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Identification of lonely barycentric parameters of parallel kinematics mechanism with rank-deficient observation matrix

In parameter identification of dynamic system presented as linear system, the observation matrix is commonly rank-deficient. The widely used approach is transforming the system to new, full-rank system and accordingly estimating the dynamic parameters as linear combinations. The treatment becomes relatively more difficult when dealing with parallel kinematics mechanism due to lengthy expression of their inverse dynamics and hence difficulty to transform it to dynamic identification model manually. This paper presents a new approach which does not require such transformation and is able to present the estimates as lonely parameters. This is conducted by iteratively minimizing the residual instead of solving the estimates by using linear least squares technique. The transformation from the inverse dynamics model to the dynamic identification model is accomplished by symbolic computation.