Disturbance estimator as a state observer with extended Kalman filter for robotic manipulator

In most of the existing literature, disturbance observer theory has been developed only for constant disturbance, while in the present work, by defining the disturbance as a state observer, we are able to track and reject disturbances varying with time. This is possible with only joint position variables unlike other works where derivative of position variables is also needed. In the novel technique proposed by us, the standard disturbance observer output is treated as a part of the state variable of a nonlinear system. The disturbance estimation error is treated as a white Gaussian noise (WGN) independent of the WGN in the dynamics of the robot. The extended Kalman filter (EKF) is then applied based on noisy measurements of the position to obtain estimates of the angular coordinate and the disturbance. Superior estimates of the disturbance are possible because we are first using the nonlinear disturbance observer to produce a new state and then we are applying the EKF to remove the residual noise in the disturbance estimate. Stability and convergence analysis of the EKF is established using linearization of the state equations around the estimated state. Using the Lyapunov method, we also establish convergence of the disturbance estimation error to zero. Finally, robustness of the EKF to uncertainty is established by linearizing the dynamical equation w.r.t the parametric uncertainty and the dynamics w.r.t the state estimation error, thereby yielding an upper bound for the error variance in terms of the norm square of the parametric uncertainty. The proposed technique is applied to an Omni®Robot Manipulator. The results are encouraging and demonstrate better disturbance rejection ability of the proposed scheme as compared to other techniques available in the literature.