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Abstract: This paper offers some analytical results concerning simplified models of Raibert's hopper. We represent the task of achieving a recurring hopping height for an actuated "ball" robot as a stability problem in a nonlinear discrete dynamical control system. We model the properties of Raibert's control scheme in a simplified fashion, and argue that his strategy leads to closed loop dynamics governed by a well known class of functions, the unimodal maps. The rich mathematical literature on this... (Update)
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BibTeX entry: (Update)
@misc{ and-analysis,
author = "Daniel Koditschek And",
title = "Analysis of a Simplified Hopping Robot",
url = "citeseer.ist.psu.edu/762720.html" }
Citations (may not include all citations):176 Legged Robots That Balance (context) - Raibert - 1986
176 Introduction to Chaotic Dynamical Systems (context) - Devaney - 1987
170 and Bifurcations of Vector Fields (context) - Guckenheimer, Holmes et al. - 1983
102 Passive dynamic walking (context) - McGeer - 1990
90 and Linear Algebra (context) - Hirsch, Smale et al. - 1974
76 Mechanics and planning of manipulator pushing operations (context) - Mason - 1986
66 Iterated Maps on the Interval as Dynamical Systems (context) - Collet, Eckmann - 1980
34 Dynamic walk of a biped (context) - Miura, Shimoyama - 1984
34 Analysis of a Simplified Hopping Robot - Buhler, Koditschek - 1988
34 Analysis of a simplified hopping robot - Koditschek, Buhler - 1988
29 Sensor-based manipulation planning as a game with nature (context) - Taylor, Mason et al. - 1987
17 Modeling impact dynamics for robotics operations (context) - Wang, Mason - 1987
15 the periodic motions of a hopping robot with vertical and fo.. (context) - M'Closkey, Burdick - 1990
14 Task-level robot learning: Juggling a tennis ball more accur.. (context) - Aboaf, Drucker et al. - 1989
9 Sensitive Dependence to Initial Conditions for One Dimension.. (context) - Guckenheimer - 1979
9 Stable orbits and bifurcations of maps of the interval (context) - Singer - 1978
8 From Stable to Chaotic Juggling: Theory (context) - Buhler, Koditschek - 1976
7 A Family of Robot Control Strategies for Intermittent Dynami.. (context) - Buhler, Koditschek et al. - 1990
6 Planning and Control of Robotic Juggling Tasks (context) - Buhler, Koditschek et al. - 1989
5 A Simple Juggling Robot: Theory and Experimentation (context) - Buhler, Koditschek et al. - 1989
4 Chaotic motions of a simplified hopping robot (context) - Vakakis, Burdick - 1990
4 An energy perturbation approach to limit cycle analysis in l.. (context) - Li, He - 1990
3 Dynamical walk of quadruped robot (context) - Miura, Shimoyama et al. - 1985
3 The dynamics of density dependent population models (context) - Guckenheimer, Oster et al. - 1977
2 Aggressive trajectory generator for a robot ping-pong player (context) - Andersson - 1988
1 Control of a dynamical biped locomotion (context) - Furusho, Masubuchi - 1987
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