Accurate Dynamic Model Research Articles

Complete Kinematics/Dynamics Modeling and Performance Analysis of a Novel SCARA Parallel Manipulator Based on Screw Theory

Abstract In this paper, a novel Selective Compliance Assembly Robot Arm (SCARA) high-speed parallel manipulator that can realize three-translation and one-rotation motion is proposed, and an accurate dynamic modeling methodology is investigated. The mechanism is composed of four limbs with a double parallelogram structure and a single moving platform. The high bearing capacity and high dynamic response of the novel mechanism make it a viable alternative choice for this kind of automation equipment. The degree-of-freedom (DOF) of the mechanism is analyzed by the screw theory. At the same time, the velocity mapping model of the mechanism is established by the twist screw and the actuated Jacobian matrix. Then, the acceleration mapping model of the mechanism, including the generalized kinematic pairs, is established by reduced acceleration state, the modified Lie screw, and the acceleration Hessian matrix. On this basis, the complete dynamic model with a compact form of the mechanism is deduced by the combination of screw theory and virtual work principle, and the correctness of the developed model is verified by multibody simulation software. Finally, considering the inertial characteristics of the mechanism, the dynamic performance distribution in the reachable workspace of the mechanism is analyzed by the Joint-Reflected Inertia (JRI) index and Coefficient of Variation of joint-space Inertia (CVI) index, and some areas are selected as the task workspace using the above index to guarantee good dynamic performance.

Adaptive Compensation Tracking Control for Parallel Robots Actuated by Pneumatic Artificial Muscles With Error Constraints

As pneumatic artificial muscles (PAMs) are similar to biological muscles in structure and movement mechanisms, parallel robots actuated by PAMs have development prospects in rehabilitation and industry, with advantages such as compliance, high safety, strong bearing capacity, and satisfactory dynamic performance. However, the parameter uncertainties and model complexity related to inherent characteristics of parallel robots actuated by PAMs (e.g., time-varying, coupling, hysteresis, creep, and high nonlinearity), bring challenges to accurate dynamic modeling and controller design. Therefore, to achieve satisfactory tracking performance, this paper presents an adaptive compensation tracking controller with error constraints for parallel robots actuated by PAMs. The proposed controller deals with parameter uncertainties by estimating system parameters to ensure accurate tracking, which is indicated as an effective solution for a combination of PAMs and parallel robots. Furthermore, using desired trajectory signals in the complicated regression matrix, the online computational burden is significantly reduced. Moreover, to improve operation safety further, an auxiliary term with a theoretical demonstration guarantees that the tracking errors are maintained within allowable ranges. Then, the closed-loop stability is demonstrated by Lyapunov techniques. As far as we know, it is the first time that the challenges of parameter uncertainties, computational burdens, and error constraints of parallel robots actuated by PAMs are simultaneously addressed, which has both theoretical significance and practical value. Finally, the hardware experiments are implemented under different scenarios, and the results indicate that the proposed method achieves satisfactory tracking performance.

On Accurate Discrete-Time Dynamic Models of an Induction Machine

Induction machines have become the standard for highly demanding industrial applications. This has led to the utilization of modern discrete-time control techniques (such as model predictive control) that require the estimation of internal variables that are not subject to measurement (such as the rotational velocity in sensorless applications). From this point of view, it is fundamental to have accurate discrete-time models of induction machines, particularly given their nonlinear nature, so that control techniques perform according to design requirements. In spite of the above, the modeling of induction machines has not received much attention in the literature, even though more powerful machines and faster microcontrollers are currently being used. To better understand induction machine models for control, in this paper, we develop and compare various discrete-time models of induction machines based on Euler, Taylor, and Runge–Kutta methods. In addition, we compare the Extended Kalman Filter and Unscented Kalman Filter for state estimation in terms of accuracy and computational burden. The models are derived and compared through extensive Monte Carlo simulations and the state estimation techniques are compared in terms of root mean squared error, execution time, and maximum absolute error. Our simulations show that, in general, the Taylor method yields more accurate models than both the Runge–Kutta and Euler methods. In particular, the Taylor method results in a root mean square error that is one order of magnitude smaller than the Euler method for stator current and rotor flux linkages. For rotor angular speed, the Runge–Kutta methods are more accurate than both the Taylor and Euler methods, resulting in a root mean square error that is two orders of magnitude smaller than the Euler method. On the other hand, the Extended Kalman Filter results in smaller execution time than the Unscented Kalman Filter, up to two orders of magnitude. In terms of root mean squared error and maximum absolute error, both filtering algorithms perform similarly.

