Lyapunov Self-triggered Controller for Nonlinear Trajectory Tracking of Unicycle-type Robot

Abstract

This paper focuses on the design and implementation of an aperiodic control of nonholonomic robots tracking nonlinear trajectories. The main objective of our controller is to reduce the number of updates while preserving control performance guarantees. To solve the problem in a more efficient way, we design two aperiodic control solutions, one to reach a target point and a second to track a predefined nonlinear trajectory. Unlike most previous work, our triggering condition only updates the controller when the time derivative of the Lyapunov function becomes non-negative, without taking into account the measurement error. Multiple simulated results with different initial conditions are included, showing how our control solution significantly reduces the need for communication in comparison with periodic and other aperiodic strategies while preserving a desired tracking performance. To validate the proposal experimental tests of each control technique with a P3-DX robot remotely controlled through an IEEE 802.11g wireless network are also carried out.

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Correspondence to Carlos Santos.

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Carlos Santos received his B.S. degree in Telecommunications Engineering in 2010 and an M.Sc. in Electrical Engineering in 2011, both from the University of Alcala, Spain, and a Ph.D. degree in Electronics in 2016. He is currently at the Department of Electronics of the University of Alcala D with a Postdoctoral Research Contract. His research interest focuses on the field of fusion algorithms, trajectory generation for navigation in mobile robotics and varying-time sampling control techniques.

Felipe Espinosa received his M.S. degree (Polytechnics University of Madrid, Spain) and a Ph.D. degree (University of Alcala, Spain) in telecommunication, in 1991 and 1999 respectively. He became an Associate Professor in 2000 and a Full Professor in 2016 in the Electronics De-partment with the University of Alcala, regularly involved in electronic control and automation subjects in the Post-Degree programme (Quality Awared of the Education and Science Spanish Ministry). His current research interests include control, communication and sensorial systems applied to intelligent transportation systems, industrial automation and smart cities.

Enrique Santiso is an assistant professor at the Electronics Department, University of Alcala. He received his M.Sc. degree (Polytechnic University of Valencia, Spain) in 1996, and a Ph.D. (University of Alcala, Spain) in Telecommunications in 2003. His main research interest focuses on sensorial systems, control and electronics instrumentation.

David Gualda received his B.S. degree in Electronics Systems and an M.Sc. degree in Advanced Electronics System, from the University of Alcala (Spain), in 2009 and 2011, respectively; and a Ph.D. degree in Electronics in 2016. He is currently at the Department of Electronics of the University of Alcala with a Postdoctoral Research Contract. His main research interests are in the areas of ultrasonic indoor location, signal processing and information fusion.

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Santos, C., Espinosa, F., Santiso, E. et al. Lyapunov Self-triggered Controller for Nonlinear Trajectory Tracking of Unicycle-type Robot. Int. J. Control Autom. Syst. 18, 1829–1838 (2020). https://doi.org/10.1007/s12555-018-0576-x

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Keywords

  • Lyapunov-based controller
  • nonlinear trajectory-tracking
  • self-triggered
  • semiglobal practical stability