New Wavelet Functions for Realistic Flexible Robots Modeling

In this paper new wavelet functions, to build suitable basis functions to model a flexible robot, are proposed. These functions, continuous with second derivatives, allow to derive a very precise model, above all at low frequencies, numerically stable and efficient from a computational point of view, also under the hypothesis of links having varying cross-section and gravitational loads. Moreover the deformation Lagrangian variables are displacements, rotations and curvatures in suitable points of the links; this is very useful if inclinometers, piezoelectrics and stay rods, to monitor and/or control the robot, are used. The proposed method has been validated with several simulations of almost realistic robots, especially by modeling, controlling and simulating a mobile base robot with two flexible links carrying a variable mass body.