Abstract
Discussed in this paper is a novel method for the generation of Jacobian matrices which is particularly suitable for object-oriented implementations of multibody dynamics programs. The method starts from a description of multibody kinematics as a series of general mappings between manifolds, from which the overall Jacobian results — via the chain rule — as a sequence of matrix products. For these matrices, a new sparse-matrix scheme is suggested. Their “elements” are, besides zeroes, the well-known spatial transformation matrices and the local Jacobians of the individual transmission elements. It is shown how the main approaches for calculation of Jacobians in robotics can be viewed as particular decompositions and multiplication schemes of the sparse-matrices discussed above. Furthermore, two new schemes are derived which may be advantageous for dynamics calculations. The exposition is complemented by a comparison of Jacobian-based methods with composite rigid body and recursive methods for the generation of dynamical equations together with some comments on our current C++-implementation.
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Kecskeméthy, A. Sparse-matrix generation of Jacobians for the object-oriented modeling of multibody systems. Nonlinear Dyn 9, 185–204 (1996). https://doi.org/10.1007/BF01833300
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DOI: https://doi.org/10.1007/BF01833300