Adaptive high-order sliding mode control based on quasi-time delay estimation for uncertain robot manipulator


This paper presents the design, and validation of a new adaptive control system based on quasi-time delay estimation (QTDE) augmented with new integral second-order terminal sliding mode control (ISOTSMC) for a manipulator robot with unknown dynamic uncertainty and disturbances. Contrary to the conventional TDE, the proposed Q-TDE becomes sufficient to invoke a fixed artificial time delay and utilize the past data only of the control input to approximate the unknown system’s dynamic uncertainties. The incorporating of new adaptive reaching law with ISOTSMC augmented with Q-TDE policy ensures the continuous performance tracking of the robot manipulator’s trajectories using output feedback. This combination may achieve high performance with a significant chattering reducing procedure. By utilizing the Lyapunov function theory, it can be demonstrated that the robot system is stable and all signals in closed-loop are converging in finite time. Consequently, Simulation and comparative studies with two degrees of freedom robot manipulator were carried out to validate the effectiveness of the designed control scheme.

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Corresponding author

Correspondence to Brahim Brahmi.

Additional information

Brahim BRAHMI received the B.Eng. degree from the Department of Electronic and Automatic, University of Science and Technology, Oran, Algeria in 2011, the Master’s degree in Computer and Control System from Lviv Polytechnic National University in Lviv, Ukraine in 2014. He received the Ph.D. in Engineering from the Ecole de technologie superieure (ETS) in Montreal, Quebec, Canada in 2019. With his thesis and specialization being in nonlinear control and robotics, he is currently a postdoctoral fellow with the Department of Mechanical Engineering, McGill University, Montreal, Canada. His research interests are in nonlinear control, adaptive control, robotics, rehabilitation robots, intelligent systems and machine learning.

Mark DRISCOLL is an Assistant Professor in Mechanical Engineering at McGill University, who focuses his research on musculoskeletal biomechanics with a primary interest in spine. Dr. Driscoll more specifically works to improve the understanding, from a biomechanical perspective, in low back pain and to devise devices to improve diagnosis or treatment thereof. One main project currently being developed is the conception and commercialization of a novel physics driven VR/AR surgical training device of a spinal operation with visual, audible and haptic feedback.

Mohamed-Hamza LARAKI was born in Benslimane, Morocco in 1993. He received his B.E. in Electrical Engineering from Ecole Nationale superieure d Electricite et de la Mecanique (ENSEM), Casablanca, Morocco in 2015. He is currently pursuing a Master’s degree in Ecole de Technologie superieure (ETS), Montreal, Canada. His area of interests includes development of smart power management strategies for stand-alone systems as well as power quality improvement.

Abdelkrim BRAHMI received the B.Sc. and M.Sc. degrees in Electrical Engineering from the University of Sciences and Technologies of Oran, Algeria, in 1997 and 2009, respectively, and the Ph.D. degree in Electrical Engineering from Quebec University (Ecole de Technologie Superieure), Montreal, QC, Canada. His current research interests include nonlinear control, and adaptive control applied to coordinated robotic systems.

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Brahmi, B., Driscoll, M., Laraki, M.H. et al. Adaptive high-order sliding mode control based on quasi-time delay estimation for uncertain robot manipulator. Control Theory Technol. (2020).

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  • Second-order sliding mode
  • quasi-time delay estimation (Q-TDE)
  • adaptive reaching law