Andrzej Urbaś

THE INFLUENCE OF FLEXIBILITY OF THE SUPPORT ON DYNAMIC BEHAVIOR OF A CRANE

The problem of control of the motion of a crane is considered in the paper. The mathematical model of the system is formulated using joint coordinates and homogenous transformations. The dynamic optimization method is applied in order to find drive functions realizing the desired trajectory and stabilizing the final position of the load at the end of motion in spite of the flexibility of the support. The results of numerical calculations and possible applications of models developed using artificial neural networks are also presented.

Automated generation of reference dynamical models for constrained robotic systems in the presence of friction and damping effects

This paper details a new automated generation method of dynamic models of structures allowing presence of friction and damping in their models as well as subjected to position or kinematic constraints. The constraints may be material, which come from the system interaction with environment, or may be programmed. The novelty of the presented dynamics generation method is to include friction and damping into modeling and to require predefined constraint satisfaction as well. The latter requirement is critical, since when friction and damping are neglected, controllers may be inadequately designed, constraints may be violated, and overall system performance may be poor. The developed method is applied to a manipulator model, whose end‐effector performance is predefined by programmed constraints. Simulation results present manipulator constrained motion. The advantage of this method is that it serves both reference and control oriented dynamics derivation, and the final dynamics models are obtained in the reduced state form, ie, constraint reaction forces are eliminated. This is the fundamental difference between the presented approach and the Lagrange based approaches to constrained system modeling.

Development of a Computational Based Reference Dynamics Model of a Flexible Link Manipulator

Development of a new derivation method of a reference dynamics model of a flexible link manipulator is presented in the paper. The model including flexibility can map dynamics and performance of lightweight and fast manipulators correctly and may serve their motion analysis and control design in the presence of kinematic or programmed constraints, which are assumed to be position or first order nonholonomic. The reference dynamics model is derived using the formalism of joint coordinates and homogeneous transformation matrices. This approach allows generating dynamics equations of a manipulator without formulating additional material constraint equations. The constraints present in the reference dynamics model are the programmed ones only. The flexibility of a link is modelled using the rigid finite element method. The main advantage of this method is its ability of application of the rigid-body approach to modeling dynamics of multi-body systems with flexible links. The novelty of the presented method relies on the combination of dynamics modeling of flexible system models with the programmed constraints satisfaction problem for them. The computational algorithm underlying the derivation method presented in the paper is based on Generalized Programmed Motion Equations (GPME) approach. The reference dynamics model derivation is demonstrated for a flexible link manipulator model.