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

• Published in: International journal of systems science Vol. 53; no. 10; pp. 2149 - 2164
• Main Authors: Álvarez, J., Servín, J., Díaz, J. A., Bernal, M.
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis 27.07.2022; Taylor & Francis Ltd
• Subjects: Algebra; computed-torque; Control systems design; Differential algebraic equation; Differential calculus; Differential equations; Feedback; Linear matrix inequalities; Mathematical analysis; observer-based controller design; parallel robots; Robots; Tracking; trajectory tracking
• ISSN: 0020-7721; 1464-5319
• DOI: 10.1080/00207721.2022.2043482

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.