Modelling and control of electromechanical disc brake for heavy-duty vehicles

This paper proposes a validated procedure that can be used for development stage of model-based controller for heavy-duty electromechanical disc brakes. Firstly, system dynamics model of a single piston electromechanical disc brake is constructed in Matlab/Simulink environment in consideration of nonlinear friction model. To ensure the accuracy of system dynamics model, open loop measurements (clamping force, motor angle and motor current) are conducted on a prototype of single piston electromechanical disc brake. Experimental data is used for the determination of system variables. The predicted outputs are verified by comparison of experimental measurement results. For the control purpose of electromechanical brake, a multi-stage closed loop architecture is introduced. To regulate clamping force, PID and sliding mode controllers are developed in Matlab/Simulink in consideration of braking performance requirements for heavy-duty vehicles. For management of running clearance between brake disc and pad, PID position controller is developed in simulation environment. Those controller parameters obtained in the simulation process are introduced to the control hardware. After that closed loop clamping force and position measurements are conducted. When the rise time values of both clamping force controllers are compared, it is seen that sliding mode controller can reach to the settling point faster than PID controller. As for the position controller, the rise time requirement has been achieved by the designed PID controller. The switching process of force and position controllers are implemented and functional closed loop measurements are conducted for different reference input signals. It is seen from the results that the rise time requirement for position controller has been achieved. The system response of clamping force parameter is considerably stable.

In-plane free vibration analysis of multi-folded beam structures

Folded beam structures have been widely used in mechanical engineering, aerospace engineering, and other fields due to their flexibility and extensibility in applications. Although the components of a folded beam are simple beam structures, building an accurate dynamic model is complex due to its multi-degree-of-freedom, multi-mode, and close-mode features. This study presents a novel method to analyze in-plane free vibration of a multi-folded beam structure with arbitrary numbers of beam segments with different beam lengths and folding angles. The governing equations of the system can be easily obtained based on the beam theory and the work-energy principle. However, the key issue is how to solve the eigenvalue problem of a multi degree of freedom system defined by a 6 n × 6 n matrix. As the coefficient solution vector of the modal function is unknown, solving equations defined by high-order determinants involving variables has considerable complexity. In this work, the intricate matrix is initially turned into a single matrix of block Hessenberg form using numerous "6 × 6" block square matrices. Furthermore, by combining the characteristics of the block Hessenberg matrix with the approach to solve block determinants, a considerable reduction in the determinant's size can be attained, diminishing it from a dimension of 6 n × 6 n to 6 × 6. This procedure markedly simplifies the computational intricacies involved in the analysis. Finally, four kinds of multi-folded beams, namely L-shaped beams, Z-shaped beams, C-shaped beams, and four-segment folded beams with arbitrary lengths, folding angles, and numbers of beam segments are considered and studied, and the mode shapes and the influence of geometric parameters on the first three natural frequencies are discussed in detail. The results are also verified by the finite element method (FEM), and good agreement is found between the two methods. The results show that the proposed method can offer a unified framework for the in-plane vibration analysis of multi-folded beam structures.

Numerical Investigation of Thermal Energy Storage Systems for Collective Heating of Buildings

This study aims to investigate and identify the most effective thermal energy storage (TES) system configuration for the collective heating of buildings. It compares three TES technologies, i.e., sensible, latent, and cascade latent shell and tube storage, and examines their respective performances. A fast and accurate lumped thermal dynamic model to efficiently simulate TES system performances under different operation conditions is developed. The validation of this model’s accuracy is achieved by aligning numerical findings with data from prior experimental studies. Key findings indicated that the latent and cascade latent shell and tube storage systems demonstrate superior thermal energy storage capacities compared to the sensible configuration. Using a single-phase change material (PCM) tank increases the duration of constant thermal power storage by about 50%, and using a cascade PCM tank further enhances this duration by approximately 65% compared to the sensible TES case. Moreover, the study revealed that adjusting the PCM composition within the cascade TES significantly influenced both thermal power storage durations and pumping energy consumption. In summary, the recommended cascade PCM configuration for collective heating of buildings offers a balanced solution, ensuring prolonged stable thermal power production, elevated HTF outlet temperatures, and improved energy efficiency, presenting promising prospects for enhancing TES systems in district heating applications.

