DEPENDENCE OF OBSERVABILITY INDEXES' EFFICIENCY ON THE COMPLETENESS OF THE ERROR MODEL

Abstract

In robot calibration, the selection of measurement poses is reduced to the problem of maximizing an observability index constructed based on the singular values of the identification Jacobian. Five indices are widely used in the literature and are associated with alphabetical optimalities in experimental design theory. This work addresses a different question: is the order of efficiency of the indices preserved when the model composition changes, and do they generally offer an advantage over random selection? Methodology. A set of 300 candidate poses was formed for a six-degree-of-freedom manipulator, from which 30 were selected. Two model variants were considered: A – geometric errors only (34 parameters); B – geometric errors and joint compliance (37 parameters). Poses for each index were selected using a DETMAX-style exchange algorithm; the initial set was the same for all indices, ensuring fairness of comparison. Evaluation was performed in 40 independent realizations, under measurement noise conditions of σ = 30 µm, on 100 poses not involved in calibration. 20 independent random selections were used as a baseline, recording not only their average but also the worst result. Results. In model A (where elastic deformations present in the robot were not accounted for), all five indices yielded practically the same results as random selection, as the residual error is limited by model inadequacy. In model B (complete model), the best indices (O₅ and O₁) outperformed random selection by 14% on average and by 23% from the worst random draw. The order of efficiency of the indices was almost reversed between the two models. Conclusion. Pose selection based on an observability index is beneficial only when the error model is complete. If the model is incomplete, the residual error is limited by model inadequacy, and computational resources spent on selection do not affect the result; in this case, completing the model is a priority over improving the selection algorithm. Even with a complete model, the advantage is not absolute, averaging 14%, but its importance is greater in terms of protection against the worst-case scenario (23%). Finally, the order of efficiency of the indices depends on the model composition, so the choice of index should be justified separately for each specific model. The results indicate the necessity of performing the model completeness verification step before the selection step in planning measurement experiments.