to (1) efficiently replicating the aircraft motion, (2) minimising the detrimental effects generated during HCS motion, and (3) reducing the overall cost of the system. The applied methodology can be adapted to HCSs with different structures and DoFs.

Lower Limb Joint Torque Prediction Using Long Short-Term Memory Network and Gaussian Process Regression

The accurate prediction of joint torque is required in various applications. Some traditional methods, such as the inverse dynamics model and the electromyography (EMG)-driven neuromusculoskeletal (NMS) model, depend on ground reaction force (GRF) measurements and involve complex optimization solution processes, respectively. Recently, machine learning methods have been popularly used to predict joint torque with surface electromyography (sEMG) signals and kinematic information as inputs. This study aims to predict lower limb joint torque in the sagittal plane during walking, using a long short-term memory (LSTM) model and Gaussian process regression (GPR) model, respectively, with seven characteristics extracted from the sEMG signals of five muscles and three joint angles as inputs. The majority of the normalized root mean squared error (NRMSE) values in both models are below 15%, most Pearson correlation coefficient (R) values exceed 0.85, and most decisive factor (R2) values surpass 0.75. These results indicate that the joint prediction of torque is feasible using machine learning methods with sEMG signals and joint angles as inputs.