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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.

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Abstract. This paper deals with continuous contact force models applied to the human-in-the

The aim of this work is to provide a thorough research on the implementation of some non-linear Kalman filters (KF) using multibody (MB) models and to compare their performances in terms of accuracy and computational cost. The filters considered in this study are the extended KF (EKF) in its continuous form, the unscented KF (UKF) and the spherical simplex unscented KF (SSUKF). The MB formulation taken into consideration to convert the differential algebraic equations (DAE) of the MB model into the ordinary differential equations (ODE) required by the filters is a state-space reduction method known as projection matrix-R method. Additionally, both implicit and explicit integration schemes are used to evaluate the impact of explicit integrators over implicit integrators in terms of accuracy, stability and computational cost. However, state estimation through KFs is a closed- loop estimation correcting the model drift according to the difference between the predicted measurement and the actual measurement, what limits the interest in using implicit integrators despite being commonly employed in MB simulations. Performance comparisons of all the aforemen- tioned non-linear observers have been carried out in simulation on a 5-bar linkage. The mechanism parameters have been obtained from an experimental 5-bar linkage and the sensor characteristics from off-the-shelf sensors to reproduce a realistic simulation. The results should highlight useful clues for the choice of the most suitable filters and integration schemes for the aforementioned MB formulation

Abstract. The continuously improved performance of personal computers enables the realtime motion simulation of complex multibody systems

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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.