Abstract Rotations for Uniform Adaptive Control and Soft Modeling of Mechanical Devices

Abstract

The model-based controllers generally suffer from the lack of precise dynamic models. Making reliable analytical models can be evaded by soft modeling techniques, while the consequences of modeling imprecisions are tackled by either robust or adaptive techniques. In robotics, the prevailing adaptive techniques are based on Lyapunov’s “direct method” that normally uses special error metrics and adaptation rules containing fragments of the Lyapunov function. The soft models and controllers need massive parallelism and suffer from the curse of dimensionality. A different adaptive approach based on Banach’s fixed point theorem and using special abstract rotations was recently suggested. Similar rotations were suggested to develop particular neural network-like soft models, too. Presently, via integrating these approaches, a uniform adaptive controlling and modeling methodology is suggested with especial emphasis on the effects of the measurement noises. Its applicability is investigated via simulations for a two degree of freedom mechanical system in which one of the generalized coordinates is under control, while the other one belongs to a coupled parasite dynamical system. The results are promising for allowing the development of relatively coarse soft models and a simple adaptive rule that can be implemented in embedded systems.

Keywords

• adaptive control
• soft computing
• Banach space
• Banach’s fixed point theorem
• iterative control
• Lyapunov function