Formal and practical completion of Lagrangian hybrid systems

Authors:
Yizhar Or;Aaron D. Ames
Affiliations:
Control and Dynamical Systems Department, California Institute of Technology, Pasadena, CA;Mechanical Engineering Department, Texas A&M University, College Station, TX
Venue:
ACC'09 Proceedings of the 2009 conference on American Control Conference
Year:
2009

Citing 2
Cited 2

A Mathematical Introduction to Robotic Manipulation

A Mathematical Introduction to Robotic Manipulation
Linear Complementarity Systems: Zeno States

SIAM Journal on Control and Optimization

Existence of Periodic Orbits with Zeno Behavior in Completed Lagrangian Hybrid Systems

HSCC '09 Proceedings of the 12th International Conference on Hybrid Systems: Computation and Control
Characterizing knee-bounce in bipedal robotic walking: a zeno behavior approach

Proceedings of the 14th international conference on Hybrid systems: computation and control

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper presents a method for completing Lagrangian hybrid systems models in a formal manner. That is, given a Lagrangian hybrid system, i.e., a hybrid system that models a mechanical system undergoing impacts, we present a systematic method in which to extend executions of this system past Zeno points by adding an additional domain to the hybrid model. Moreover, by utilizing results that provide sufficient conditions for Zeno behavior and for stability of Zeno equilibria in Lagrangian hybrid systems, we are able to give explicit bounds on the error incurred through the practical simulation of these completed hybrid system models. These ideas are illustrated on a series of examples, and are shown to be consistent with observed reality.