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Persistent passive hopping and juggling is possible even with plastic collisions

Chatterjee, A and Pratap, R and Reddy, CK and Ruina, A (2002) Persistent passive hopping and juggling is possible even with plastic collisions. In: The International Journal of Robotics Research, 21 (7). pp. 621-634.

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Official URL: http://ijr.sagepub.com/content/21/7/621


We describe simple one-dimensional models of passive (no energy input, no control), generally dissipative, vertical hopping and one-ball juggling. The central observation is that internal passive system motions can conspire to eliminate collisions in these systems. For hopping, two point masses are connected by a spring and the lower mass has inelastic collisions with the ground. For juggling, a lower point-mass hand is connected by a spring to the ground and an upper point-mass ball is caught with an inelastic collision and then re-thrown into gravitational free flight. The two systems have identical dynamics. Despite inelastic collisions between non-zero masses, these systems have special symmetric energy-conserving periodic motions where the collision is at zero relative velocity. Additionally, these special periodic motions have a non-zero sized, one-sided region of attraction on the higher-energy side. For either very large or very small mass ratios, the one-sided region of attraction is large. These results persist for mildly non-linear springs and non-constant gravity. Although non-collisional damping destroys the periodic motions, small energy injection makes the periodic motions stable, with a two-sided region of attraction. The existence of such special energy conserving solutions for hopping and juggling points to possibly useful strategies for both animals and robots. The lossless motions are demonstrated with a table-top experiment.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Sage Publications.
Keywords: hopping robot;juggling robot;passive-dynamic;collisions; efficiency;periodic;map;
Department/Centre: Division of Mechanical Sciences > Mechanical Engineering
Depositing User: Ms V Mangala
Date Deposited: 22 Jul 2011 07:52
Last Modified: 12 Oct 2018 14:48
URI: http://eprints.iisc.ac.in/id/eprint/39349

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