Adaptive Velocity Estimation for Lagrangian Systems using Modulating Functions

Information about the internal position and velocity of a robotic system is crucial for its control. Especially, under uncertain models, changing dynamic parameters and noisy position measurement signals, an adaptive differentiation is needed combining structural knowledge of the model with adequate filtering of the sensor data. To this end, the Modulating Function Method is applied to the Lagrange formulation of the robotic system to preserve the structure while enabling to incorporate nonlinear terms into the integral transform methodology. Different types of Modulating Functions and the function projection approach are used to develop a simultaneous parameter and state estimation procedure for the general structure of open kinematic chains. The developed algorithm for an adaptive velocity estimation is capable of robustly reconstructing the generalized state and consists of an efficient Finite Impulse Response (FIR) filter type implementation. The resulting architecture is demonstrated on a two-link robot setup.