Interface stress transfer model and modulus parameter equivalence method for composite materials embedded with tensile pre-strain shape memory alloy fibers.

The constitutive model and modulus parameter equivalence of shape memory alloy composites (SMAC) serve as the foundation for the structural dynamic modeling of composite materials, which has a direct impact on the dynamic characteristics and modeling accuracy of SMAC. This article proposes a homogenization method for SMA composites considering interfacial phases, models the interface stress transfer of three-phase cylinders physically, and derives the axial and shear stresses of SMA fiber phase, interfacial phase, and matrix phase mathematically. The homogenization method and stress expression were then used to determine the macroscopic effective modulus of SMAC as well as the stress characteristics of the fiber phase and interface phase of SMA. The findings demonstrate the significance of volume fraction and tensile pre-strain in stress transfer between the fiber phase and interface phase at high temperatures. The maximum axial stress in the fiber phase is 705.05 MPa when the SMA is fully austenitic and the pre-strain increases to 5%. At 10% volume fraction of SMA, the fiber phase's maximum axial stress can reach 1000 MPa. Ultimately, an experimental verification of the theoretical calculation method's accuracy for the effective modulus of SMAC lays the groundwork for the dynamic modeling of SMAC structures.

Adaptive control of transonic buffet and buffeting flow with deep reinforcement learning

The optimal control of flow and fluid–structure interaction (FSI) systems often requires an accurate model of the controlled system. However, for strongly nonlinear systems, acquiring an accurate dynamic model is a significant challenge. In this study, we employ the deep reinforcement learning (DRL) method, which does not rely on an accurate model of the controlled system, to address the control of transonic buffet (unstable flow) and transonic buffeting (structural vibration). DRL uses a deep neural network to describe the control law and optimizes it based on data obtained from interaction between control law and flow or FSI system. This study analyzes the mechanism of transonic buffet and transonic buffeting to guide the design of control system. Aiming at the control of transonic buffet, which is an unstable flow system, the control law optimized by DRL can quickly suppress fluctuating load of buffet by taking the lift coefficient as feedback signal. For the frequency lock-in phenomenon in transonic buffeting flow, which is an unstable FSI system, we add the moment coefficient and pitching displacement to feedback signal to observe pitching vibration mode. The control law optimized by DRL can also effectively eliminate or reduce pitching vibration displacement of airfoil and buffet load. The simulation results in this study show that DRL can adapt to the control of two different dynamic modes: typical forced response and FSI instability under transonic buffet, so it has a wide application prospect in the design of control laws for complex flow or FSI systems.

Identification of the friction model of a single elastic robot actuator from video

Obtaining a highly accurate dynamic model from video data is a challenging task within system Identification. More specifically, in robotics, there is a constant need for precise models to optimize the performance and safety of these systems. With the developments in machine learning, algorithms such as convolutional neural networks (CNNs) have shown good performances in extracting features from images. Techniques like transfer learning (TL) can lower the computational cost and optimize the training task. This work aims to make the gray-box Identification of friction parameters of an actuator from video. The proposed approach is composed of three steps. Firstly, it compares the transfer learning performance of three pre-trained CNNs to estimate the pose of the motor and the link from video data. Secondly, a long-term short-term (LSTM) network is added to estimate the velocity and acceleration. Thirdly, the parameters of the two friction models are estimated using the estimated states and the dynamic equations of the system. Through these steps, a vision-based gray-box Identification is obtained. The approach is tested using an original elastomer-based series of elastic actuators (eSEA) benchmark. The results show that the VGG19 model combined with the LSTM layer is the optimal pre-trained CNN for the vision module, obtaining a coefficient of determination higher than 0.96 for all three states. From the state estimates, the parameters of the friction models are optimized. The best-performing friction model is the Coulomb-Stribeck, which decreases the mean absolute error (MAE) by 15.50% compared to the viscous linear model.

