Defense of Jorge Alberto Ibarra Angulo (automatic control department)

This thesis develops estimation and control methods for robotic systems intended for the assisted rehabilitation of patients suffering from motor disorders, with the aim of promoting active human participation.

To this end, assistance-on-demand (AOD) techniques are widely used to adapt the level of assistance provided by the robot to the patient according to his or her performance.

In these methodologies, it is necessary to know the human's intention or contribution to the movement task, which adds difficulty to the design of the control system.

This problem can be solved by methodologies that estimate the unknown inputs of nonlinear systems, such as observer-based estimation.

However, since observer design is a model-based approach, its performance is linked to the mathematical model that represents the system, which is likely to be affected by parametric uncertainties.

Thus, this work presents a solution by estimating the human torque using an extended observer born of the assumption that the third derivative of the human torque is zero, meaning that the torque itself varies slowly during the rehabilitation task.

The approach used to design the observer consists in taking advantage of the system's physical limits to rewrite it exactly as a polytopic representation, where the gains are calculated by satisfying the LMI conditions derived from the Lyapunov formulation.

This methodology is then used in conjunction with the multimodel approach to deal with the case where parametric uncertainties are non-linear.

Rapporteurs:

• Mr Kevin GUELTON, Professeur des Universités, Université de Reims Champagne-Ardenne
• Mr Dalil ICHALAL, Professeur des Universités, Université d'Évry Val d'Essonne

Examiners:

• Mr Alexandre KRUSZEWSKI, Professeur des Universités, École Centrale de Lille

Thesis supervisor:

• Mr. Jimmy LAUBER, University Professor, Université Polytechnique Hauts-de-France

Co-supervisors:

• Mrs. Kaouther MOUSSA, Senior Lecturer, Université Polytechnique Hauts-de-France
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