Miguel A. Naya

A combined penalty and recursive real-time formulation for multibody dynamics

The continuously improved performance of personal computers enables the real-time motion simulation of complex multibody systems, such as the whole model of an automobile, on a conventional PC, provided the adequate formulation is applied. There exist two big families of dynamic formulations, depending on the type of coordinates they use to model the system: global and topological. The former leads to a simple and systematic programming while the latter is very efficient. In this work, a hybrid formulation is presented, obtained by combination of one of the most efficient global formulations and one of the most systematic topological formulations. It shows, at the same time, easiness of implementation and a high level of efficiency. In order to verify the advantages that the new formulation has over its predecessors, the following four examples are solved using the three formulations and the corresponding results are compared: a planar mechanism which goes through a singular position, a car suspension with stiff behavior, a 6-dof robot with changing configurations, and the full model of a car vehicle. Furthermore, the last example is also analyzed using a commercial tool, so as to provide the readers with a well-known reference for comparison.

Performance and Application Criteria of Two Fast Formulations for Flexible Multibody Dynamics

Abstract The performance of the simulation of flexible multibody systems can be improved by means of the use of topological formulations, which have provided good results in the simulation of large rigid multibody systems. In this work, a topological formulation for rigid bodies is extended to the flexible case, and tests are carried out in order to compare its performance with that of a global formulation. Three systems are simulated: a double four-bar mechanism, a vehicle suspension, and a full vehicle. As it happens in the rigid case, the topological formulation is faster than the global one only for large mechanisms.

Online Kinematic and Dynamic-State Estimation for Constrained Multibody Systems Based on IMUs.

This article addresses the problems of online estimations of kinematic and dynamic states of a mechanism from a sequence of noisy measurements. In particular, we focus on a planar four-bar linkage equipped with inertial measurement units (IMUs). Firstly, we describe how the position, velocity, and acceleration of all parts of the mechanism can be derived from IMU signals by means of multibody kinematics. Next, we propose the novel idea of integrating the generic multibody dynamic equations into two variants of Kalman filtering, i.e., the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), in a way that enables us to handle closed-loop, constrained mechanisms, whose state space variables are not independent and would normally prevent the direct use of such estimators. The proposal in this work is to apply those estimators over the manifolds of allowed positions and velocities, by means of estimating a subset of independent coordinates only. The proposed techniques are experimentally validated on a testbed equipped with encoders as a means of establishing the ground-truth. Estimators are run online in real-time, a feature not matched by any previous procedure of those reported in the literature on multibody dynamics.

Real-time multi-body formulation for virtual-reality-based design and evaluation of automobile controllers

Abstract Nowadays, modelling and simulation of vehicle dynamics play a great role in the design and evaluation of vehicle control systems, as they reduce costly and time-consuming construction of prototypes and experimentation. Multi-body simulation can be used for controller design, tuning and testing of electronic control units, optimum control, or onboard devices providing driver advice and/or actuation. This article reports on the application of a robust real-time formulation to the development of a low-cost and efficient computational framework for the design and evaluation of automobile motion controllers. The core elements of the tool are the real-time formalism for the dynamics of multi-body systems, a virtual-reality (VR) interface for human-in-the-loop simulation, and Matlab for the controllers. A detailed model of an existing prototype car has been implemented in the Fortran language, and controllers have been designed for several purposes, in order to test the developed framework. It has been demonstrated that the dynamic formalism is fast enough to enable human-in-the-loop simulation, that the VR interface is of great help for both control design and evaluation, and that Matlab algorithms can be efficiently connected to the Fortran computational model of the car.

