Guaranteed Parameter Estimation of Hunt-Crossley Model with Chebyshev Polynomial Approximation for Teleoperation

In haptic time delayed teleoperation as the time delay from the communication channel increases, teleoperation system stability and performance degrade. To increase performance and provide better stability margins, various estimation methods and observers have been implemented in literature to more accurately capture the force exerted by the remote system. Previously, solutions focused on environment force estimation methods that primarily rely on linearization of the Hunt-Crossley (HC) contact model, which has limiting assumptions for use. This work addresses the shortcomings of the aforementioned methods by investigating alternative HC parameter estimation techniques. A new application of Chebyshev polynomial approximation for adaptive parameter estimation of the HC model is proposed. This approximation is compared to current linearization methods as well as nonlinear estimation methods that are not well covered in literature. Moreover, the Chebyshev approximation is used in a new estimation approach that provides control via backstepping with adaptive parameter estimation using Lyapunov methods. This method reduces excitation requirements by using nonlinear swapping and the data accumulation concept to guarantee parameter convergence. A simulated full teleoperation system with time delay demonstrates the effectiveness of this approach.