A Comparative Study of Control Laws for a Maritime Surface Vessel Tracking an Underwater Vehicle

This paper compares the tradeoffs between performance and implementation efforts of three pure pursuit control laws; a proportional-integral-derivative (PID), nonlinear model predictive (NMPC) and a deep reinforcement learning (DRL) trained neural network (NN). The control laws are employed on a target tracking problem where the issue is to keep an unmanned surface vessel (USV) within proximity to a submerged autonomous underwater vessel (AUV) for optical communication to operate. The results from a simulation case study, show that the PID settled with a steady error of 2.0 m from the target, the NMPC at 2.4 m and the NN at 2.3 m. The relative control effort is highest for the PID at 100%, the NMPC settled at 98% and the NN at 96%. The PID represents a methodology that has transparent and time-efficient tuning rules together with a high update rate of 11,5 kHz. The NMPC provides a flexible tuning method but requires an accurate dynamic model and has the slowest update rate of 5.2 Hz. The DRL stand as a viable solution to solve the control problem and has an update rate of 4,2 kHz, but it bears the most time-consuming implementation and tuning of the three alternatives presented here.

Sliding-mode control of a soft robot based on data-driven sparse identification

Soft robots are increasingly finding their way into many applications, especially those involving manipulation of sensitive and delicate objects or interaction with humans. However, their high-compliance characteristics pose considerable challenges in obtaining low-complexity yet accurate dynamical models that are suitable for advanced feedback control. This paper proposes a framework for end-effector positioning of a soft robot. First, physics-informed sparse regression is used for deriving a nonlinear mathematical model of the robot dynamics. Then, a control scheme comprising a super-twisting sliding mode controller and a nonlinear input estimator is designed for the positioning of the robot end-effector. Conditions for uniform asymptotic stability of the closed-loop system are given. Finally, experimental tests carried on a real soft robot show the efficacy of the proposed design and its tracking accuracy.

Ensuring the accuracy of indirect nonlinear dynamic reduced-order models

Numerous powerful methods exist for developing reduced-order models (ROMs) from finite element (FE) models. Ensuring the accuracy of these ROMs is essential; however, the validation using dynamic responses is expensive. In this work, we propose a method to ensure the accuracy of ROMs without extra dynamic FE simulations. It has been shown that the well-established implicit condensation and expansion (ICE) method can produce an accurate ROM when the FE model’s static behaviour are captured accurately. However, this is achieved via a fitting procedure, which may be sensitive to the selection of load cases and ROM’s order, especially in the multi-mode case. To alleviate this difficulty, we define an error metric that can evaluate the ROM’s fitting error efficiently within the displacement range, specified by a given energy level. Based on the fitting result, the proposed method provides a strategy to enrich the static dataset, i.e. additional load cases are found until the ROM’s accuracy reaches the required level. Extending this to the higher-order and multi-mode cases, some extra constraints are incorporated into the standard fitting procedure to make the proposed method more robust. A curved beam is utilised to validate the proposed method, and the results show that the method can robustly ensure the accuracy of the static fitting of ROMs.

An Accurate Dynamic Model Identification Method of an Industrial Robot Based on Double-Encoder Compensation

Aiming at the challenges to accurately simulate complex friction models, link dynamics, and part uncertainty for high-precision robot-based manufacturing considering mechanical deformation and resonance, this study proposes a high-precision dynamic identification method with a double encoder. Considering the influence of the dynamic model of the manipulator on its control accuracy, a three-iterative global parameter identification method based on the least square method and GMM (Gaussian Mixture Model) under the optimized excitation trajectory is proposed. Firstly, a bidirectional friction model is constructed to avoid using residual torque to reduce the identification accuracy. Secondly, the condition number of the block regression matrix is used as the optimization objective. Finally, the joint torque is theoretically identified with the weighted least squares method. A nonlinear model distinguishing between high and low speeds was established to fit the nonlinear friction of the robot. By converting the position and velocity of the motor-side encoder to the linkage side using the deceleration ratio, the deformation quantity could be calculated based on the discrepancy between theoretical and actual values. The GMM algorithm is used to compensate the uncertainty torque that was caused by model inaccuracy. The effectiveness of the proposed method is verified by a simulation and experiment on a 6-DoF industrial robot. Results prove that the proposed method can enhance the online torque estimation performance by up to 20%.

