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In this work an efficient dynamics algorithm is developed, which is applicable to a wide range of multibody systems, including underactuated systems, branched or tree-topology systems, robots, and walking machines. The dynamics algorithm is differentiated with respect to the input parameters in order to form sensitivity equations. The algorithm makes use of techniques and notation from the theory of Lie groups and Lie algebras, which is reviewed briefly. One of the strengths of our formulation is the ability to easily differentiate the dynamics algorithm with respect to parameters of interest. We demonstrate one important use of our dynamics and sensitivity algorithms by using them to solve difficult optimal control problems for underactuated systems. The algorithms in this paper have been implemented in a software package named Cstorm (Computer simulation tool for the optimization of robot manipulators), which runs from within Matlab and Simulink. It can be downloaded from the website http://www.eng.uci.edu/∼bobrow/
Sohl et al. (Mon,) studied this question.