Stiff ODE's

edkadik's picture

Dynamic Simulation of a Parallel Robot: Coulomb Friction And Stick–Slip In Robot Joints

Journal Title, Volume, Page: 
Robotica, Volume 28, Issue 01, January 2010, pp 35-45
Year of Publication: 
Nidal Farhat
Departamento de Ingeniería Mecánica y de Materiales, Universidad Politécnica de Valencia, Spain
Current Affiliation: 
Department of Mechanical Engineering, Faculty of Engineering, An-Najah National University, Nablus, P.O. Box 7, Palestine
Vicente Mata
Departamento de Ingeniería Mecánica y de Materiales, Universidad Politécnica de Valencia, Spain
Álvaro Page
Departamento de Física Aplicada, Universidad Politécnica de Valencia, Spain
Miguel Dıaz-Rodriguez
Departamento de Tecnología y Diseño, Facultad de Ingeniería, Universidad de Los Andes, Venezuela
Preferred Abstract (Original): 
Dynamic simulation in robotic systems can be considered as a useful tool not only for the design of both mechanical and control systems, but also for planning the tasks of robotic systems. Usually, the dynamic model suffers from discontinuities in some parts of it, such as the use of Coulomb friction model and the contact problem. These discontinuities could lead to stiff differential equations in the simulation process. In this paper, we present an algorithm that solves the discontinuity problem of the Coulomb friction model without applying any normalization. It consists of the application of an external switch that divides the integration interval into subintervals, the calculation of the friction force in the stick phase, and further improvements that enhance its stability. This algorithm can be implemented directly in the available commercial integration routines with event-detecting capability. Results are shown by a simulation process of a simple 1-DoF oscillator and a 3-DoF parallel robot prototype considering Coulomb friction in its joints. Both simulations show that the stiffness problem has been solved. This algorithm is presented in the form of a flowchart that can be extended to solve other types of discontinuity.
Syndicate content