Flatness-based disturbance observer for exoskeleton robots under time-delayed contact forces

The article proposes flatness-based control and a Kalman filter-based disturbance observer for solving the control problem of a robotic exoskeleton under time-delayed exogenous disturbances. A two-link lower-limb robotic exoskeleton is used as a case study. It is proven that this robotic system is differentially flat. The robot is considered to be subject to unknown contact forces at its free-end which in turn generate unknown disturbance torques at its joints. It is shown that the dynamic model of the robotic exoskeleton can be transformed into the input–output linearized form and equivalently into the linear canonical Brunovsky form. This linearized description of the exoskeleton's dynamics is both controllable and observable. It allows for designing a stabilizing feedback controller with the use of the pole-placement (eigenvalues assignment) method. Moreover, it allows for solving the state estimation problem with the use of Kalman Filtering (the use of the Kalman filter on the flatness-based linearized model of nonlinear dynamical systems is also known as derivative-free nonlinear Kalman filtering). Furthermore, (i) by extending the state vector of the exoskeleton after considering as additional state variables the additive disturbance torques which affect its joints and (ii) by redesigning the Kalman filter as a disturbance observer, one can achieve the real-time estimation of the perturbations that affect this robotic system. Finally, by including in the controller of the exoskeleton additional terms that compensate for the estimated disturbance torques, the perturbations' effects can be eliminated and the precise tracking of reference trajectories by the joints of this robot can be ensured.