Differential algebraic observer-based trajectory tracking for parallel robots via linear matrix inequalities

Abstract

This paper develops a novel observer-based trajectory tracking technique for parallel robots, modelled as differential algebraic equations, which assumes that only positions are available for control purposes while joint velocities should be estimated. Based on the direct Lyapunov method and a recently appeared factorisation for expressions in the differential mean value theorem, convex modelling and Finsler's lemma are combined to incorporate restrictions into the analysis. Two generalisations are thus achieved: the inner-loop feedback is allowed to use velocity estimates instead of the real values and the outer-loop feedback becomes fully nonlinear while taking into account the parallel characteristics of mechanisms. Moreover, both the observer and the controller design conditions are linear matrix inequalities, which can be efficiently solved via commercially available software. Illustrative examples are provided that show the advantages of the proposal against former works on the subject.

Keywords:

• Differential algebraic equation
• observer-based controller design
• trajectory tracking
• computed-torque
• parallel robots

Disclosure statement

The authors declare that they do not have any conflict of interest.

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article [and/or] its supplementary materials.

Additional information

Funding

This work was supported by the CONACYT (Consejo Nacional de Ciencia y Tecnología) scholarships for CVUs [grant numbers 1013714 and 785410] and the ITSON PROFAPI CA-18 2021-0027 Project 2021.

Notes on contributors

J. Álvarez

J. Álvarez obtained his BSc degree in Mechatronics Engineering and MSc degree in Control Systems at the Sonora Institute of Technology in 2016 and 2018, respectively. He is currently PhD student at the Sonora Institute of Technology. His research interests include controller design of nonlinear systems through Takagi-Sugeno models and linear matrix inequalities.

J. Servín

J. Servín obtained his MSc degree from the Sonora Institute of Technology in 2021. His interests are parallel robots, differential algebraic equations, and singular systems.

J. A. Díaz

J. A. Díaz obtained his MSc degree from the Sonora Institute of Technology in 2021 with honors. His interests are nonlinear generalisations of computed-torque techniques, convex modelling, and convex optimisation.

M. Bernal

M. Bernal received his PhD in Automatic Control from the Czech Technical University at Prague in 2005. He was a Post-Doctoral researcher at the University of Valenciennes and Hainaut-Cambresis, France, from 2006 to 2009. He is a member of the National Research System of Mexico since 2007. In 2011 he was appointed Full Professor at the Sonora Institute of Technology, Mexico. He currently leads and supervises several research projects and PhD theses in Mexico and abroad on nonlinear control via convex structures and linear matrix inequalities, an area where he counts with more than 50 journal papers and over 1800 citations.