The authors construct a simplified model of a dynamically dexterous robot, M.H. Raibert's hopper, and investigate its elegant, physically based control strategies. Analysis of induced discrete dynamics leads to strong conclusions concerning global limiting properties. These conclusions are then verified by computer simulation of the simplified models, the correspondence of which to the true physical apparatus is seen to be acceptable as well. Comments Copyright 1988 IEEE. Reprinted from Proceedings of the IEEE International Conference on Robotics andAutomation, Volume 2, 1988, pages 817-819. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it. Yale University, D e p a r t m e n t of Electrical EngineeringWe offer some preliminary analytical results concerning simplified models of Raibert's hopper. T h e motivation for this work is the hope t h a t it will facilitate the development of general design principles for "dynamically dexterous" robots.

This article develops a formalism for describing and analyzing a very simple representative class of robotic tasks that require "dynamical dexterity" -among them, the task of juggling. The authors review their empirical success, to date, with a new class of control algorithms for this task domain, called "mirror algorithms." The formalism for representing the task domain and encoding within it the desired robot behavior enables them to prove that a suitable mirror algorithm is correct with respect to a specified task. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it. NOTE: At the time of publication, the author Daniel Koditschek was affiliated with Yale University. Currently, he is a faculty member of the School of Engineering at the University of Pennsylvania. ABSTRACT: This article develops a formalism for describing and analyzing a very simple representative class of robotic tasks that require "dynamical dexterity"-among them, the task of juggling. The authors review their empirical success, to date, with a new class of control algorithms for this task domain, called "mirror algorithms." The formalism for representing the task domain and encoding within it the desired robot behavior enables them to prove that a suitable mirror algorithm is correct with respect to a specified task.

We develop a formalism for describing and analyzing a very simple representative of a class of robotic tasks which require "dynamical dexterity," among them the task of juggling. We introduce and report on our preliminary empirical experience with a new class of control algorithms for this task domain that we call "mirror algorithms." Comments