Multibody System Dynamics最新文献

With the widespread implementation of robotics exoskeletons in rehabilitation, modeling and dynamics analysis of such highly nonlinear coupled systems has become significantly important. In this paper, a swift numerical human–robot dynamics modeling has been developed to achieve accurate and realistic interpretation. This takes into consideration the separation and impact between multiple bodies for rehabilitation planning. To this end, first, a novel parallel algorithm combined with sequential interaction conditions is proposed based on the numerical recursive Newton–Euler method. The approach begins by deriving separated numerical models for the complicated system: i.e. both the human and the robot. These models are then augmented, with a primary focus on reducing the error of the interaction conditions, including forces and positions. The accuracy of the proposed model, with a computational complexity of O(n), is assessed by comparing to a previously validated nonrecursive analytical model with a higher computational complexity of O(n^4). Additionally, the quality of the connection between the human and the robot is assessed to establish a suitable control objective and an effective interaction strategy for rehabilitation planning. The study employs a lower-limb walking assistive robot developed in the ARAS lab (RoboWalk) to validate the proposed method. The algorithm is empirically implemented on the RoboWalk test stand, ensuring the integrity of the proposed dynamics modeling. The human–robot interaction forces are estimated with an accuracy of 2 N, in the presence of friction and measurement noise. Finally, the effectiveness of the model-based controller is assessed by using the proposed method, providing valuable tools for the enhancement of overall performance of such a complex dynamics system.

As commonly known, standard time integration of the kinematic equations of rigid bodies modeled with three rotation parameters is infeasible due to singular points. Common workarounds are reparameterization strategies or Euler parameters. Both approaches typically vary in accuracy depending on the choice of rotation parameters. To efficiently compute different kinds of multibody systems, one aims at simulation results and performance that are independent of the type of rotation parameters. As a clear advantage, Lie group integration methods are rotation parameter independent. However, few studies have addressed whether Lie group integration methods are more accurate and efficient compared to conventional formulations based on Euler parameters or Euler angles. In this paper, we close this gap using the (mathbb{R}^{3}times SO(3)) Lie group formulation and several typical rigid multibody systems. It is shown that explicit Lie group integration methods outperform the conventional formulations in terms of accuracy. However, it turns out that the conventional Euler parameter-based formulation is the most accurate one in the case of implicit integration, while the Lie group integration method is computationally the more efficient one. It also turns out that Lie group integration methods can be implemented at almost no extra cost in an existing multibody simulation code if the Lie group method used to describe the configuration of a body is chosen accordingly.

The purpose of this research is to present an alternative multibody dynamic model for soft robots and to analyze the intrinsic mechanism of motion. It is difficult to directly apply traditional robot modeling methods due to the large structural deformation of soft walking robots. This paper establishes the dynamic modeling of a soft robot system with contact/impact based on the corotational formulation of the special Euclidean group (SE)(2). The experiments are designed to verify the dynamic model of the robot. The history of the marked points on the robot prototype is measured in real time by an ARAMIS Adjustable Camera System. Based on the dynamic model, we conducted an in-depth analysis of the entire process through which the robot achieves directional walking utilizing complex friction characteristics. Notably, the robot’s kick-up phenomenon attracted our attention, and an analytical model for predicting the critical drive acceleration is proposed. The conditions and mechanisms of the robot’s kick-up are analyzed, and effective direction is provided for designing new drive laws. Finally, several sets of key parameters affecting the walking efficiency are analyzed using the multibody model, which can provide scientific guidance for the material selection and optimization of the robot. The presented dynamic modeling approach can be freely extended to other soft robots, which will provide valuable references for the design and analysis of soft robots.