Curriculum-based humanoid robot identification using large-scale human motion database

Identifying an accurate dynamics model remains challenging for humanoid robots. The difficulty is mainly due to the following two points. First, a good initial model is required to evaluate the feasibility of motions for data acquisition. Second, a highly nonlinear optimization problem needs to be solved to design movements to acquire the identification data. To cope with the first point, in this paper, we propose a curriculum of identification to gradually learn an accurate dynamics model from an unreliable initial model. For the second point, we propose using a large-scale human motion database to efficiently design the humanoid movements for the parameter identification. The contribution of our study is developing a humanoid identification method that does not require the good initial model and does not need to solve the highly nonlinear optimization problem. We showed that our curriculum-based approach was able to more efficiently identify humanoid model parameters than a method that just randomly picked reference motions for identification. We evaluated our proposed method in a simulation experiment and demonstrated that our curriculum was led to obtain a wide variety of motion data for efficient parameter estimation. Consequently, our approach successfully identified an accurate model of an 18-DoF, simulated upper-body humanoid robot.

Simulation and experimental study on impact dynamic characteristics of the spline rotor system

The development of accurate impact dynamics models in rotating machinery with spline couplings is a challenging problem that demands special attention. The dynamic behavior of the system is highly dependent on the spline coupling stiffness, which is nonlinear under different loads. To address this challenge, rotor dynamics models that incorporate spline couplings have been developed. In this paper, firstly, the mechanical model of spline coupling considering large deformation under different loads is established and verified by finite element software. Furthermore, a spline rotor dynamics model considering nonlinear stiffness is established, and the influence of different impact loads on the vibration response of the system is emphatically analyzed. Finally, the proposed model is experimentally verified to accurately predict the impact dynamics of the rotor system, which provides a certain theoretical reference for the impact resistance design of the spline rotor system.

Particle filtering for dynamic systems with future constraints

This work focuses on a new state estimation problem for dynamic systems with future constraints. It is well known that constraints, as a priori, should always be satisfied by states of some dynamic systems, and thus sufficiently fusing the valuable information into filters will produce more accurate estimates. To this end, a particle smoothing framework is proposed by incorporating future constraints, instead of only current constraints. Next, we construct a criterion function by making the center value of dynamic model satisfy constraints to improve dynamic modeling accuracy, and investigate a cost function to compensate for the impact of the modified dynamic model on the original predicted distribution. Based on this, we present a new particle filter that future constraints are applied in importance sampling and updating particle weights. Especially, the modified dynamic model is chosen as the importance density function so that the sampled particles satisfy constraints at consecutive times as much as possible. Finally, two simulations verify the superiority of the proposed filter.

Identification and high-precision trajectory tracking control for space robotic manipulator

In this paper, an effective control and parameters identification scheme was proposed for high-precision trajectory tracking of space robotic manipulators. Our proposed control method employed a linear-extended-state-observer (LESO) based model predictive control (MPC) scheme. The feedback linearization approach was utilized to develop a model predictive controller. The optimization objective function was simplified to a standard quadratic programming (QP) problem for solution. To minimize the impact of the inaccuracy in the dynamics model, a LESO was designed to estimate the disturbance, and its convergence was demonstrated. In order to improve the accuracy of dynamic model, the physical consistency of inertial parameters was constrained using linear matrix inequality (LMI) techniques. Moreover, the dynamics parameters were estimated through semidefinite programming (SDP) techniques. To validate the effectiveness of the proposed control method, it was compared with existing controllers through simulations and experiments. The results demonstrated the superior performance of the proposed scheme, highlighting its potential for achieving high-precision trajectory tracking control in space robotic manipulators.

