This paper describes the parameterization of robot excitation trajectories for optimal robot identification based on finite Fourier series. The coefficients of the Fourier series are optimized for minimal sensitivity of the identification to measurement disturbances, which is measured as the condition number of a regression matrix, taking into account motion constraints in joint and cartesian space. This approach allows obtaining small condition numbers with few coefficients for each joint, which simplifies the optimization problem significantly. The periodicity of the resulting trajectories and the fact that one has total control over their frequency content, are additional features of the presented parameterization approach. They allow further optimization of the excitation experiments through time domain data averaging and optimal selection of the excitation bandwidth, which both help the reduction of the disturbance level on the measurements, and therefore improve the identification accuracy.

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