LMI-based Human Torque Estimation and Control Design for Assistive Robots

Overview & Synopsis

This thesis develops estimation and control methods for robotic systems for assisted rehabilitation of motor-impaired patients with the goal of promoting active participation of the human part. For this, Assist-as-Needed (AAN) techniques are widely used to adapt the level of assistance that the robot provides to the patient based on their performance. In these methodologies, it is necessary to know the intention or contribution of the human to the movement task, which adds a challenge to the design of the control system. This can be addressed by methodologies that allow to estimate unknown inputs of nonlinear systems, such as observer-based estimation. However, the observer design being a model-based approach ties its performance to the mathematical model that represents the system, which is prone to being affected by parametric uncertainties. Thus, this work presents a solution by estimating the human torque with an extended observer born from the assumption that the third derivative of the human torque is zero, meaning that the torque itself is slowly-varying during the rehabilitation task. The approach used for the observer design consist in taking advantage of the physical limits of the system to exactly rewrite it as a polytopic representation, where the gains are computed by fulfilling LMI conditions originated from Lyapunov formulation. This methodology is then used along with the multi-model approach to address the case where parametric uncertainties are in the nonlinear model. Since the model comes from the human-robot interaction being represented with Euler-Lagrange equations, which is naturally in a descriptor form, the inversion of the descriptor matrix is avoided to avoid the propagation of the uncertainties to the rest of the system. The final control design integrates the resulting estimation into computed-torque control for trajectory-tracking rewritten as polytopic problems. Disturbance rejection due to model mismatched is addressed through H∞ attenuation. The estimation and control proposals are validated and compared with other methods in various simulation scenarios. Keywords: Automation, Robotic Assistance, Observation, Linear Inequality Matrices, Rehabilitation