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The nonlinear problem of sensing the attitude of a solid body is solved by a novel implementation of the Kalman Filter. This implementation combines the use of quaternions to represent attitudes, time-varying matrices to model the dynamic behavior of the process and a particular state vector. This vector was explicitly created from measurable physical quantities, which can be estimated from the filter input and output. The specifically designed arrangement of these three elements and the way they are combined allow the proposed attitude estimator to be formulated following a classical Kalman Filter approach. The result is a novel estimator that preserves the simplicity of the original Kalman formulation and avoids the explicit calculation of Jacobian matrices in each iteration or the evaluation of augmented state vectors.

SUMMARYIn this paper, a new method for the dynamic simulation of mechanisms with flexible bodies is presented. The principal object of this work is to define the flexible bodies based on the modelization technique developed for rigid bodies using 'natural co-ordinates'. In the rigid case, each body is defined by means of the Cartesian co-ordinates of some of its points and the Cartesian components of some of its unit vectors, which are pointed in the direction of the pairs axis that connect the body to its neighbours. In the flexible case, more variables are needed to define each body: on the one hand, two additional unit vectors are considered, rigidly attached to an already existing one, constituting a rigid orthogonal triedron, that will become the local reference frame of the body and on the other, amplitudes of static and dynamic modes, corresponding to component synthesis with fixed boundaries, are considered. There are an infinite number of dynamic modes, so that the analyst should make a selection of the most relevant ones for each problem; their amplitudes will be added to the body variables. However, there are a finite number of static modes: three for each point, except for the local frame origin, and two for each unit vector, except for the three that define the local frame; static modes amplitudes will not increase the number of body variables, since they may be expressed as the difference between the values of the points in local co-ordinates (respectively, the values of the unit vectors) in a body deformed configuration and their values in the undeformed one, that is, they may be expressed in terms of the co-ordinates of points and components of unit vectors that already define the body. This idea leads to a totally new dynamic formulation.