The computational design of a fractal-inspired soft robotic

Soft robotics, with their application in biomedical fields like flexible surgical tools and wearable exo-suits, have revolutionized biomedical practices. To adapt to different scales of application scenarios, our research emphasizes fractal-inspired soft robotics, leveraging the unique scalable and reconfigurable properties of fractal structures. This study focuses on the computational design and simulation of these robots. Traditional modeling methods, apt for rigid robotic arms, falter for soft materials due to their extensive flexibility. We introduced a deep learning strategy with physics-informed neural network for accurate soft robot dynamics modeling. Unlike existing networks optimized for rigid systems, our approach integrates elastic beam theory and deformation laws into Lagrangian Dynamics, making it ideal for simulating fractal soft robotic arms. Compared to conventional finite element simulations and learning approaches, our method shows superior effectiveness. We also conducted simple simulation experiments to show that fractal soft arm is potentially suitable for medical procedures (such as dilating passages) and proved that this fractal-designed soft robotic arm exhibits good portability and adaptability to various scenarios, making it a promising candidate for guiding the design of future surgical robots.

Data-driven prediction of the equivalent sand-grain roughness

Surface roughness affects the near-wall fluid velocity profile and surface drag, and is commonly quantified by the equivalent sand-grain roughness {k}_{s}. It is essential to estimate {k}_{s} for accurate fluid dynamic problem modeling. While numerous roughness correlation formulas have been proposed to predict {k}_{s} in the fully rough regime, most of them are restricted to certain roughness types, with various geometric parameters considered in each case, leading to ongoing disagreements regarding its parameterization and lack of universality. In this study, a Particle Swarm Optimized Backpropagation (PSO-BP) method is proposed to predict {k}_{s} based on the selected surface parameters from previous DNS, LES, and experimental results for flow behavior over various surface roughness. The PSO-BP model’s ability to predict {k}_{s} in the fully rough region is evaluated and compared with both the existing roughness correction formulas as well as the traditional BP model. An optimized polynomial function is also proposed to serve as a ‘white box’ for predicting {k}_{s}. It turns out that the PSO-BP method has better performance in the evaluation metrics compared to other methods, yielding a Mean Absolute Error (MAE) of 0.0390, a Mean Squared Error (MSE) of 0.0026 and a Mean Absolute Percentage Error (MAPE) of 28.12%. This novel approach for estimating {k}_{s} has practical applicability and holds promise for improving the precision and efficiency of calculations related to equivalent sand-grain roughness, and thus provides more accurate and effective solutions for CFD and other engineering applications.

Physics-informed Neural Network for Quadrotor Dynamical Modeling

The explosive growth of civil applications of Unmanned Aerial Vehicles (UAVs) calls for control algorithms that enable safe and trustworthy operations, especially in complex environments to facilitate real-world deployment. Although Model-Based Control (MBC) has found great applicability in the last decades, it relies heavily on the accuracy of the underlying mathematical models. Thanks to their powerful approximation capability, data-driven approaches such as Artificial Neural Networks (ANNs) have raised a great interest in UAV dynamical modeling in recent years. Despite the promising results achieved in learning either full or partial dynamics such as aerodynamic effects, prior studies merely pay little to no attention to the black-box nature of ANNs, yielding poorly interpretable learning processes and implying a lack of generalization capability due to undesirably learned spurious relationships among features and labels. While nowadays practitioners and society are far from being concerned just with performance, such risk evidently reduces the overall trustworthiness of the control system with ANNs as control-oriented models. With the goal of both accurate and interpretable neural modeling of nonlinear dynamics, we propose a novel modeling approach that utilizes Physics-Informed Neural Networks (PINN), designed to seamlessly embed physical laws into Deep Neural Networks (DNN). To further enhance model interpretability, we adopt the Covariance Confidence Ellipse (CCE) as post-hoc visualization to help understand the model behavior. We also set up a visual and physical simulator based on AirSim with custom implementation on quadrotor ground effect, which is made publicly available to facilitate further experiments for the community. An extensive simulation campaign validates our approach on data sets including aerodynamics and periodic wind, highlighting advantages regarding the accuracy and physical consistency, pointing to further insight on the development of learning-based control-oriented models for quadrotors, and facilitating flight controller design with performance guarantees.