Journal article
Comparison of automatic and symbolic differentiation in mathematical modeling and computer simulation of rigid-body systems

Publication Details
Dürrbaum, A.
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Multibody System Dynamics
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The objective of this paper is to check the efficiency and validity of two approaches for computing derivatives of complex functions, automatic differentiation using ADOLC and symbolic differentiation using MACSYMA. This has been done in three benchmark examples, where the gradient of a Helmholtz energy function has been computed for different dimensions of independent variables (Example 1) and Jacobian matrices of inverse kinematics of planar and spatial parallel robots (Examples 2 and 3) have been computed. The results have been evaluated under six criteria: preliminary implementation work, computation time, flexibility in applications, limits of applicability, accuracy, and memory requirements.
ADOLC was superior to MACSYMA concerning preliminary work (programming, source code generation, and compilation) and modifications of the functions to be differentiated and the differentiation task to be performed. In addition, contrary to MACSYMA, no limits of applicability were observed for ADOLC, even in the simulation of complex multi-body systems.
On the other hand, for ADOLC the computation time of derivatives was 10 to 40 times higher than for MACSYMA. As a consequence, differentiation by MACSYMA is better suited for real-time applications like hardware in the loop simulation, real-time control and real-time data processing than ADOLC.
Both programs provide numerical results of equal accuracy.


Last updated on 2019-25-07 at 17:53