Adaptive Liapunov controllers for nonlinear robotic dynamics

Abstract

A robotic manipulator mounted on a moving platform and subject to uncertainty in gravity and payload is modelled by the general format of nonautonomous Lagrangian and Hamiltonian motion equations. In the first model, inertial decoupling via controller is designed. Both Lagrangian and Hamiltonian functions are explicitly time dependent, the models involving rheonomic constraints. Adjusting some tools in Liapunov formalism, algorithms for signal adaptive feedback model tracking controllers, and state and parameters identifiers, are modified to cover the case of time dependent constraints and flexible links. The latter, modelled via Ritz-Kantorovitch series approximation require reduction of dimension in their dynamics, which is made by introducing less dimensional observer. Original effort is made to allow for simultaneus investigation of identification and tracking of a reference model, while allowing different dimensionality in the robot state equations, the reference model and the identifier. The technique used is a nonlinear version of MRAC (control and identification), based on the Liapunov Direct Method, and introduced in recent years as the product-state-space method. The work is theoretic and will require experimental confirmation.