A novel robust adaptive control algorithm with finite-time online parameter estimation of a humanoid robot arm

A novel robust adaptive control algorithm is proposed and implemented in real-time on two degrees-of-freedom (DOF) of the humanoid Bristol-ElumotionRobotic-Torso II (BERT II) arm in joint-space. In addition to having a significant robustness property for the tracking, the algorithm also features a sliding-mode term based adaptive law that captures directly the parameter estimation error. An auxiliary filtered regression vector and filtered computed torque is introduced. This allows the definition of another auxiliary matrix, a filtered regression matrix, which facilitates the introduction of a sliding mode term into the adaptation law. Parameter error convergence to zero can be guaranteed within finite-time with a Persistent-Excitation (PE) condition or Sufficient Richness condition for the demand. The proposed scheme also exhibits robustness both in the tracking and parameter estimation errors to any bounded additive disturbance. This theoretical result is then exemplified for the BERT II robot arm in simulation and for experiments. Email addresses: [email protected] (M.N. Mahyuddin), [email protected] (S.G. Khan), [email protected] (G. Herrmann) Muhammad Nasiruddin Mahyuddin is currently doing a PhD in the Bristol Robotics Laboratory and the Department of Mechanical Engineering, University of Bristol. His PhD is sponsored by University Sains Malaysia and Ministry of Higher Education Malaysia. Said Ghani Khan is a post-doctorate holding a research assistant position at the Department of Mechanical Engineering, University of Bristol. Guido Herrmann is a Reader in Control and Dynamics at the Department of Mechanical Engineering, University of Bristol and a theme leader at the Bristol Robotics Laboratory. Preprint submitted to Robotics and Autonomous System July 11, 2013