In this work we present a multibody dynamics system composed of geometrically exact nonlinear beams with inelastic behavior, representing flexible system components. The main focus of the work is to introduce advanced energy dissipation models using hardening and softening plasticity into such beam models and to show how they can also recover a vibration amplitude decay typical of viscous damping. The damping model is represented by the constitutive behavior of the flexible beam element chosen as an elasto-viscoplastic response with linear isotropic hardening and subsequent softening plasticity. The formulation is cast within the mixed variational framework, where the strong embedded discontinuity is introduced into displacement/rotation fields in the softening phase leading to localized plastic deformation. We also aim to ensure model capabilities to deliver results for long-term loading simulations, which is of interest for quantifying the risk of fatigue failure for such flexible system component. The corresponding numerical implementation combines the space discretization based on the finite element method with the time discretization based upon energy-conserving or energy-decaying integration schemes. The results of several numerical simulations are presented in the dynamics of flexible-rigid multi-body systems to illustrate a very satisfying performance of the proposed model.

Real-world multibody systems do not have ideal joints; most joints have some clearance. The clearance allows the connected bodies to undergo a misalignment, and the resulting dynamics is governed by the contacts thus formed. Two approaches are typically taken to deal with contacts: the commonly used continuous dynamics approaches assume the Hertzian nature of the contact modeled by nonlinear unilateral spring-damper elements; while the nonsmooth dynamics approach results in a complementarity problem. This paper employs a nonsmooth dynamics approach to develop a coherent framework for the simulation of multibody systems having frictionless joints with clearances. Because clearances are of small magnitude relative to the dimensions of the mechanical components, the nature of the contact in the joints is assumed to be inelastic. Using this assumption and the general nonsmooth dynamics framework, the parametric formulations for cylindrical, prismatic, and revolute joints with clearances are derived. The equations of motion are formulated, and their time-discretized counterparts are cast as a nonlinear programming problem. The proposed scheme also enforces normalization constraint on Euler parameters in contrast to state-of-the-art methods that is conducive to stability of the solution for a suitable range of step sizes. In addition, a variable time-stepping scheme that includes the step size as an extra variable in the optimization is introduced and its stability properties are discussed. The versatility of the proposed framework is demonstrated through numerical experiments.

This article presents a strategy of self adaptation for planar undulatory locomotion of an elongated, snake-like multibody robotic system under both non-varying and varying surface friction. Based on the system dynamics, an algorithm is developed to investigate the locomotion performance and its dependence upon the lateral undulation parameters. The celerity of the lateral undulatory wave propagating over the body of the robot is taken as a key parameter, since the variation of the celerity affects the forward propulsion speed of the robot. Moreover, celerity of the lateral undulatory wave is a linear function of the angular frequency of the sinusoidal motion imposed on the joints of the robot. Considering the static-kinetic lateral friction, the proposed algorithm computes the important point of separation between no-lateral slip and lateral slip simply with the help of celerity and speed of propulsion. Therefore, the results identify the optimum speed of propulsion for ground-adaptivity and efficient undulatory locomotion of the robot. The simulation results further verify the influence of the angular frequency of the sinusoidal joint motion upon the speed of propagation of the undulatory wave and also upon the speed of propulsion of the robot. This research work can provide useful basis for the control, optimization and self-adaptive locomotion of such and similar robots.

Interval uncertainty analysis plays a fundamental role in performance evaluation, reliability design, and parameter optimization of a multibody system. In this work, the method for correlation propagation of a multibody system considering multiple interval parameters is investigated. To this end, a method of bivariate Chebyshev-polynomials difference combining with the Lagrangian-multiplier method (BCDLM) is proposed. First, the multiple-ellipsoid model is employed to quantify simultaneously the correlated and independent interval parameters examined in this work. The bivariate Chebyshev difference method is developed to calculate the partial derivatives of the relevant responses with respect to the uncertain parameters subsequently. To obtain the response bounds the Lagrangian-multiplier method is incorporated with the Taylor-series expansion. Additionally, the uncertain domain of the uncertain output responses is constructed by the developed BCDLM. Several examples are illustrated to verify the effectiveness of the proposed method to propagate correlations for the multibody system considering independent and correlated interval parameters. Results show that the BCDLM is more suitable for correlation propagation of a high-dimensional interval problem with relatively small uncertainty levels.