Efficient calculation of the inertia terms in floating frame of reference formulations for flexible multibody dynamics

Abstract One of the characteristics of floating frame of reference (FFR) formulations for flexible multibody dynamics is the fact that the inertia terms are highly non-linear. At every time-step, both the mass matrix and the velocity-dependent forces vector must be updated, and this can become the most CPU intensive task. This work studies the efficiency of two different methods for performing this operation, when applied to both a formulation in absolute coordinates and another in relative coordinates. The first method calculates the inertia terms by projecting the finite element (FE) mass matrix into the generalized coordinates, by means of a variable projection matrix. The second one calculates the inertia shape integrals at a preprocessing stage and uses them for obtaining the inertia terms in a more efficient way, at the cost of a more involved implementation. Both methods have been tested when used in combination with either the FFR absolute or relative formulation, by simulating a vehicle with 12 flexible elements. The results show that the performance can be considerably increased by means of the preprocessing method, especially in the case of large FE models, whereas, for small models, the projection method can be more convenient due to its simplicity.

Real-Time MBS Formulations: Towards Virtual Engineering

This paper presents the research conducted during the last years by the Laboratory of Mechanical Engineering on real-time formulations for the dynamics of multi-body systems, a topic of great relevance for the development of new virtual reality applications. The work carried out by our group has been focused on: a) the development of real-time formulations capable of performing very fast calculations of the dynamics of complex rigid-flexible multi-body systems; b) the experimental validation of the motions, deformations and forces obtained through the application of the above-mentioned formulations, so as to verify that reality is being reasonably well imitated; c) the study of the aptitude of such formulations for becoming part of a virtual reality environment, in connection with user-interface devices. In the paper, a real-time formulation developed by the authors is described, along with some examples of rigid-flexible multi-body systems simulated with such formulation. Moreover, results of the experimental validation of one of the examples are shown. Finally, a simulator based on the proposed formulation is presented.

Real-Time Multibody Dynamics and Applications

The simulation of multibody dynamics in real-time is becoming more and more relevant, since it is required by the growing and technologically advanced hardware- and human-in-the-loop applications. Both the efficient calculation of multibody dynamics and the adequate consideration of mechanical phenomena, like flexibility or contact, are essential for such applications. Accordingly, this contribution presents the following contents: a) two variants of a real-time formalism, capable of performing very fast calculations of the dynamics of complex multibody systems; b) the experimental validation of the formalism in the case of a prototype car; c) the use of the formalism for the design of vehicle controllers through a human-in-the-loop application. As conclusion, the work provides a reliable tool for the real-time simulation of multibody dynamics, which can be used to develop practical industrial applications.

Performance of an Energy-Conserving Algorithm for Multi-Body Dynamics

Abstract This work presents the application to the dynamics of multibody systems of three methods based on the augmented Lagrangian techniques, compares them, and gives some criteria for their use in realistic problems. The methods are: an augmented Lagrangian formulation with trapezoidal rule plus projections of velocities and accelerations, an augmented Lagrangian energy-conserving formulation, and an augmented Lagrangian formulation with conserving integrator plus projections of velocities and accelerations. The simulation of two mechanical systems is carried out in this work: a spherical compound pendulum, which is an academic example that permits to see the properties of the formulations; andthe whole model of a car, which is a realistic and demanding example to test the efficiency and robustness of the formulations.

A ROBUST TOOL FOR TUNING AND EVALUATION OF AUTOMOBILE MOTION CONTROLLERS

During the last years, our group has worked on real-time formulations for the dynamics of multi-body systems. Now, in order to find out whether such methods are suitable to address real industrial problems, we intend to develop control algorithms for a car on its computer model (virtual prototyping), and evaluate the performance of such controllers when implemented on the corresponding physical prototype. This paper addresses the first part of the work. Two maneuvers are to be considered: straight line and obstacle avoidance. The computer model of the car has been coded in Fortran language. Fuzzy logic has been chosen to design the control algorithms, which have been implemented on the Matlab environment. Several alternatives to connect Fortran and Matlab-based functions have been studied, concluding that the most appropriate election depends on the purpose being pursued: controller tuning or onboard use of an already tuned controller. Simulator capabilities have been given to the program by means of a realistic graphical output and game-type driving peripherals (steering wheel and pedals), so that comparison may be established between human and designed automatic control.