Group-theoretical methods in manipulator kinematics and symbolic computations

This paper may be considered as a logical continuation of previous investigations where all manipulator problems are treated on the basis of the vector-parametrization of the SO(3) group. The simple composition law of the vector-parameter Lie group, as of its nice properties, reduces the computational burden in solving the direct kinematical problem (DKP) and the inverse kinematical problem (IKP), as in dynamic modelling, by about 25–30% in comparison with other methods used until now. This fact has been proved in our earlier works and it becomes stronger when the manipulator problems are considered at the ‘pure’ group configurational manifold level. The last statement is the subject of the present paper. Through the vector parametrization of the space motions, DKP and IKP take more efficient forms and this efficiency is increased by using symbolic computations.

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