Nonlinear Functional Observer Design for Robot Manipulators

In this paper, a nonlinear functional observer (NFO) is first proposed for the control design of robot manipulators under model uncertainties, external disturbances, and a lack of joint velocity information. In principle, the proposed NFO can estimate not only lumped disturbances and uncertainties but also unmeasurable joint velocities, which are then fed back into the main controller. Compared to the well-known ESO design, the proposed NFO has a simpler structure, more accurate estimations, and less computational effort, and consequently, it is easier for practical implementation. Moreover, unnecessary observations of joint displacements are avoided when compared to the well-known extended state observer (ESO). Based on the Lyapunov theory, globally uniformly ultimately bounded estimation performance is guaranteed by the proposed NFO. Consequently, it is theoretically proven that the estimation performances of the NFO are better than those of the ESO. Simulations with a two-degree-of-freedom (2-DOF) robot manipulator are conducted to verify the effectiveness of the proposed algorithm in terms of not only the estimation performance but also the closed-loop control performance.