Abstract: This paper introduces a robust adaptive controller tailored for collaborative multiple robots and equipped with elastic joints. It utilizes a simple model of manipulator dynamics, treating all other dynamics as lumped uncertainty. The proposed approach integrates Function Approximation Techniques (FAT), specifically Bernstein-type rational functions, to estimate lumped uncertainty. Recent advancements have utilized FAT-based robust adaptive controllers for uncertainty estimation. However, our innovation distinguishes itself from prior research by minimizing the required regressor matrices. This advantage becomes particularly pronounced as the number of manipulators and their degrees of freedom increase. In addition, the coefficients of the Bernstein-type rational functions are adjusted by the adaptation laws derived from stability analysis, which are not presented in the previous literature. To the best of our knowledge, this paper marks the first engineering application of Bernstein-type rational functions for function approximation in adaptive form. Stability analysis guarantees that all error signals remain uniformly ultimately bounded (UUB). The theoretical advancements are validated by employing two elastic joint manipulators to transport a rigid object. The outcomes are also compared with two advanced approximation techniques to show the precision and effectiveness of the proposed controller design. The results exhibit the usefulness of the proposed control scheme, facing uncertainties and disturbances