Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems

The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this problem class. Recent numerical methods for nonsmooth dynamical systems subject to unilateral contact and friction illustrate the topicality of this development.Comment: Preprint of Book Chapte

Multibody dynamics in robotics with focus on contact events

Multibody dynamics methodologies have been fundamental tools utilized to model and simulate robotic systems that experience contact conditions with the surrounding environment, such as in the case of feet and ground interactions. In addressing such problems, it is of paramount importance to accurately and efficiently handle the large body displacement associated with locomotion of robots, as well as the dynamic response related to contact-impact events. Thus, a generic computational approach, based on the Newton-Euler formulation, to represent the gross motion of robotic systems, is revisited in this work. The main kinematic and dynamic features, necessary to obtain the equations of motion, are discussed. A numerical procedure suitable to solve the equations of motion is also presented. The problem of modeling contacts in dynamical systems involves two main tasks, namely the contact detection and the contact resolution, which take into account for the kinematics and dynamics of the contacting bodies, constituting the general framework for the process of modeling and simulating complex contact scenarios. In order to properly model the contact interactions, the contact kinematic properties are established based on the geometry of contacting bodies, which allow to perform the contact detection task. The contact dynamics is represented by continuous contact force models, both in terms of normal and tangential contact directions. Finally, the presented formulations are demonstrated by the application to several robotics systems that involve contact and impact events with surrounding environment. Special emphasis is put on the systems’ dynamic behavior, in terms of performance and stability

6D Frictional Contact for Rigid Bodies

International audienceWe present a new approach to modeling contact between rigid objects that augments an individual Coulomb friction point-contact model with rolling and spinning friction constraints. Starting from the intersection volume, we compute a contact normal from the volume gradient. We compute a contact position from the first moment of the intersection volume, and approximate the extent of the contact patch from the second moment of the intersection volume. By incorporating knowledge of the contact patch into a point contact Coulomb friction formulation, we produce a 6D constraint that provides appropriate limits on torques to accommodate displacement of the center of pressure within the contact patch, while also providing a rotational torque due to dry friction to resist spinning. A collection of examples demonstrate the power and benefits of this simple formulation