The active safety system of a vehicle typically relies on real-time monitoring of the sideslip angle and other critical signals, such as the yaw rate. The vehicle sideslip angle cannot be measured directly due to the high cost and impracticality of sensor networks. The vehicle sideslip can be estimated using kinematic, dynamic, or machine-learning models and available vehicle states. This paper combines recurrent neural networks and the particle-swarm optimization (PSO) algorithm to estimate the vehicle sideslip angle accurately. First, a vehicle-dynamics model is constructed to conduct dynamics simulations of vehicles under various driving conditions and road environments for data collection. Secondly, the obtained vehicle states, including velocity, acceleration, yaw rate, and steering, are used to develop machine-learning models that estimate the vehicle sideslip angle. Two machine-learning models are proposed using the long short-term memory neural network (LSTM) and the bidirectional long short-term memory neural network (BiLSTM). Thirdly, the PSO algorithm is employed to optimize the hyperparameters of the LSTM and BilLSTM models for enhanced estimation precision. The Gaussian noise is added to the datasets to evaluate the robustness of the estimation models. The results indicate that the estimation models are capable of accurately predicting the vehicle’s sideslip angle. The (R^{2}) values of the results are mostly greater than 0.96. The PSO algorithm can improve estimation precision, and the PSO-LSTM model performs the best.

The thermal elastohydrodynamic (TEHD) effect contributes significantly to the improvement of dynamic behavior of mechanical presses, especially under the complex conditions of high speed, heavy load, and high temperature. In this work, a novel mixed-TEHD model and the numerical algorithm for the multiphysics problem are proposed to predict the nonlinear behavior of the mechanical press considering multiple clearance-induced joints. The propounded lubrication principle includes the thermal effects caused by contact event and the influence of TEHD on the clearance dimension under complex lubrication conditions. The equivalent nodal force method is adapted as the unified treatment of elastic and thermal deformation in the clearance joints. With the introduction of non-conservative forces, the system’s dynamic model is formulated and solved by the Lagrange approach and Newmark-(beta ) integration algorithm, respectively. Numerical simulations are performed considering different fluid viscosities and crank speeds to investigate the nonlinear behavior of the mechanical press under various lubrication conditions. The results demonstrate the significance of frictional contact on the bearing thermal characteristics. Compared to the elastic deformation effect of transmission components, the variation of system position accuracy is primarily governed by the dynamics of mixed-lubricated joints. Furthermore, experimental studies are performed to validate the numerical findings.

The optimization of multibody systems requires accurate and efficient methods for sensitivity analysis. The adjoint method is probably the most efficient way to analyze sensitivities, especially for optimization problems with numerous optimization variables. This paper discusses sensitivity analysis for dynamic systems in gradient-based optimization problems. A discrete adjoint gradient approach is presented to compute sensitivities of equality and inequality constraints in dynamic simulations. The constraints are combined with the dynamic system equations, and the sensitivities are computed straightforwardly by solving discrete adjoint algebraic equations. The computation of these discrete adjoint gradients can be easily adapted to deal with different time integrators. This paper demonstrates discrete adjoint gradients for two different time-integration schemes and highlights efficiency and easy applicability. The proposed approach is particularly suitable for problems involving large-scale models or high-dimensional optimization spaces, where the computational effort of computing gradients by finite differences can be enormous. Three examples are investigated to validate the proposed discrete adjoint gradient approach. The sensitivity analysis of an academic example discusses the role of discrete adjoint variables. The energy optimal control problem of a nonlinear spring pendulum is analyzed to discuss the efficiency of the proposed approach. In addition, a flexible multibody system is investigated in a combined optimal control and design optimization problem. The combined optimization provides the best possible mechanical structure regarding an optimal control problem within one optimization.