No abstract

No abstract

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.

No abstract

Sensitivity analysis of multibody systems is essential for several applications, such as dynamics-based design optimization. Dynamic sensitivities, when needed, are often calculated by means of finite differences. This procedure is computationally expensive when the number of parameters is large, and numerical errors can severely limit its accuracy. This paper explores several analytical approaches to perform sensitivity analysis of multibody systems. Direct and adjoint sensitivity equations are developed in the context of Maggi's formulation of multibody dynamics equations. The approach can be generalized to other formulations of multibody dynamics as systems of ordinary differential equations (ODEs). The sensitivity equations are validated numerically against the third party code fatode and against finite difference solutions with real and complex perturbations.

No abstract

This work is a preliminary study on the use of the extended Kalman filter (EKF) for the state estimation of multibody systems. The observers based on the EKF are described by first-order differential equations, with independent, non-constrained coordinates. Therefore, it should be investigated how to formulate the equations of motion of the multibody systems so that efficient, robust and accurate observers can be derived, which can serve to develop advanced real-time applications. In the paper, two options are considered: a state-space reduction method and the penalty method. Both methods are tested on a four-bar mechanism with a linear spring-damper. The results enable us to analyze the pros and cons of each method and provide clues for future research.

This work is part of a project aimed to develop automotive real-time observers based on detailed multibody models and the extended Kalman filter (EKF). In previous works, a four-bar mechanism was studied to get insight into the problem. Regarding the formulation of the equations of motion, it was concluded that the state-space reduction method known as matrix-R is the most suitable one for this application. Regarding the sensors, it was shown that better stability, accuracy and efficiency are obtained as the sensored magnitude is a lower derivative and when it is a generalized coordinate of the problem. In the present work, the automotive problem has been already addressed, through the selection of a Volkswagen Passat as a case-study. A model of the car containing fourteen degrees of freedom has been developed. The observer algorithm that combines the equations of motion and the integrator has been reformulated so that duplication of the problem size is avoided, in order to improve efficiency. A maneuver of acceleration from rest and double lane change has been defined, and tests have been run for the "prototype", the "model" and the "observer", all the three computational, with the model having 100 kg more than the prototype. Results have shown that good convergence is obtained, but the computational cost is high, still far from real-time performance.